Linear Algebra With Applications
5th Edition
ISBN: 9780321796943
Author: BRETSCHER, Otto.
Publisher: Pearson Education
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 3.4, Problem 64E
Is matrix
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
5) You are purchasing a game for $30. You have a 5% off coupon and sales tax is 5%. What
will your final price be? Does it matter if you take off the coupon first or add in the tax first?
6) You have ten coupons that allow you to take 10% off the sales price of a jacket, and for
some strange reason, the store is going to allow you to use all ten coupons! Does this mean
you get the jacket for free? Let's really think about what would happen at the checkout.
First, the teller would scan the price tag on the jacket, and the computer would show the
price is $100. After the teller scans the first coupon, the computer will take 10% off of
$100, and show the price is $90. (Right? Think about why this is.) Then after the teller scans
the second coupon, the computer will take 10% off of $90.
(a) Continue this reasoning to fill in the table below showing the price of the jacket (y) after
you apply x coupons.
(b) Make a graph showing the price of the jacket from x = 0 to x = 10 coupons applied.…
(a)
(b)
(c)
(d)
de
unique?
Answer the following questions related to the linear system
x + y + z = 2
x-y+z=0
2x + y 2 3
rewrite the linear system into the matrix-vector form A = 5
Fuse elementary row operation to solve this linear system. Is the solution
use elementary row operation to find the inverse of A and then solve
the linear system. Verify the solution is the same as (b).
give the null space of matrix A and find the dimension of null space.
give the column space of matrix A and find the dimension of the column
space of A (Hint: use Rank-Nullity Theorem).
please explain in a clear way
Chapter 3 Solutions
Linear Algebra With Applications
Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...
Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 1 through 13, find...Ch. 3.1 - For each matrix A in Exercises 14 through 16, find...Ch. 3.1 - For each matrix A in Exercises 14 through 16, find...Ch. 3.1 - For each matrix A in Exercises 14 through 16, find...Ch. 3.1 - For each matrix A in Exercises 17 through 22,...Ch. 3.1 - For each matrix A in Exercises 17 through 22,...Ch. 3.1 - For each matrix A in Exercises 17 through 22,...Ch. 3.1 - For each matrix A in Exercises 17 through 22,...Ch. 3.1 - For each matrix A in Exercises 17 through 22,...Ch. 3.1 - For each matrix A in Exercises 17 through 22,...Ch. 3.1 - Describe the images and kernels of the...Ch. 3.1 - Prob. 24ECh. 3.1 - Describe the images and kernels of the...Ch. 3.1 - What is the image of a function f from to given...Ch. 3.1 - Give an example of a noninvertible function f from...Ch. 3.1 - Prob. 28ECh. 3.1 - Give an example of a function whose image is the...Ch. 3.1 - Give an example of a matrix A such that im(A)...Ch. 3.1 - Give an example of a matrix A such that im(A) is...Ch. 3.1 - Give an example of a linear transformation whose...Ch. 3.1 - Give an example of a linear transformation whose...Ch. 3.1 - Give an example of a linear transformation whose...Ch. 3.1 - Consider a nonzero vector v in 3 . Arguing...Ch. 3.1 - Prob. 36ECh. 3.1 - For the matrix A=[010001000] , describe the images...Ch. 3.1 - Consider a square matrix A. a. What is the...Ch. 3.1 - Consider an np matrix A and a pm matrix B. a. What...Ch. 3.1 - Consider an np matrix A and a pm matrix B. If...Ch. 3.1 - Consider the matrix A=[0.360.480.480.64] . a....Ch. 3.1 - Express the image of the matrix...Ch. 3.1 - Prob. 43ECh. 3.1 - Consider a matrix A, and let B=rref(A) . a. Is...Ch. 3.1 - Prob. 45ECh. 3.1 - Prob. 