College Algebra MATH 1111
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This 3 page Class Notes was uploaded by Carolyn Farrell on Monday October 12, 2015. The Class Notes belongs to MATH 1111 at Gordon College taught by Thomas Gaines in Fall. Since its upload, it has received 27 views. For similar materials see /class/222090/math-1111-gordon-college in Mathematics (M) at Gordon College.
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Date Created: 10/12/15
5 4 Polynomial Inequalities Solving Polm omial Inequalities 1 Write inequality as 2 Find and plot the Xintercepts real zeros 3 Sketch the graph through the Xintercepts fX gt 0 fX lt 0 fX 2 0 fX S 0 You must use your knowledge of End Behavior and X Axis Behavior 4 Observe your graph and solve the inequality from step 1 using interval notation REMEMBER that To Solve fX gt O fX lt O fX 2 0 fX S 0 Practice Problems give the interval of Xvalues Xvalues Xvalues Xvalues 1 x 72x 6gt0 2 x 5x 3x 4gt0 3 x 4x 5x 7lt0 4 x 4x2x1gt0 5 x3 9x2 gt0 6 x32x2 15xgt0 7 xx35 x20 8 x4lt 36x2 9 X3 2 3X2 10 X4 5X2 36gt0 11 x32 27 for which the graph is above the XaXis below the XaXis above or on the XaXis below or on the XaXis Math 1 11 1 25 Variation Direct Variation y varies directly as X y is directly proportional to X General Direct Variation Eguation y k39X k is the variation constant Inverse Variation y varies inversely as X y is inversely proportional to X General Inverse Variation Eguation y E k is the variation constant I oint Variation y varies jointly as X and W General Ioint Variation Eguation y k39X39W k is the variation constant Solving Variation Problems 1 Write the variatlon equauon usmg the constant k y kX y etc X 2 Substitute value s and solve for k 3 Write the general variation equation using the value for k 4 If asked substitute to solve for a requested variable Examples of Variation Direct Variation The volume of a sphere van39cs dl39l39cc ywith the cube of its radius The monthly payments on a mortgage m dircc yvvith amount borrowed The distance an object falls is directlz grogortional to the square of the time of the fall The elongation of a spring vazics directlyvvith the applied weight Inverse Variation The demand for candy at the movie theatre is inversch growltional to the price of the candy The time it takes to get to school is leCI SCIZ QIOQOI ZiOHaI to your average speed The volume of a gas in a closed container mics I39llvclsclz39with its pressure The current in a circuit is inversclz growth01121 to the resistance in the circuit Ioint Variation The square of the length of the hypotenuse of a right triangle mics faintly with the sum of the squares of the lengths of its legs The perimeter of a rectangle varies lblh ywith the sum of the lengths of its sides Combination Variation The loss of heat through a wall mics lbin ywith the area of the wall and the difference between the inside and outside temperatures and m thCISCIYVVith the thickness of the wall The force of attraction between 2 bodies varies ioin z39with their masses and miss IhVCISCIYVVith the square of the distance between them
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