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UNIVERSITY OF LOUISIANA AT LAFAYETTE / Math / MATH 302 / What is distance formula and what are its examples?

What is distance formula and what are its examples?

What is distance formula and what are its examples?

Description

School: University of Louisiana at Lafayette
Department: Math
Course: Calculus 3
Professor: Julie roy
Term: Fall 2015
Tags: Math, Calculus 3, and Study Guide
Cost: 25
Name: Math 302 Unit 1 Study Guide
Description: These notes can be used to prepare for the Unit 1 exam in Calculus 3.
Uploaded: 02/04/2016
3 Pages 38 Views 1 Unlocks
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"}ul.lst-kix_r3uvk2hyw1by-6{list-style-type:none}.lst-kix_1osiewg5f0zk-0 > li:before{content:"● "}.lst-kix_ltea2g481i55-0 > li:before{content:"● "}.lst-kix_d87x2tnjeviy-5 > li{counter-increment:lst-ctn-kix_d87x2tnjeviy-5}ol.lst-kix_b4hxna1le1rg-4.start{counter-reset:lst-ctn-kix_b4hxna1le1rg-4 0}.lst-kix_5ozdxj9yzw2s-4 > li:before{content:"(" counter(lst-ctn-kix_5ozdxj9yzw2s-4,lower-latin) ") "}.lst-kix_knat06iz8div-6 > li:before{content:"● "}.lst-kix_9a6ebvvpap80-7 > li:before{content:"○ "}.lst-kix_knat06iz8div-5 > li:before{content:"■ "}.lst-kix_knat06iz8div-7 > li:before{content:"○ "}.lst-kix_9a6ebvvpap80-6 > li:before{content:"● "}.lst-kix_9a6ebvvpap80-8 > li:before{content:"■ "}.lst-kix_ltea2g481i55-2 > li:before{content:"■ "}.lst-kix_ltea2g481i55-4 > li:before{content:"○ "}.lst-kix_ltea2g481i55-1 > li:before{content:"○ "}.lst-kix_ltea2g481i55-5 > li:before{content:"■ "}.lst-kix_uul46d8g2i7o-8 > li:before{content:"■ "}.lst-kix_knat06iz8div-2 > li:before{content:"■ "}.lst-kix_9a6ebvvpap80-3 > li:before{content:"● "}.lst-kix_uul46d8g2i7o-7 > li:before{content:"○ "}.lst-kix_knat06iz8div-3 > li:before{content:"● "}.lst-kix_9a6ebvvpap80-2 > li:before{content:"■ "}ol.lst-kix_3fzf89n8yoed-3.start{counter-reset:lst-ctn-kix_3fzf89n8yoed-3 0}.lst-kix_knat06iz8div-4 > li:before{content:"○ "}.lst-kix_9a6ebvvpap80-1 > li:before{content:"○ "}.lst-kix_cign8cnrqwyd-8 > li{counter-increment:lst-ctn-kix_cign8cnrqwyd-8}.lst-kix_ltea2g481i55-3 > li:before{content:"● "}ul.lst-kix_dlbk0s8fdwt8-1{list-style-type:none}ul.lst-kix_dlbk0s8fdwt8-0{list-style-type:none}.lst-kix_r3uvk2hyw1by-4 > li:before{content:"○ "}ul.lst-kix_dlbk0s8fdwt8-3{list-style-type:none}.lst-kix_9a6ebvvpap80-0 > li:before{content:"● "}ul.lst-kix_dlbk0s8fdwt8-2{list-style-type:none}ul.lst-kix_dlbk0s8fdwt8-5{list-style-type:none}ul.lst-kix_dlbk0s8fdwt8-4{list-style-type:none}.lst-kix_r3uvk2hyw1by-2 > li:before{content:"■ "}.lst-kix_r3uvk2hyw1by-3 > li:before{content:"● "}ul.lst-kix_dlbk0s8fdwt8-7{list-style-type:none}ul.lst-kix_dlbk0s8fdwt8-6{list-style-type:none}ol.lst-kix_cign8cnrqwyd-5.start{counter-reset:lst-ctn-kix_cign8cnrqwyd-5 0}.lst-kix_r3uvk2hyw1by-0 > li:before{content:"● "}.lst-kix_r3uvk2hyw1by-1 > li:before{content:"○ "}.lst-kix_knat06iz8div-1 > li:before{content:"○ "}.lst-kix_ltea2g481i55-6 > li:before{content:"● "}.lst-kix_ltea2g481i55-8 > li:before{content:"■ "}.lst-kix_3fzf89n8yoed-5 > li{counter-increment:lst-ctn-kix_3fzf89n8yoed-5}.lst-kix_knat06iz8div-0 > li:before{content:"● "}.lst-kix_ltea2g481i55-7 > li:before{content:"○ "}.lst-kix_5ozdxj9yzw2s-2 > li{counter-increment:lst-ctn-kix_5ozdxj9yzw2s-2}.lst-kix_5ozdxj9yzw2s-5 > li{counter-increment:lst-ctn-kix_5ozdxj9yzw2s-5}.lst-kix_6g3fp2rwn5rn-1 > li:before{content:"○ "}.lst-kix_6g3fp2rwn5rn-0 > li:before{content:"● "}.lst-kix_jorsgqeq2cd7-8 > li{counter-increment:lst-ctn-kix_jorsgqeq2cd7-8}.lst-kix_9a6ebvvpap80-4 > li:before{content:"○ "}.lst-kix_knat06iz8div-8 > li:before{content:"■ "}.lst-kix_9a6ebvvpap80-5 > li:before{content:"■ "}.lst-kix_b4hxna1le1rg-6 > li{counter-increment:lst-ctn-kix_b4hxna1le1rg-6}.lst-kix_3fzf89n8yoed-1 > li{counter-increment:lst-ctn-kix_3fzf89n8yoed-1}ol.lst-kix_5ozdxj9yzw2s-4.start{counter-reset:lst-ctn-kix_5ozdxj9yzw2s-4 0}.lst-kix_jorsgqeq2cd7-1 > li:before{content:"" counter(lst-ctn-kix_jorsgqeq2cd7-1,lower-latin) ".) "}.lst-kix_cign8cnrqwyd-5 > li{counter-increment:lst-ctn-kix_cign8cnrqwyd-5}.lst-kix_jorsgqeq2cd7-3 > li:before{content:"(" counter(lst-ctn-kix_jorsgqeq2cd7-3,decimal) ") "}ol.lst-kix_cign8cnrqwyd-8.start{counter-reset:lst-ctn-kix_cign8cnrqwyd-8 0}.lst-kix_okhjq7flcjmx-3 > li{counter-increment:lst-ctn-kix_okhjq7flcjmx-3}ol.lst-kix_d87x2tnjeviy-1.start{counter-reset:lst-ctn-kix_d87x2tnjeviy-1 0}.lst-kix_cign8cnrqwyd-4 > li{counter-increment:lst-ctn-kix_cign8cnrqwyd-4}ul.lst-kix_at6eq57y97u3-2{list-style-type:none}ul.lst-kix_c70dvhrp3xl4-7{list-style-type:none}ul.lst-kix_at6eq57y97u3-1{list-style-type:none}ul.lst-kix_c70dvhrp3xl4-6{list-style-type:none}ul.lst-kix_at6eq57y97u3-4{list-style-type:none}ul.lst-kix_c70dvhrp3xl4-5{list-style-type:none}ul.lst-kix_at6eq57y97u3-3{list-style-type:none}.lst-kix_jorsgqeq2cd7-4 > li{counter-increment:lst-ctn-kix_jorsgqeq2cd7-4}ul.lst-kix_c70dvhrp3xl4-4{list-style-type:none}ul.lst-kix_at6eq57y97u3-0{list-style-type:none}ul.lst-kix_c70dvhrp3xl4-8{list-style-type:none}.lst-kix_uul46d8g2i7o-0 > li:before{content:"● "}ol.lst-kix_okhjq7flcjmx-3.start{counter-reset:lst-ctn-kix_okhjq7flcjmx-3 