46ECh. 3.1 - Prob. 47ECh. 3.1 - Consider a 22 matrix A with A2=A . a. If w is in...Ch. 3.1 - Verify that the kernel of a linear transformation...Ch. 3.1 - Consider a square matrix A with ker(A2)=ker(A3) ....Ch. 3.1 - Consider an np matrix A and a pm in matrix B...Ch. 3.1 - Prob. 52ECh. 3.1 - In Exercises 53 and 54, we will work with the...Ch. 3.1 - See Exercise 53 for some background. When...Ch. 3.2 - Which of the sets W in Exercises 1 through 3 are...Ch. 3.2 - Which of the sets W in Exercises 1 through 3 are...Ch. 3.2 - Which of the sets W in Exercises 1 through 3 are...Ch. 3.2 - Consider the vectors v1,v2,...,vm in n . Is span...Ch. 3.2 - Give a geometrical description of all subspaces of...Ch. 3.2 - Consider two subspaces V and W of n . a. Is the...Ch. 3.2 - Consider a nonempty subset W of n that is closed...Ch. 3.2 - Find a nontrivial relation among the following...Ch. 3.2 - Consider the vectors v1,v2,...,vm in n , with vm=0...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 10 through 20, use paper and pencil...Ch. 3.2 - In Exercises 21 through 26, find a redundant...Ch. 3.2 - In Exercises 21 through 26, find a redundant...Ch. 3.2 - In Exercises 21 through 26, find a redundant...Ch. 3.2 - In Exercises 21 through 26, find a redundant...Ch. 3.2 - In Exercises 21 through 26, find a redundant...Ch. 3.2 - In Exercises 21 through 26, find a redundant...Ch. 3.2 - Find a basis of the image of the matrices in...Ch. 3.2 - Find a basis of the image of the matrices in...Ch. 3.2 - Find a basis of the image of the matrices in...Ch. 3.2 - Find a basis of the image of the matrices in...Ch. 3.2 - Find a basis of the image of the matrices in...Ch. 3.2 - Find a basis of the image of the matrices in...Ch. 3.2 - Prob. 33ECh. 3.2 - Consider the 54 matrix A=[ v 1 v 2 v 3 v 4] ....Ch. 3.2 - Prob. 35ECh. 3.2 - Consider a linear transformation T from n to p...Ch. 3.2 - Consider a linear transformation T from n to p...Ch. 3.2 - Prob. 38ECh. 3.2 - Consider some linearly independent vectors...Ch. 3.2 - Consider an np matrix A and a pm matrix B. Weare...Ch. 3.2 - Prob. 41ECh. 3.2 - Consider some perpendicular unit vectors...Ch. 3.2 - Consider three linearly independent vectors...Ch. 3.2 - Consider linearly independent vectors v1,v2,...,vm...Ch. 3.2 - Prob. 45ECh. 3.2 - Find a basis of the kernel of the matrix...Ch. 3.2 - Consider three linearly independent vectors...Ch. 3.2 - Express the plane V in 3 with equation...Ch. 3.2 - Express the line L in 3 spanned by the vector...Ch. 3.2 - Consider two subspaces V and W of n . Let V+W...Ch. 3.2 - Prob. 51ECh. 3.2 - Prob. 52ECh. 3.2 - Consider a subspace V of n . We define the...Ch. 3.2 - Consider the line L spanned by [123] in 3 . Find a...Ch. 3.2 - Consider the subspace L of 5 spanned by the...Ch. 3.2 - Prob. 56ECh. 3.2 - Consider the matrix...Ch. 3.2 - Prob. 58ECh. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 1 through 20, find the redundant...Ch. 3.3 - In Exercises 21 through 25, find the reduced...Ch. 3.3 - In Exercises 21 through 25, find the reduced...Ch. 3.3 - In Exercises 21 through 25, find the reduced...Ch. 3.3 - In Exercises 21 through 25, find the reduced...Ch. 3.3 - In Exercises 21 through 25, find the reduced...Ch. 3.3 - Consider the matrices C=[ 1 1 1 1 0 0 1 1 1],H=[ 1...Ch. 3.3 - Determine whether the following vectors form a...Ch. 3.3 - For which value(s) of the constant k do the...Ch. 3.3 - Find a basis of the subspace of 3 defined by...Ch. 3.3 - Find a basis of the subspace of 4 defined by the...Ch. 3.3 - Let V be the subspace of 4 defined by the equation...Ch. 3.3 - Find a basis of the subspace of 4 that consists of...Ch. 3.3 - A subspace V of n is called a hyperplane if V...Ch. 3.3 - Consider a subspace