 3.4.1: Fill in the blank to correctly complete each sentence. As necessary...
 3.4.2: Fill in the blank to correctly complete each sentence. As necessary...
 3.4.3: Fill in the blank to correctly complete each sentence. As necessary...
 3.4.4: Fill in the blank to correctly complete each sentence. As necessary...
 3.4.5: Fill in the blank to correctly complete each sentence. As necessary...
 3.4.6: Fill in the blank to correctly complete each sentence. As necessary...
 3.4.7: Suppose that point P is on a circle with radius r, and ray OP is ro...
 3.4.8: Suppose that point P is on a circle with radius r, and ray OP is ro...
 3.4.9: Suppose that point P is on a circle with radius r, and ray OP is ro...
 3.4.10: Suppose that point P is on a circle with radius r, and ray OP is ro...
 3.4.11: Use the formula v = u t to find the value of the missing variable. ...
 3.4.12: Use the formula v = u t to find the value of the missing variable. ...
 3.4.13: Use the formula v = u t to find the value of the missing variable. ...
 3.4.14: Use the formula v = u t to find the value of the missing variable. ...
 3.4.15: Use the formula v = u t to find the value of the missing variable. ...
 3.4.16: Use the formula v = u t to find the value of the missing variable. ...
 3.4.17: Use the formula v = u t to find the value of the missing variable. ...
 3.4.18: Use the formula v = u t to find the value of the missing variable. ...
 3.4.19: Use the formula v = u t to find the value of the missing variable. ...
 3.4.20: Use the formula v = u t to find the value of the missing variable. ...
 3.4.21: Use the formula v = rv to find the value of the missing variable. r...
 3.4.22: Use the formula v = rv to find the value of the missing variable. r...
 3.4.23: Use the formula v = rv to find the value of the missing variable. v...
 3.4.24: Use the formula v = rv to find the value of the missing variable. v...
 3.4.25: Use the formula v = rv to find the value of the missing variable. v...
 3.4.26: Use the formula v = rv to find the value of the missing variable. v...
 3.4.27: The formula v = u t can be rewritten as u = vt. Substituting vt for...
 3.4.28: The formula v = u t can be rewritten as u = vt. Substituting vt for...
 3.4.29: The formula v = u t can be rewritten as u = vt. Substituting vt for...
 3.4.30: The formula v = u t can be rewritten as u = vt. Substituting vt for...
 3.4.31: The formula v = u t can be rewritten as u = vt. Substituting vt for...
 3.4.32: The formula v = u t can be rewritten as u = vt. Substituting vt for...
 3.4.33: Find the angular speed v for each of the following the hour hand of...
 3.4.34: Find the angular speed v for each of the following the second hand ...
 3.4.35: Find the angular speed v for each of the following the minute hand ...
 3.4.36: Find the angular speed v for each of the following a gear revolving...
 3.4.37: Find the linear speed v for each of the following. the tip of the m...
 3.4.38: Find the linear speed v for each of the following. the tip of the s...
 3.4.39: Find the linear speed v for each of the following. a point on the e...
 3.4.40: Find the linear speed v for each of the following. a point on the t...
 3.4.41: Find the linear speed v for each of the following. the tip of a pro...
 3.4.42: Find the linear speed v for each of the following. a point on the e...
 3.4.43: Speed of a Bicycle The tires of a bicycle have radius 13.0 in. and ...
 3.4.44: Hours in a Martian Day Mars rotates on its axis at the rate of abou...
 3.4.45: Angular and Linear Speeds of Earth The orbit of Earth about the sun...
 3.4.46: Angular and Linear Speeds of Earth Earth revolves on its axis once ...
 3.4.47: Speeds of a Pulley and a Belt The pulley shown has a radius of 12.9...
 3.4.48: Angular Speeds of Pulleys The two pulleys in the figure have radii ...
 3.4.49: Radius of a Spool of Thread A thread is being pulled off a spool at...
 3.4.50: Time to Move along a Railroad Track A railroad track is laid along ...
 3.4.51: Angular Speed of a Motor Propeller The propeller of a 90horsepower...
 3.4.52: Linear Speed of a Golf Club The shoulder joint can rotate at 25.0 r...
Solutions for Chapter 3.4: Linear and Angular Speed
Full solutions for Trigonometry  11th Edition
ISBN: 9780134217437
Solutions for Chapter 3.4: Linear and Angular Speed
Get Full SolutionsTrigonometry was written by and is associated to the ISBN: 9780134217437. Chapter 3.4: Linear and Angular Speed includes 52 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 52 problems in chapter 3.4: Linear and Angular Speed have been answered, more than 10182 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Trigonometry, edition: 11.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.
I don't want to reset my password
Need help? Contact support
Having trouble accessing your account? Let us help you, contact support at +1(510) 9441054 or support@studysoup.com
Forgot password? Reset it here