0}ul.lst-kix_at6eq57y97u3-6{list-style-type:none}ul.lst-kix_c70dvhrp3xl4-3{list-style-type:none}ul.lst-kix_at6eq57y97u3-5{list-style-type:none}ul.lst-kix_c70dvhrp3xl4-2{list-style-type:none}ul.lst-kix_at6eq57y97u3-8{list-style-type:none}ul.lst-kix_c70dvhrp3xl4-1{list-style-type:none}ul.lst-kix_at6eq57y97u3-7{list-style-type:none}ul.lst-kix_c70dvhrp3xl4-0{list-style-type:none}.lst-kix_uul46d8g2i7o-4 > li:before{content:"○ "}ul.lst-kix_9d8et4nfx4j3-1{list-style-type:none}ul.lst-kix_9d8et4nfx4j3-0{list-style-type:none}ul.lst-kix_9d8et4nfx4j3-3{list-style-type:none}.lst-kix_r3uvk2hyw1by-5 > li:before{content:"■ "}ul.lst-kix_9d8et4nfx4j3-2{list-style-type:none}.lst-kix_uul46d8g2i7o-2 > li:before{content:"■ "}.lst-kix_uul46d8g2i7o-6 > li:before{content:"● "}.lst-kix_jorsgqeq2cd7-5 > li:before{content:"(" counter(lst-ctn-kix_jorsgqeq2cd7-5,lower-roman) ") "}ul.lst-kix_9d8et4nfx4j3-8{list-style-type:none}.lst-kix_r3uvk2hyw1by-7 > li:before{content:"○ "}ul.lst-kix_9d8et4nfx4j3-5{list-style-type:none}ul.lst-kix_9d8et4nfx4j3-4{list-style-type:none}ul.lst-kix_9d8et4nfx4j3-7{list-style-type:none}.lst-kix_d87x2tnjeviy-2 > li{counter-increment:lst-ctn-kix_d87x2tnjeviy-2}ul.lst-kix_9d8et4nfx4j3-6{list-style-type:none}.lst-kix_jorsgqeq2cd7-7 > li:before{content:"" counter(lst-ctn-kix_jorsgqeq2cd7-7,lower-latin) ". "}.lst-kix_1osiewg5f0zk-1 > li:before{content:"○ "}.lst-kix_b4hxna1le1rg-2 > li{counter-increment:lst-ctn-kix_b4hxna1le1rg-2}ul.lst-kix_tiitl0h8kw3a-8{list-style-type:none}.lst-kix_5ozdxj9yzw2s-7 > li:before{content:"" counter(lst-ctn-kix_5ozdxj9yzw2s-7,lower-latin) ". "}ul.lst-kix_tiitl0h8kw3a-7{list-style-type:none}.lst-kix_dlbk0s8fdwt8-5 > li:before{content:"■ "}ul.lst-kix_tiitl0h8kw3a-6{list-style-type:none}.lst-kix_1osiewg5f0zk-3 > li:before{content:"● "}ul.lst-kix_tiitl0h8kw3a-5{list-style-type:none}ul.lst-kix_tiitl0h8kw3a-4{list-style-type:none}.lst-kix_5bjwbwc6fza6-5 > li:before{content:"■ "}ul.lst-kix_tiitl0h8kw3a-3{list-style-type:none}ul.lst-kix_tiitl0h8kw3a-2{list-style-type:none}.lst-kix_1osiewg5f0zk-5 > li:before{content:"■ "}ul.lst-kix_tiitl0h8kw3a-1{list-style-type:none}ul.lst-kix_tiitl0h8kw3a-0{list-style-type:none}.lst-kix_5bjwbwc6fza6-7 > li:before{content:"○ "}.lst-kix_dlbk0s8fdwt8-7 > li:before{content:"○ "}.lst-kix_1osiewg5f0zk-7 > li:before{content:"○ "}ul.lst-kix_5bjwbwc6fza6-7{list-style-type:none}ul.lst-kix_5bjwbwc6fza6-6{list-style-type:none}ul.lst-kix_5bjwbwc6fza6-8{list-style-type:none}ul.lst-kix_7rqn06tuvjqu-5{list-style-type:none}ul.lst-kix_7rqn06tuvjqu-4{list-style-type:none}ol.lst-kix_b4hxna1le1rg-2.start{counter-reset:lst-ctn-kix_b4hxna1le1rg-2 0}ul.lst-kix_7rqn06tuvjqu-3{list-style-type:none}ul.lst-kix_7rqn06tuvjqu-2{list-style-type:none}ul.lst-kix_7rqn06tuvjqu-8{list-style-type:none}ul.lst-kix_7rqn06tuvjqu-7{list-style-type:none}.lst-kix_5bjwbwc6fza6-3 > li:before{content:"● "}ol.lst-kix_5ozdxj9yzw2s-2.start{counter-reset:lst-ctn-kix_5ozdxj9yzw2s-2 0}ul.lst-kix_7rqn06tuvjqu-6{list-style-type:none}.lst-kix_3fzf89n8yoed-6 > li{counter-increment:lst-ctn-kix_3fzf89n8yoed-6}ul.lst-kix_5bjwbwc6fza6-3{list-style-type:none}ul.lst-kix_5bjwbwc6fza6-2{list-style-type:none}ul.lst-kix_5bjwbwc6fza6-5{list-style-type:none}ol.lst-kix_3fzf89n8yoed-1.start{counter-reset:lst-ctn-kix_3fzf89n8yoed-1 0}ul.lst-kix_5bjwbwc6fza6-4{list-style-type:none}ul.lst-kix_7rqn06tuvjqu-1{list-style-type:none}ol.lst-kix_okhjq7flcjmx-5.start{counter-reset:lst-ctn-kix_okhjq7flcjmx-5 0}ul.lst-kix_7rqn06tuvjqu-0{list-style-type:none}ul.lst-kix_5bjwbwc6fza6-1{list-style-type:none}ul.lst-kix_5bjwbwc6fza6-0{list-style-type:none}.lst-kix_5bjwbwc6fza6-1 > li:before{content:"○ "}ol.lst-kix_3fzf89n8yoed-5.start{counter-reset:lst-ctn-kix_3fzf89n8yoed-5 0}.lst-kix_klt72c3vlz7x-4 > li:before{content:"○ "}.lst-kix_cign8cnrqwyd-3 > li:before{content:"(" counter(lst-ctn-kix_cign8cnrqwyd-3,decimal) ") "}.lst-kix_klt72c3vlz7x-5 > li:before{content:"■ "}.lst-kix_d87x2tnjeviy-6 > li:before{content:"" counter(lst-ctn-kix_d87x2tnjeviy-6,decimal) ". "}ol.lst-kix_b4hxna1le1rg-8{list-style-type:none}ol.lst-kix_b4hxna1le1rg-6{list-style-type:none}ol.lst-kix_b4hxna1le1rg-7{list-style-type:none}.lst-kix_io0c1rpej929-8 > li:before{content:"■ "}.lst-kix_okhjq7flcjmx-7 > li:before{content:"" counter(lst-ctn-kix_okhjq7flcjmx-7,lower-latin) ". "}.lst-kix_321avs9ky2gv-6 > li:before{content:"● "}.lst-kix_cign8cnrqwyd-6 > li:before{content:"" counter(lst-ctn-kix_cign8cnrqwyd-6,decimal) ". "}.lst-kix_okhjq7flcjmx-6 > li:before{content:"" counter(lst-ctn-kix_okhjq7flcjmx-6,decimal) ". "}.lst-kix_321avs9ky2gv-7 > li:before{content:"○ "}ol.lst-kix_b4hxna1le1rg-0{list-style-type:none}ol.lst-kix_okhjq7flcjmx-7.start{counter-reset:lst-ctn-kix_okhjq7flcjmx-7 0}ol.lst-kix_b4hxna1le1rg-1{list-style-type:none}.lst-kix_io0c1rpej929-7 > li:before{content:"○ "}ol.lst-kix_b4hxna1le1rg-4{list-style-type:none}.lst-kix_cign8cnrqwyd-7 > li:before{content:"" counter(lst-ctn-kix_cign8cnrqwyd-7,lower-latin) ". "}ol.lst-kix_b4hxna1le1rg-5{list-style-type:none}ol.lst-kix_b4hxna1le1rg-2{list-style-type:none}.lst-kix_klt72c3vlz7x-1 > li:before{content:"○ "}ol.lst-kix_b4hxna1le1rg-3{list-style-type:none}.lst-kix_io0c1rpej929-3 > li:before{content:"● "}.lst-kix_klt72c3vlz7x-0 > li:before{content:"● "}.lst-kix_io0c1rpej929-4 > li:before{content:"○ "}.lst-kix_okhjq7flcjmx-3 > li:before{content:"(" counter(lst-ctn-kix_okhjq7flcjmx-3,decimal) ") "}.lst-kix_321avs9ky2gv-2 > li:before{content:"■ "}.lst-kix_okhjq7flcjmx-2 > li:before{content:"" counter(lst-ctn-kix_okhjq7flcjmx-2,lower-roman) ".) "}.lst-kix_321avs9ky2gv-3 > li:before{content:"● "}.lst-kix_okhjq7flcjmx-7 > li{counter-increment:lst-ctn-kix_okhjq7flcjmx-7}.lst-kix_d87x2tnjeviy-8 > li{counter-increment:lst-ctn-kix_d87x2tnjeviy-8}ol.lst-kix_jorsgqeq2cd7-2.start{counter-reset:lst-ctn-kix_jorsgqeq2cd7-2 0}.lst-kix_io0c1rpej929-0 > li:before{content:"● "}.lst-kix_cign8cnrqwyd-0 > li{counter-increment:lst-ctn-kix_cign8cnrqwyd-0}ul.lst-kix_knat06iz8div-6{list-style-type:none}ul.lst-kix_knat06iz8div-5{list-style-type:none}.lst-kix_dlbk0s8fdwt8-4 > li:before{content:"○ "}ul.lst-kix_knat06iz8div-4{list-style-type:none}ol.lst-kix_b4hxna1le1rg-1.start{counter-reset:lst-ctn-kix_b4hxna1le1rg-1 0}ul.lst-kix_knat06iz8div-3{list-style-type:none}.lst-kix_7rqn06tuvjqu-1 > li:before{content:"○ "}.lst-kix_7rqn06tuvjqu-2 > li:before{content:"■ "}ul.lst-kix_knat06iz8div-8{list-style-type:none}ul.lst-kix_knat06iz8div-7{list-style-type:none}.lst-kix_dlbk0s8fdwt8-0 > li:before{content:"● "}.lst-kix_klt72c3vlz7x-8 > li:before{content:"■ "}.lst-kix_dlbk0s8fdwt8-1 > li:before{content:"○ "}ul.lst-kix_knat06iz8div-2{list-style-type:none}.lst-kix_cign8cnrqwyd-2 > li:before{content:"" counter(lst-ctn-kix_cign8cnrqwyd-2,lower-roman) ".) "}ul.lst-kix_knat06iz8div-1{list-style-type:none}ul.lst-kix_knat06iz8div-0{list-style-type:none}.lst-kix_7rqn06tuvjqu-6 > li:before{content:"● "}.lst-kix_f851k4w19tqy-8 > li:before{content:"■ "}.lst-kix_7rqn06tuvjqu-5 > li:before{content:"■ "}ol.lst-kix_jorsgqeq2cd7-8.start{counter-reset:lst-ctn-kix_jorsgqeq2cd7-8 0}.lst-kix_cign8cnrqwyd-2 > li{counter-increment:lst-ctn-kix_cign8cnrqwyd-2}.lst-kix_d87x2tnjeviy-4 > li{counter-increment:lst-ctn-kix_d87x2tnjeviy-4}.lst-kix_9ed5jyo95z8c-8 > li:before{content:"■ "}ol.lst-kix_5ozdxj9yzw2s-6.start{counter-reset:lst-ctn-kix_5ozdxj9yzw2s-6 0}ol.lst-kix_jorsgqeq2cd7-1.start{counter-reset:lst-ctn-kix_jorsgqeq2cd7-1 0}.lst-kix_9ed5jyo95z8c-7 > li:before{content:"○ "}.lst-kix_3fzf89n8yoed-4 > li{counter-increment:lst-ctn-kix_3fzf89n8yoed-4}ul.lst-kix_ltea2g481i55-3{list-style-type:none}ol.lst-kix_d87x2tnjeviy-6.start{counter-reset:lst-ctn-kix_d87x2tnjeviy-6 0}ul.lst-kix_ltea2g481i55-2{list-style-type:none}ul.lst-kix_ltea2g481i55-1{list-style-type:none}ul.lst-kix_ltea2g481i55-0{list-style-type:none}.lst-kix_9ed5jyo95z8c-3 > li:before{content:"● "}.lst-kix_9ed5jyo95z8c-0 > li:before{content:"● "}.lst-kix_9ed5jyo95z8c-4 > li:before{content:"○ "}ul.lst-kix_ltea2g481i55-8{list-style-type:none}.lst-kix_9d8et4nfx4j3-0 > li:before{content:"● "}ul.lst-kix_ltea2g481i55-7{list-style-type:none}ul.lst-kix_ltea2g481i55-6{list-style-type:none}ul.lst-kix_ltea2g481i55-5{list-style-type:none}ul.lst-kix_ltea2g481i55-4{list-style-type:none}ol.lst-kix_5ozdxj9yzw2s-5.start{counter-reset:lst-ctn-kix_5ozdxj9yzw2s-5 0}.lst-kix_rk2uxnun2hto-6 > li:before{content:"● "}.lst-kix_rk2uxnun2hto-3 > li:before{content:"● "}.lst-kix_rk2uxnun2hto-7 > li:before{content:"○ "}.lst-kix_rk2uxnun2hto-2 > li:before{content:"■ "}.lst-kix_d87x2tnjeviy-2 > li:before{content:"" counter(lst-ctn-kix_d87x2tnjeviy-2,lower-roman) ".) "}.lst-kix_okhjq7flcjmx-2 > li{counter-increment:lst-ctn-kix_okhjq7flcjmx-2}.lst-kix_f851k4w19tqy-0 > li:before{content:"● "}.lst-kix_f851k4w19tqy-4 > li:before{content:"○ "}.lst-kix_okhjq7flcjmx-5 > li{counter-increment:lst-ctn-kix_okhjq7flcjmx-5}.lst-kix_d87x2tnjeviy-1 > li:before{content:"" counter(lst-ctn-kix_d87x2tnjeviy-1,lower-latin) ".) "}.lst-kix_d87x2tnjeviy-5 > li:before{content:"(" counter(lst-ctn-kix_d87x2tnjeviy-5,lower-roman) ") "}.lst-kix_f851k4w19tqy-1 > li:before{content:"○ "}.lst-kix_f851k4w19tqy-5 > li:before{content:"■ "}ol.lst-kix_d87x2tnjeviy-5.start{counter-reset:lst-ctn-kix_d87x2tnjeviy-5 0}ol.lst-kix_okhjq7flcjmx-8.start{counter-reset:lst-ctn-kix_okhjq7flcjmx-8 0}ol.lst-kix_3fzf89n8yoed-4.start{counter-reset:lst-ctn-kix_3fzf89n8yoed-4 0}ol.lst-kix_jorsgqeq2cd7-7.start{counter-reset:lst-ctn-kix_jorsgqeq2cd7-7 0}ol.lst-kix_jorsgqeq2cd7-3.start{counter-reset:lst-ctn-kix_jorsgqeq2cd7-3 0}.lst-kix_b4hxna1le1rg-5 > li:before{content:"(" counter(lst-ctn-kix_b4hxna1le1rg-5,lower-roman) ") "}.lst-kix_d87x2tnjeviy-1 > li{counter-increment:lst-ctn-kix_d87x2tnjeviy-1}.lst-kix_jorsgqeq2cd7-2 > li:before{content:"" counter(lst-ctn-kix_jorsgqeq2cd7-2,lower-roman) ".) "}ul.lst-kix_6g3fp2rwn5rn-2{list-style-type:none}.lst-kix_tiitl0h8kw3a-3 > li:before{content:"● "}ul.lst-kix_6g3fp2rwn5rn-1{list-style-type:none}ul.lst-kix_6g3fp2rwn5rn-0{list-style-type:none}ol.lst-kix_jorsgqeq2cd7-6.start{counter-reset:lst-ctn-kix_jorsgqeq2cd7-6 0}ul.lst-kix_6g3fp2rwn5rn-6{list-style-type:none}ul.lst-kix_6g3fp2rwn5rn-5{list-style-type:none}ol.lst-kix_cign8cnrqwyd-0.start{counter-reset:lst-ctn-kix_cign8cnrqwyd-0 0}ul.lst-kix_6g3fp2rwn5rn-4{list-style-type:none}ul.lst-kix_6g3fp2rwn5rn-3{list-style-type:none}ul.lst-kix_6g3fp2rwn5rn-8{list-style-type:none}ul.lst-kix_6g3fp2rwn5rn-7{list-style-type:none}.lst-kix_tiitl0h8kw3a-7 > li:before{content:"○ "}.lst-kix_fq53fh4u8a7l-2 > li:before{content:"■ "}ol.lst-kix_3fzf89n8yoed-6.start{counter-reset:lst-ctn-kix_3fzf89n8yoed-6 0}ol.lst-kix_cign8cnrqwyd-3.start{counter-reset:lst-ctn-kix_cign8cnrqwyd-3 