V in m that is defined by...Ch. 3.3 - Consider a nonzero vector v in n . What is the...Ch. 3.3 - Can you find a 33 matrix A such that im(A)=ker(A)...Ch. 3.3 - Give an example of a 45 matrix A with dim(kerA)=3...Ch. 3.3 - a. Consider a linear transformation T from 5 to 3...Ch. 3.3 - Prob. 39ECh. 3.3 - Prob. 40ECh. 3.3 - Prob. 41ECh. 3.3 - In Exercises 40 through 43, consider the problem...Ch. 3.3 - Prob. 43ECh. 3.3 - For Exercises 44 through 61, consider the problem...Ch. 3.3 - Prob. 45ECh. 3.3 - Prob. 46ECh. 3.3 - Prob. 47ECh. 3.3 - Prob. 48ECh. 3.3 - Prob. 49ECh. 3.3 - Prob. 50ECh. 3.3 - Prob. 51ECh. 3.3 - Prob. 52ECh. 3.3 - Prob. 53ECh. 3.3 - For Exercises 44 through 61, consider the problem...Ch. 3.3 - Prob. 55ECh. 3.3 - Prob. 56ECh. 3.3 - Prob. 57ECh. 3.3 - Prob. 58ECh. 3.3 - Prob. 59ECh. 3.3 - Prob. 60ECh. 3.3 - Find all points P in the plane such that you can...Ch. 3.3 - Prob. 62ECh. 3.3 - Consider two subspaces V and W of n , where Vis...Ch. 3.3 - Consider a subspace V of n with dim(V)=n . Explain...Ch. 3.3 - Consider two subspaces V and W of n , with VW={0}...Ch. 3.3 - Two subspaces V and W of n arc called...Ch. 3.3 - Consider linearly independent vectors v1,v2,...vp...Ch. 3.3 - Use Exercise 67 to construct a basis of 4 that...Ch. 3.3 - Consider two subspaces V and W of n . Show that...Ch. 3.3 - Use Exercise 69 to answer the following question:...Ch. 3.3 - Prob. 71ECh. 3.3 - Prob. 72ECh. 3.3 - Prob. 73ECh. 3.3 - Prob. 74ECh. 3.3 - Prob. 75ECh. 3.3 - Consider the matrix A=[1221] . Find scalars...Ch. 3.3 - Prob. 77ECh. 3.3 - An nn matrix A is called nilpotent if Am=0 for...Ch. 3.3 - Consider a nilpotent nn matrix A. Use the...Ch. 3.3 - Prob. 80ECh. 3.3 - Prob. 81ECh. 3.3 - If a 33 matrix A represents the projection onto a...Ch. 3.3 - Consider a 42 matrix A and a 25 matrix B. a. What...Ch. 3.3 - Prob. 84ECh. 3.3 - Prob. 85ECh. 3.3 - Prob. 86ECh. 3.3 - Prob. 87ECh. 3.3 - Prob. 88ECh. 3.3 - Prob. 89ECh. 3.3 - Prob. 90ECh. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 1 through 18, determine whether the...Ch. 3.4 - In Exercises 19 through 24, find the matrix B of...Ch. 3.4 - In Exercises 19 through 24, find the matrix B of...Ch. 3.4 - In Exercises 19 through 24, find the matrix B of...Ch. 3.4 - In Exercises 19 through 24, find the matrix B of...Ch. 3.4 - In Exercises 19 through 24, find the matrix B of...Ch. 3.4 - In Exercises 19 through 24, find the matrix B of...Ch. 3.4 - In Exercises 25 through 30, find the matrix B of...Ch. 3.4 - In Exercises 25 through 30, find the matrix B of...Ch. 3.4 - In Exercises 25 through 30, find the matrix B of...Ch. 3.4 - In Exercises 25 through 30, find the matrix B of...Ch. 3.4 - In Exercises 25 through 30, find the matrix B of...Ch. 3.4 - In Exercises 25 through 30, find the matrix B of...Ch. 3.4 - Let =(v1,v2,v3)be any basis of 3consisting of...Ch. 3.4 - Let =(v1,v2,v3)be any basis of 3consisting of...Ch. 3.4 - Let =(v1,v2,v3)be any basis of 3consisting of...Ch. 3.4 - Let =(v1,v2,v3)be any basis of 3consisting of...Ch. 3.4 - Let =(v1,v2,v3)be any basis of 3consisting of...Ch. 3.4 - Let =(v1,v2,v3)be any basis of 3consisting of...Ch. 3.4 - In Exercises 37 through 42, find a basis of n such...Ch. 3.4 - In Exercises 37 through 42, find a basis of n such...Ch. 3.4 - In Exercises 37 through 42, find a basis of n such...Ch. 3.4 - Prob. 40ECh. 3.4 - In Exercises 37 through 42, find a basis of n such...Ch. 3.4 - In Exercises 37 through 42, find a basis of n such...Ch. 3.4 - Consider the plane x1+2x2+x3=0 with basis...Ch. 3.4 - Consider the plane 2x13x2+4x3=0 with basis...Ch. 3.4 - Consider the plane 2x13x2+4x3=0. Find a basis of...Ch. 3.4 - Consider the plane x1+2x2+x3=0. Find a basis of...Ch. 3.4 - Consider a linear transformation T from 2 to 2...Ch. 3.4 - In the accompanying figure, sketch the vector x...Ch. 3.4 - Prob. 49ECh. 3.4 - Given a hexagonal tiling of the plane, such as you...Ch. 3.4 - Prob. 51ECh. 3.4 - If is a basis of n , is the transformation T from...Ch. 3.4 - Consider the basis of 2 consisting of the vectors...Ch. 3.4 - Let be the basis of n consisting of the vectors...Ch. 3.4 - Consider the basis of 2 consisting of the vectors...Ch. 3.4 - Find a basis of 2 such that andCh. 