0}.lst-kix_3fzf89n8yoed-2 > li{counter-increment:lst-ctn-kix_3fzf89n8yoed-2}.lst-kix_c70dvhrp3xl4-6 > li:before{content:"● "}.lst-kix_9d8et4nfx4j3-3 > li:before{content:"● "}.lst-kix_jorsgqeq2cd7-1 > li{counter-increment:lst-ctn-kix_jorsgqeq2cd7-1}ul.lst-kix_9ed5jyo95z8c-6{list-style-type:none}ul.lst-kix_9ed5jyo95z8c-5{list-style-type:none}.lst-kix_uul46d8g2i7o-3 > li:before{content:"● "}ul.lst-kix_9ed5jyo95z8c-4{list-style-type:none}ul.lst-kix_9ed5jyo95z8c-3{list-style-type:none}.lst-kix_jorsgqeq2cd7-6 > li:before{content:"" counter(lst-ctn-kix_jorsgqeq2cd7-6,decimal) ". "}ol.lst-kix_d87x2tnjeviy-7.start{counter-reset:lst-ctn-kix_d87x2tnjeviy-7 0}ul.lst-kix_9ed5jyo95z8c-8{list-style-type:none}ul.lst-kix_9ed5jyo95z8c-7{list-style-type:none}ol.lst-kix_jorsgqeq2cd7-6{list-style-type:none}.lst-kix_r3uvk2hyw1by-8 > li:before{content:"■ "}ol.lst-kix_jorsgqeq2cd7-5{list-style-type:none}ol.lst-kix_jorsgqeq2cd7-4{list-style-type:none}ol.lst-kix_5ozdxj9yzw2s-7.start{counter-reset:lst-ctn-kix_5ozdxj9yzw2s-7 0}ol.lst-kix_jorsgqeq2cd7-3{list-style-type:none}ul.lst-kix_9ed5jyo95z8c-2{list-style-type:none}ol.lst-kix_jorsgqeq2cd7-2{list-style-type:none}ul.lst-kix_9ed5jyo95z8c-1{list-style-type:none}ol.lst-kix_jorsgqeq2cd7-1{list-style-type:none}ul.lst-kix_9ed5jyo95z8c-0{list-style-type:none}ol.lst-kix_jorsgqeq2cd7-0{list-style-type:none}.lst-kix_c70dvhrp3xl4-2 > li:before{content:"■ "}.lst-kix_9d8et4nfx4j3-7 > li:before{content:"○ "}.lst-kix_5ozdxj9yzw2s-0 > li{counter-increment:lst-ctn-kix_5ozdxj9yzw2s-0}ol.lst-kix_jorsgqeq2cd7-8{list-style-type:none}ol.lst-kix_jorsgqeq2cd7-7{list-style-type:none}ol.lst-kix_cign8cnrqwyd-2.start{counter-reset:lst-ctn-kix_cign8cnrqwyd-2 0}.lst-kix_jorsgqeq2cd7-6 > li{counter-increment:lst-ctn-kix_jorsgqeq2cd7-6}.lst-kix_1osiewg5f0zk-2 > li:before{content:"■ "}ol.lst-kix_3fzf89n8yoed-7.start{counter-reset:lst-ctn-kix_3fzf89n8yoed-7 0}.lst-kix_5ozdxj9yzw2s-8 > li:before{content:"" counter(lst-ctn-kix_5ozdxj9yzw2s-8,lower-roman) ". "}ol.lst-kix_jorsgqeq2cd7-5.start{counter-reset:lst-ctn-kix_jorsgqeq2cd7-5 0}.lst-kix_cign8cnrqwyd-7 > li{counter-increment:lst-ctn-kix_cign8cnrqwyd-7}.lst-kix_5bjwbwc6fza6-6 > li:before{content:"● "}.lst-kix_okhjq7flcjmx-0 > li{counter-increment:lst-ctn-kix_okhjq7flcjmx-0}.lst-kix_dlbk0s8fdwt8-8 > li:before{content:"■ "}.lst-kix_1osiewg5f0zk-6 > li:before{content:"● "}ul.lst-kix_80aufoedlq30-6{list-style-type:none}ul.lst-kix_80aufoedlq30-5{list-style-type:none}ul.lst-kix_80aufoedlq30-4{list-style-type:none}ul.lst-kix_80aufoedlq30-3{list-style-type:none}.lst-kix_fq53fh4u8a7l-6 > li:before{content:"● "}ul.lst-kix_80aufoedlq30-8{list-style-type:none}ol.lst-kix_jorsgqeq2cd7-4.start{counter-reset:lst-ctn-kix_jorsgqeq2cd7-4 0}ul.lst-kix_80aufoedlq30-7{list-style-type:none}ol.lst-kix_d87x2tnjeviy-8.start{counter-reset:lst-ctn-kix_d87x2tnjeviy-8 0}ul.lst-kix_80aufoedlq30-2{list-style-type:none}ul.lst-kix_80aufoedlq30-1{list-style-type:none}ul.lst-kix_80aufoedlq30-0{list-style-type:none}.lst-kix_d87x2tnjeviy-6 > li{counter-increment:lst-ctn-kix_d87x2tnjeviy-6}ul.lst-kix_2l4nupwjhojg-5{list-style-type:none}.lst-kix_2l4nupwjhojg-6 > li:before{content:"● "}ul.lst-kix_2l4nupwjhojg-6{list-style-type:none}ul.lst-kix_2l4nupwjhojg-3{list-style-type:none}ul.lst-kix_2l4nupwjhojg-4{list-style-type:none}ol.lst-kix_cign8cnrqwyd-1.start{counter-reset:lst-ctn-kix_cign8cnrqwyd-1 0}ul.lst-kix_2l4nupwjhojg-7{list-style-type:none}ul.lst-kix_2l4nupwjhojg-8{list-style-type:none}.lst-kix_2l4nupwjhojg-2 > li:before{content:"■ "}.lst-kix_b4hxna1le1rg-1 > li:before{content:"" counter(lst-ctn-kix_b4hxna1le1rg-1,lower-latin) ".) "}.lst-kix_5bjwbwc6fza6-2 > li:before{content:"■ "}ul.lst-kix_2l4nupwjhojg-1{list-style-type:none}ul.lst-kix_2l4nupwjhojg-2{list-style-type:none}ul.lst-kix_2l4nupwjhojg-0{list-style-type:none}ol.lst-kix_okhjq7flcjmx-4.start{counter-reset:lst-ctn-kix_okhjq7flcjmx-4 0}.lst-kix_80aufoedlq30-8 > li:before{content:"■ "}.lst-kix_80aufoedlq30-7 > li:before{content:"○ "}.lst-kix_80aufoedlq30-5 > li:before{content:"■ "}.lst-kix_80aufoedlq30-4 > li:before{content:"○ "}.lst-kix_80aufoedlq30-6 > li:before{content:"● "}.lst-kix_3fzf89n8yoed-7 > li{counter-increment:lst-ctn-kix_3fzf89n8yoed-7}.lst-kix_at6eq57y97u3-8 > li:before{content:"■ "}ol.lst-kix_5ozdxj9yzw2s-8.start{counter-reset:lst-ctn-kix_5ozdxj9yzw2s-8 0}ol.lst-kix_3fzf89n8yoed-2.start{counter-reset:lst-ctn-kix_3fzf89n8yoed-2 0}ul.lst-kix_f851k4w19tqy-4{list-style-type:none}.lst-kix_at6eq57y97u3-6 > li:before{content:"● "}ul.lst-kix_f851k4w19tqy-3{list-style-type:none}.lst-kix_b4hxna1le1rg-4 > li{counter-increment:lst-ctn-kix_b4hxna1le1rg-4}ul.lst-kix_f851k4w19tqy-2{list-style-type:none}ul.lst-kix_f851k4w19tqy-1{list-style-type:none}ul.lst-kix_f851k4w19tqy-0{list-style-type:none}.lst-kix_at6eq57y97u3-3 > li:before{content:"● "}.lst-kix_at6eq57y97u3-7 > li:before{content:"○ "}.lst-kix_d87x2tnjeviy-7 > li{counter-increment:lst-ctn-kix_d87x2tnjeviy-7}ul.lst-kix_f851k4w19tqy-8{list-style-type:none}.lst-kix_at6eq57y97u3-4 > li:before{content:"○ "}ul.lst-kix_f851k4w19tqy-7{list-style-type:none}ul.lst-kix_f851k4w19tqy-6{list-style-type:none}.lst-kix_at6eq57y97u3-5 > li:before{content:"■ "}ul.lst-kix_f851k4w19tqy-5{list-style-type:none}ul.lst-kix_1osiewg5f0zk-8{list-style-type:none}ul.lst-kix_io0c1rpej929-1{list-style-type:none}ul.lst-kix_io0c1rpej929-0{list-style-type:none}ul.lst-kix_1osiewg5f0zk-6{list-style-type:none}ul.lst-kix_io0c1rpej929-3{list-style-type:none}ul.lst-kix_1osiewg5f0zk-7{list-style-type:none}ul.lst-kix_io0c1rpej929-2{list-style-type:none}ul.lst-kix_1osiewg5f0zk-4{list-style-type:none}ul.lst-kix_1osiewg5f0zk-5{list-style-type:none}ul.lst-kix_1osiewg5f0zk-2{list-style-type:none}ul.lst-kix_1osiewg5f0zk-3{list-style-type:none}ul.lst-kix_io0c1rpej929-8{list-style-type:none}ul.lst-kix_io0c1rpej929-5{list-style-type:none}ol.lst-kix_d87x2tnjeviy-2{list-style-type:none}.lst-kix_5ozdxj9yzw2s-7 > li{counter-increment:lst-ctn-kix_5ozdxj9yzw2s-7}ul.lst-kix_io0c1rpej929-4{list-style-type:none}ol.lst-kix_d87x2tnjeviy-1{list-style-type:none}ul.lst-kix_io0c1rpej929-7{list-style-type:none}ol.lst-kix_d87x2tnjeviy-0{list-style-type:none}ul.lst-kix_io0c1rpej929-6{list-style-type:none}ol.lst-kix_d87x2tnjeviy-6{list-style-type:none}.lst-kix_80aufoedlq30-1 > li:before{content:"○ "}ol.lst-kix_d87x2tnjeviy-5{list-style-type:none}ol.lst-kix_d87x2tnjeviy-4{list-style-type:none}.lst-kix_80aufoedlq30-0 > li:before{content:"● "}.lst-kix_80aufoedlq30-2 > li:before{content:"■ "}ol.lst-kix_d87x2tnjeviy-3{list-style-type:none}.lst-kix_80aufoedlq30-3 > li:before{content:"● "}ol.lst-kix_d87x2tnjeviy-8{list-style-type:none}ol.lst-kix_d87x2tnjeviy-7{list-style-type:none}ul.lst-kix_1osiewg5f0zk-0{list-style-type:none}ul.lst-kix_1osiewg5f0zk-1{list-style-type:none}.lst-kix_3fzf89n8yoed-5 > li:before{content:"(" counter(lst-ctn-kix_3fzf89n8yoed-5,lower-roman) ") "}.lst-kix_3fzf89n8yoed-4 > li:before{content:"(" counter(lst-ctn-kix_3fzf89n8yoed-4,lower-latin) ") "}.lst-kix_3fzf89n8yoed-6 > li:before{content:"" counter(lst-ctn-kix_3fzf89n8yoed-6,decimal) ". "}ol.lst-kix_b4hxna1le1rg-5.start{counter-reset:lst-ctn-kix_b4hxna1le1rg-5 0}.lst-kix_at6eq57y97u3-2 > li:before{content:"■ "}.lst-kix_b4hxna1le1rg-0 > li{counter-increment:lst-ctn-kix_b4hxna1le1rg-0}.lst-kix_3fzf89n8yoed-0 > li:before{content:"" counter(lst-ctn-kix_3fzf89n8yoed-0,decimal) ".) "}.lst-kix_3fzf89n8yoed-8 > li:before{content:"" counter(lst-ctn-kix_3fzf89n8yoed-8,lower-roman) ". "}.lst-kix_3fzf89n8yoed-7 > li:before{content:"" counter(lst-ctn-kix_3fzf89n8yoed-7,lower-latin) ". "}.lst-kix_at6eq57y97u3-0 > li:before{content:"● "}.lst-kix_at6eq57y97u3-1 > li:before{content:"○ "}ul.lst-kix_321avs9ky2gv-0{list-style-type:none}ul.lst-kix_321avs9ky2gv-1{list-style-type:none}ul.lst-kix_321avs9ky2gv-2{list-style-type:none}ul.lst-kix_321avs9ky2gv-3{list-style-type:none}.lst-kix_3fzf89n8yoed-1 > li:before{content:"" counter(lst-ctn-kix_3fzf89n8yoed-1,lower-latin) ".) "}.lst-kix_okhjq7flcjmx-8 > li{counter-increment:lst-ctn-kix_okhjq7flcjmx-8}ul.lst-kix_321avs9ky2gv-4{list-style-type:none}ul.lst-kix_321avs9ky2gv-5{list-style-type:none}.lst-kix_3fzf89n8yoed-2 > li:before{content:"" counter(lst-ctn-kix_3fzf89n8yoed-2,lower-roman) ".) "}ul.lst-kix_321avs9ky2gv-6{list-style-type:none}ul.lst-kix_321avs9ky2gv-7{list-style-type:none}.lst-kix_3fzf89n8yoed-3 > li:before{content:"(" counter(lst-ctn-kix_3fzf89n8yoed-3,decimal) ") "}ul.lst-kix_321avs9ky2gv-8{list-style-type:none}ol.lst-kix_cign8cnrqwyd-4.start{counter-reset:lst-ctn-kix_cign8cnrqwyd-4 0}.lst-kix_b4hxna1le1rg-6 > li:before{content:"" counter(lst-ctn-kix_b4hxna1le1rg-6,decimal) ". "}ul.lst-kix_fq53fh4u8a7l-7{list-style-type:none}ul.lst-kix_fq53fh4u8a7l-8{list-style-type:none}.lst-kix_b4hxna1le1rg-4 > li:before{content:"(" counter(lst-ctn-kix_b4hxna1le1rg-4,lower-latin) ") "}.lst-kix_b4hxna1le1rg-8 > li:before{content:"" counter(lst-ctn-kix_b4hxna1le1rg-8,lower-roman) ". "}.lst-kix_tiitl0h8kw3a-2 > li:before{content:"■ "}ol.lst-kix_5ozdxj9yzw2s-1.start{counter-reset:lst-ctn-kix_5ozdxj9yzw2s-1 0}.lst-kix_tiitl0h8kw3a-4 > li:before{content:"○ "}ol.lst-kix_d87x2tnjeviy-4.start{counter-reset:lst-ctn-kix_d87x2tnjeviy-4 0}.lst-kix_tiitl0h8kw3a-6 > li:before{content:"● "}.lst-kix_rk2uxnun2hto-0 > li:before{content:"● "}ol.lst-kix_jorsgqeq2cd7-0.start{counter-reset:lst-ctn-kix_jorsgqeq2cd7-0 0}.lst-kix_jorsgqeq2cd7-3 > li{counter-increment:lst-ctn-kix_jorsgqeq2cd7-3}ul.lst-kix_fq53fh4u8a7l-1{list-style-type:none}ol.lst-kix_b4hxna1le1rg-0.start{counter-reset:lst-ctn-kix_b4hxna1le1rg-0 0}ul.lst-kix_fq53fh4u8a7l-2{list-style-type:none}ul.lst-kix_fq53fh4u8a7l-0{list-style-type:none}ul.lst-kix_fq53fh4u8a7l-5{list-style-type:none}ul.lst-kix_fq53fh4u8a7l-6{list-style-type:none}.lst-kix_5ozdxj9yzw2s-3 > li{counter-increment:lst-ctn-kix_5ozdxj9yzw2s-3}.lst-kix_tiitl0h8kw3a-8 > li:before{content:"■ "}ul.lst-kix_fq53fh4u8a7l-3{list-style-type:none}ul.lst-kix_fq53fh4u8a7l-4{list-style-type:none}.lst-kix_fq53fh4u8a7l-3 > li:before{content:"● "}.lst-kix_okhjq7flcjmx-4 > li{counter-increment:lst-ctn-kix_okhjq7flcjmx-4}.lst-kix_9d8et4nfx4j3-2 > li:before{content:"■ "}.lst-kix_9d8et4nfx4j3-4 > li:before{content:"○ "}.lst-kix_c70dvhrp3xl4-7 > li:before{content:"○ "}.lst-kix_cign8cnrqwyd-3 > li{counter-increment:lst-ctn-kix_cign8cnrqwyd-3}.lst-kix_c70dvhrp3xl4-5 > li:before{content:"■ "}.lst-kix_fq53fh4u8a7l-1 > li:before{content:"○ "}.lst-kix_c70dvhrp3xl4-1 > li:before{content:"○ "}.lst-kix_c70dvhrp3xl4-3 > li:before{content:"● "}.lst-kix_5ozdxj9yzw2s-4 > li{counter-increment:lst-ctn-kix_5ozdxj9yzw2s-4}.lst-kix_9d8et4nfx4j3-6 > li:before{content:"● "}.lst-kix_9d8et4nfx4j3-8 > li:before{content:"■ "}.lst-kix_tiitl0h8kw3a-0 > li:before{content:"● "}ol.lst-kix_cign8cnrqwyd-1{list-style-type:none}ul.lst-kix_uul46d8g2i7o-4{list-style-type:none}ol.lst-kix_cign8cnrqwyd-0{list-style-type:none}ul.lst-kix_uul46d8g2i7o-3{list-style-type:none}ul.lst-kix_uul46d8g2i7o-2{list-style-type:none}ul.lst-kix_uul46d8g2i7o-1{list-style-type:none}ul.lst-kix_uul46d8g2i7o-0{list-style-type:none}ol.lst-kix_cign8cnrqwyd-8{list-style-type:none}.lst-kix_b4hxna1le1rg-8 > li{counter-increment:lst-ctn-kix_b4hxna1le1rg-8}ol.lst-kix_cign8cnrqwyd-7{list-style-type:none}.lst-kix_2l4nupwjhojg-1 > li:before{content:"○ "}ol.lst-kix_cign8cnrqwyd-6{list-style-type:none}ol.lst-kix_cign8cnrqwyd-5{list-style-type:none}ul.lst-kix_uul46d8g2i7o-8{list-style-type:none}ol.lst-kix_cign8cnrqwyd-4{list-style-type:none}ol.lst-kix_cign8cnrqwyd-6.start{counter-reset:lst-ctn-kix_cign8cnrqwyd-6 0}ul.lst-kix_uul46d8g2i7o-7{list-style-type:none}ol.lst-kix_cign8cnrqwyd-3{list-style-type:none}ul.lst-kix_uul46d8g2i7o-6{list-style-type:none}ol.lst-kix_cign8cnrqwyd-2{list-style-type:none}ul.lst-kix_uul46d8g2i7o-5{list-style-type:none}.lst-kix_b4hxna1le1rg-1 > li{counter-increment:lst-ctn-kix_b4hxna1le1rg-1}.lst-kix_d87x2tnjeviy-3 > li{counter-increment:lst-ctn-kix_d87x2tnjeviy-3}.lst-kix_b4hxna1le1rg-7 > li{counter-increment:lst-ctn-kix_b4hxna1le1rg-7}ol.lst-kix_okhjq7flcjmx-6.start{counter-reset:lst-ctn-kix_okhjq7flcjmx-6 0}ol.lst-kix_b4hxna1le1rg-3.start{counter-reset:lst-ctn-kix_b4hxna1le1rg-3 0}.lst-kix_fq53fh4u8a7l-5 > li:before{content:"■ "}ol.lst-kix_3fzf89n8yoed-0.start{counter-reset:lst-ctn-kix_3fzf89n8yoed-0 0}ol.lst-kix_5ozdxj9yzw2s-3.start{counter-reset:lst-ctn-kix_5ozdxj9yzw2s-3 0}.lst-kix_fq53fh4u8a7l-7 > li:before{content:"○ "}.lst-kix_2l4nupwjhojg-5 > li:before{content:"■ "}.lst-kix_2l4nupwjhojg-7 > li:before{content:"○ "}.lst-kix_b4hxna1le1rg-0 > li:before{content:"" counter(lst-ctn-kix_b4hxna1le1rg-0,decimal) ".) "}ol.lst-kix_cign8cnrqwyd-7.start{counter-reset:lst-ctn-kix_cign8cnrqwyd-7 0}.lst-kix_b4hxna1le1rg-2 > li:before{content:"" counter(lst-ctn-kix_b4hxna1le1rg-2,lower-roman) ".) "}.lst-kix_2l4nupwjhojg-3 > li:before{content:"● "}.lst-kix_3fzf89n8yoed-0 > li{counter-increment:lst-ctn-kix_3fzf89n8yoed-0}ol.lst-kix_d87x2tnjeviy-2.start{counter-reset:lst-ctn-kix_d87x2tnjeviy-2 0}.lst-kix_okhjq7flcjmx-1 > li:before{content:"" counter(lst-ctn-kix_okhjq7flcjmx-1,lower-latin) ".) "}.lst-kix_cign8cnrqwyd-0 > li:before{content:"" counter(lst-ctn-kix_cign8cnrqwyd-0,decimal) ".) "}.lst-kix_cign8cnrqwyd-1 > li:before{content:"" counter(lst-ctn-kix_cign8cnrqwyd-1,lower-latin) ".) "}.lst-kix_klt72c3vlz7x-6 > li:before{content:"● "}.lst-kix_d87x2tnjeviy-8 > li:before{content:"" counter(lst-ctn-kix_d87x2tnjeviy-8,lower-roman) ". "}.lst-kix_okhjq7flcjmx-0 > li:before{content:"" counter(lst-ctn-kix_okhjq7flcjmx-0,decimal) ".) "}.lst-kix_okhjq7flcjmx-4 > li:before{content:"(" counter(lst-ctn-kix_okhjq7flcjmx-4,lower-latin) ") "}.lst-kix_b4hxna1le1rg-5 > li{counter-increment:lst-ctn-kix_b4hxna1le1rg-5}.lst-kix_okhjq7flcjmx-5 > li:before{content:"(" counter(lst-ctn-kix_okhjq7flcjmx-5,lower-roman) ") "}.lst-kix_321avs9ky2gv-8 > li:before{content:"■ "}.lst-kix_cign8cnrqwyd-4 > li:before{content:"(" counter(lst-ctn-kix_cign8cnrqwyd-4,lower-latin) ") "}.lst-kix_cign8cnrqwyd-5 > li:before{content:"(" counter(lst-ctn-kix_cign8cnrqwyd-5,lower-roman) ") "}.lst-kix_klt72c3vlz7x-2 > li:before{content:"■ "}.lst-kix_d87x2tnjeviy-7 > li:before{content:"" counter(lst-ctn-kix_d87x2tnjeviy-7,lower-latin) ". "}.lst-kix_klt72c3vlz7x-3 > li:before{content:"● "}.lst-kix_io0c1rpej929-6 > li:before{content:"● "}ol.lst-kix_okhjq7flcjmx-1.start{counter-reset:lst-ctn-kix_okhjq7flcjmx-1 0}.lst-kix_321avs9ky2gv-4 > li:before{content:"○ "}.lst-kix_cign8cnrqwyd-8 > li:before{content:"" counter(lst-ctn-kix_cign8cnrqwyd-8,lower-roman) ". "}.lst-kix_io0c1rpej929-5 > li:before{content:"■ "}.lst-kix_321avs9ky2gv-1 > li:before{content:"○ "}.lst-kix_321avs9ky2gv-5 > li:before{content:"■ "}.lst-kix_3fzf89n8yoed-8 > li{counter-increment:lst-ctn-kix_3fzf89n8yoed-8}.lst-kix_jorsgqeq2cd7-7 > li{counter-increment:lst-ctn-kix_jorsgqeq2cd7-7}.lst-kix_io0c1rpej929-2 > li:before{content:"■ "}ol.lst-kix_5ozdxj9yzw2s-0.start{counter-reset:lst-ctn-kix_5ozdxj9yzw2s-0 0}.lst-kix_io0c1rpej929-1 > li:before{content:"○ "}.lst-kix_321avs9ky2gv-0 > li:before{content:"● "}.lst-kix_dlbk0s8fdwt8-3 > li:before{content:"● "}.lst-kix_dlbk0s8fdwt8-2 > li:before{content:"■ "}ol.lst-kix_d87x2tnjeviy-0.start{counter-reset:lst-ctn-kix_d87x2tnjeviy-0 0}ol.lst-kix_b4hxna1le1rg-7.start{counter-reset:lst-ctn-kix_b4hxna1le1rg-7 0}.lst-kix_okhjq7flcjmx-8 > li:before{content:"" counter(lst-ctn-kix_okhjq7flcjmx-8,lower-roman) ". "}.lst-kix_7rqn06tuvjqu-0 > li:before{content:"● "}.lst-kix_klt72c3vlz7x-7 > li:before{content:"○ "}.lst-kix_7rqn06tuvjqu-7 > li:before{content:"○ "}.lst-kix_7rqn06tuvjqu-3 > li:before{content:"● "}.lst-kix_f851k4w19tqy-6 > li:before{content:"● "}ol.lst-kix_okhjq7flcjmx-2.start{counter-reset:lst-ctn-kix_okhjq7flcjmx-2 0}.lst-kix_9ed5jyo95z8c-5 > li:before{content:"■ "}ul.lst-kix_rk2uxnun2hto-6{list-style-type:none}ul.lst-kix_rk2uxnun2hto-5{list-style-type:none}ul.lst-kix_rk2uxnun2hto-8{list-style-type:none}.lst-kix_7rqn06tuvjqu-4 > li:before{content:"○ "}.lst-kix_f851k4w19tqy-7 > li:before{content:"○ "}ul.lst-kix_rk2uxnun2hto-7{list-style-type:none}ol.lst-kix_b4hxna1le1rg-6.start{counter-reset:lst-ctn-kix_b4hxna1le1rg-6 0}.lst-kix_9ed5jyo95z8c-6 > li:before{content:"● "}.lst-kix_9ed5jyo95z8c-1 > li:before{content:"○ "}.lst-kix_7rqn06tuvjqu-8 > li:before{content:"■ "}.lst-kix_9ed5jyo95z8c-2 > li:before{content:"■ "}.lst-kix_rk2uxnun2hto-8 > li:before{content:"■ "}.lst-kix_b4hxna1le1rg-3 > li{counter-increment:lst-ctn-kix_b4hxna1le1rg-3}.lst-kix_rk2uxnun2hto-1 > li:before{content:"○ "}ul.lst-kix_rk2uxnun2hto-2{list-style-type:none}.lst-kix_f851k4w19tqy-2 > li:before{content:"■ "}ul.lst-kix_rk2uxnun2hto-1{list-style-type:none}ul.lst-kix_rk2uxnun2hto-4{list-style-type:none}ul.lst-kix_rk2uxnun2hto-3{list-style-type:none}.lst-kix_d87x2tnjeviy-0 > li:before{content:"" counter(lst-ctn-kix_d87x2tnjeviy-0,decimal) ".) "}.lst-kix_d87x2tnjeviy-4 > li:before{content:"(" counter(lst-ctn-kix_d87x2tnjeviy-4,lower-latin) ") "}ul.lst-kix_rk2uxnun2hto-0{list-style-type:none}.lst-kix_5ozdxj9yzw2s-8 > li{counter-increment:lst-ctn-kix_5ozdxj9yzw2s-8}.lst-kix_rk2uxnun2hto-4 > li:before{content:"○ "}.lst-kix_jorsgqeq2cd7-2 > li{counter-increment:lst-ctn-kix_jorsgqeq2cd7-2}.lst-kix_d87x2tnjeviy-3 > li:before{content:"(" counter(lst-ctn-kix_d87x2tnjeviy-3,decimal) ") "}.lst-kix_f851k4w19tqy-3 > li:before{content:"● "}.lst-kix_jorsgqeq2cd7-5 > li{counter-increment:lst-ctn-kix_jorsgqeq2cd7-5}.lst-kix_rk2uxnun2hto-5 > li:before{content:"■ "}.lst-kix_b4hxna1le1rg-7 > li:before{content:"" counter(lst-ctn-kix_b4hxna1le1rg-7,lower-latin) ". "}.lst-kix_jorsgqeq2cd7-0 > li:before{content:"" counter(lst-ctn-kix_jorsgqeq2cd7-0,decimal) ".) "}ul.lst-kix_klt72c3vlz7x-1{list-style-type:none}ul.lst-kix_klt72c3vlz7x-0{list-style-type:none}ul.lst-kix_klt72c3vlz7x-5{list-style-type:none}ul.lst-kix_klt72c3vlz7x-4{list-style-type:none}ul.lst-kix_klt72c3vlz7x-3{list-style-type:none}ul.lst-kix_klt72c3vlz7x-2{list-style-type:none}.lst-kix_jorsgqeq2cd7-4 > li:before{content:"(" counter(lst-ctn-kix_jorsgqeq2cd7-4,lower-latin) ") "}ul.lst-kix_klt72c3vlz7x-8{list-style-type:none}ul.lst-kix_klt72c3vlz7x-7{list-style-type:none}ul.lst-kix_klt72c3vlz7x-6{list-style-type:none}.lst-kix_tiitl0h8kw3a-5 > li:before{content:"■ "}.lst-kix_d87x2tnjeviy-0 > li{counter-increment:lst-ctn-kix_d87x2tnjeviy-0}ol.lst-kix_3fzf89n8yoed-8{list-style-type:none}ol.lst-kix_b4hxna1le1rg-8.start{counter-reset:lst-ctn-kix_b4hxna1le1rg-8 0}ol.lst-kix_3fzf89n8yoed-4{list-style-type:none}ul.lst-kix_9a6ebvvpap80-7{list-style-type:none}.lst-kix_fq53fh4u8a7l-4 > li:before{content:"○ "}ol.lst-kix_3fzf89n8yoed-5{list-style-type:none}ul.lst-kix_9a6ebvvpap80-8{list-style-type:none}ol.lst-kix_3fzf89n8yoed-6{list-style-type:none}ul.lst-kix_9a6ebvvpap80-5{list-style-type:none}ol.lst-kix_3fzf89n8yoed-7{list-style-type:none}ul.lst-kix_9a6ebvvpap80-6{list-style-type:none}ol.lst-kix_3fzf89n8yoed-0{list-style-type:none}ol.lst-kix_3fzf89n8yoed-1{list-style-type:none}.lst-kix_cign8cnrqwyd-6 > li{counter-increment:lst-ctn-kix_cign8cnrqwyd-6}.lst-kix_okhjq7flcjmx-1 > li{counter-increment:lst-ctn-kix_okhjq7flcjmx-1}ol.lst-kix_3fzf89n8yoed-2{list-style-type:none}.lst-kix_c70dvhrp3xl4-8 > li:before{content:"■ "}.lst-kix_9d8et4nfx4j3-1 > li:before{content:"○ "}.lst-kix_9d8et4nfx4j3-5 > li:before{content:"■ "}ol.lst-kix_3fzf89n8yoed-3{list-style-type:none}.lst-kix_fq53fh4u8a7l-0 > li:before{content:"● "}.lst-kix_uul46d8g2i7o-1 > li:before{content:"○ "}.lst-kix_5ozdxj9yzw2s-1 > li{counter-increment:lst-ctn-kix_5ozdxj9yzw2s-1}.lst-kix_uul46d8g2i7o-5 > li:before{content:"■ "}.lst-kix_jorsgqeq2cd7-8 > li:before{content:"" counter(lst-ctn-kix_jorsgqeq2cd7-8,lower-roman) ". "}.lst-kix_r3uvk2hyw1by-6 > li:before{content:"● "}.lst-kix_c70dvhrp3xl4-0 > li:before{content:"● "}.lst-kix_c70dvhrp3xl4-4 > li:before{content:"○ "}.lst-kix_tiitl0h8kw3a-1 > li:before{content:"○ "}ul.lst-kix_9a6ebvvpap80-0{list-style-type:none}ul.lst-kix_9a6ebvvpap80-3{list-style-type:none}ol.lst-kix_okhjq7flcjmx-0.start{counter-reset:lst-ctn-kix_okhjq7flcjmx-0 0}ul.lst-kix_9a6ebvvpap80-4{list-style-type:none}ul.lst-kix_9a6ebvvpap80-1{list-style-type:none}ul.lst-kix_9a6ebvvpap80-2{list-style-type:none}.lst-kix_5ozdxj9yzw2s-6 > li{counter-increment:lst-ctn-kix_5ozdxj9yzw2s-6}.lst-kix_dlbk0s8fdwt8-6 > li:before{content:"● "}.lst-kix_2l4nupwjhojg-0 > li:before{content:"● "}.lst-kix_1osiewg5f0zk-4 > li:before{content:"○ "}.lst-kix_okhjq7flcjmx-6 > li{counter-increment:lst-ctn-kix_okhjq7flcjmx-6}.lst-kix_1osiewg5f0zk-8 > li:before{content:"■ "}.lst-kix_5bjwbwc6fza6-8 > li:before{content:"■ "}.lst-kix_jorsgqeq2cd7-0 > li{counter-increment:lst-ctn-kix_jorsgqeq2cd7-0}.lst-kix_cign8cnrqwyd-1 > li{counter-increment:lst-ctn-kix_cign8cnrqwyd-1}.lst-kix_fq53fh4u8a7l-8 > li:before{content:"■ "}.lst-kix_2l4nupwjhojg-8 > li:before{content:"■ "}.lst-kix_5bjwbwc6fza6-4 > li:before{content:"○ "}.lst-kix_3fzf89n8yoed-3 > li{counter-increment:lst-ctn-kix_3fzf89n8yoed-3}.lst-kix_b4hxna1le1rg-3 > li:before{content:"(" counter(lst-ctn-kix_b4hxna1le1rg-3,decimal) ") "}.lst-kix_5bjwbwc6fza6-0 > li:before{content:"● "}.lst-kix_2l4nupwjhojg-4 > li:before{content:"○ "}

CALCULUS 3 UNIT 1Don't forget about the age old question of Why are discouraged workers not included in the unemployment rate?
We also discuss several other topics like Why movement songs make people unified and more powerful?

11.1)   Distance Formula  w/ coordinates

           Don't forget about the age old question of White republicans southerners are called?

  • Equation of sphere with center and radius [ Opposite sign ]

            We also discuss several other topics like What is a definition of culture?

Find center and radius w/ equation

  1. Organize by like terms
  2. Complete the square
  3. Factor  
  4. Combine constants for   *Determined by dividing keep sign

  • Determine if equation is sphere, point , no graph (1-4)

            If you want to learn more check out What did aristotle believe about the heart?

11.2) Vectors

         

  • Displacement Vector with two points

             If you want to learn more check out What are the two common family units?

          Component Form:  

  • Norm with coordinates or Vector

           

  • Normalize a Vector

[ Unit vector “same direction” ]  

 

  1. Find norm
  2. Put each coordinate over norm

  • Find Center + Radius of sphere with diameter

           

            Center:  

           

          Radius:

11.3) Dot Product [Scalar]

         

  • Find orthogonal projection:

  • Find vector component:

11.4) Cross Product [ Vector ]

         

          * If asked to find the norm, just take cross product

Find area of parallelogram with vectors

  1. Take cross product
  2. Find magnitude of product vector  

Find area of triangle with 3 vertex coordinates

  1. Pick a vertex, find 2 displacement vectors
  2. Take cross product of displacement vectors
  3. Calculate magnitude of vector then divide by 2

  • Abs value of cross product determinant:

  • Scalar Triple Product:

11.5) Parametric Equations of Lines

  • Find parametric equations for line with point parallel to vector:

Vector Equation Format:

         

  • Find parametric equations with 2 points
  1. Find displacement vector
  2. Pick one coordinate and plug into equation

  • Find parametric equations of tangent line to circle with point and
  1. Implicit Differentiation
  2. Substitute point to find slope

  1. Plug into equation with given coordinate

  • Find points where Line intersects the surface with 3 equations and

     

               1.) Substitute 2 smaller equations into main one

               2.) Solve for t [ should have 2 answers ] - factoring

               3.) Substitute values into 3 smaller equations to get intersecting coordinates

  • Find Lines through point that is parallel to 3 equations *write out 3 new equations with same given t coefficients and different (N0, Y0, Z0) as given point*

11.6) Planes in 3-0

  • Find equation of plane through point with vector

  • Find the equation of the plane through 3 points.
  1. Find 2 displacement vectors
  2. Take cross product
  3. Substitute in the equation for a, b, b with x0, y0, z0 or any given coordinate [ without opposite signs ]

  • Find the distance between point and plane

           

 

         

             

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