3.4 - Show that if a 33 matrix A represents the...Ch. 3.4 - Consider a 33 matrix A and a vector v in 3...Ch. 3.4 - Is matrix [2003] similar to matrix [2113] ?Ch. 3.4 - Is matrix [1001] similar to matrix [0110] ?Ch. 3.4 - Find a basis of 2 such that the matrix of the...Ch. 3.4 - Find a basis of 2 such that the matrix of the...Ch. 3.4 - Prob. 63ECh. 3.4 - Is matrix [abcd] similar to matrix [acbd] for all...Ch. 3.4 - Prove parts (a) and (b) of Theorem 3.4.6.Ch. 3.4 - Consider a matrix A of the form A=[abba] , where...Ch. 3.4 - If c0 ,find the matrix of the linear...Ch. 3.4 - Prob. 68ECh. 3.4 - If A is a 22 matrix such that A[12]=[36] and...Ch. 3.4 - Is there a basis of 2 such that matrix B of...Ch. 3.4 - Suppose that matrix A is similar to B, with B=S1AS...Ch. 3.4 - If A is similar to B, what is the relationship...Ch. 3.4 - Prob. 73ECh. 3.4 - Consider the regular tetrahedron in the...Ch. 3.4 - Prob. 75ECh. 3.4 - Prob. 76ECh. 3.4 - Prob. 77ECh. 3.4 - This problem refers to Leontief’s input—output...Ch. 3.4 - Prob. 79ECh. 3.4 - Prob. 80ECh. 3.4 - Consider the linear transformation...Ch. 3.4 - Prob. 82ECh. 3 - If v1,v2,...,vn and w1,w2,...,wm are any twobases...Ch. 3 - If A is a 56 matrix of rank 4, then the nullity of...Ch. 3 - The image of a 34 matrix is a subspace of 4 .Ch. 3 - The span of vectors v1,v2,...,vn consists of all...Ch. 3 - Prob. 5ECh. 3 - Prob. 6ECh. 3 - The kernel of any invertible matrix consists of...Ch. 3 - The identity matrix In is similar to all...Ch. 3 - Prob. 9ECh. 3 - The column vectors of a 54 matrix must be...Ch. 3 - Prob. 11ECh. 3 - Prob. 12ECh. 3 - Prob. 13ECh. 3 - Prob. 14ECh. 3 - Prob. 15ECh. 3 - Vectors [100],[210],[321] form a basis of 3 .Ch. 3 - Prob. 17ECh. 3 - Prob. 18ECh. 3 - Prob. 19ECh. 3 - Prob. 20ECh. 3 - Prob. 21ECh. 3 - Prob. 22ECh. 3 - Prob. 23ECh. 3 - Prob. 24ECh. 3 - Prob. 25ECh. 3 - If a 22 matrix P represents the orthogonal...Ch. 3 - Prob. 27ECh. 3 - Prob. 28ECh. 3 - Prob. 29ECh. 3 - Prob. 30ECh. 3 - Prob. 31ECh. 3 - Prob. 32ECh. 3 - Prob. 33ECh. 3 - Prob. 34ECh. 3 - Prob. 35ECh. 3 - If A and B are nn matrices, and vector v is in...Ch. 3 - Prob. 37ECh. 3 - Prob. 38ECh. 3 - Prob. 39ECh. 3 - Prob. 40ECh. 3 - Prob. 41ECh. 3 - If two nn matrices A and B have the same rank,...Ch. 3 - Prob. 43ECh. 3 - If A2=0 for a 1010 matrix A, then the inequality...Ch. 3 - Prob. 45ECh. 3 - Prob. 46ECh. 3 - Prob. 47ECh. 3 - Prob. 48ECh. 3 - Prob. 49ECh. 3 - Prob. 50ECh. 3 - Prob. 51ECh. 3 - Prob. 52ECh. 3 - Prob. 53E
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Similar questions
- Solve questions by Course Name Ordinary Differential Equationsarrow_forwardDetermine whether it's true or false and the reasoning is neededarrow_forward1. (20 pts) Determine whether the following statements are true (T) or false (F)? (A reasoning is required.) (1) Let V be the set of all ordered pairs of real numbers. Consider the following addition and scalar multiplication operations on u = u= (u1, u2) and v = (v1, v2): u + v = (U₁ + V₁, U₂ + v₂), ku = (ku₁, u₂). Is V a vector space under the above operations? U2 (2) The set Mmxn of all m×n matrices with the usual operations of addition and scalar multiplication is a vector space. α (3) The dimension of the vector space of all matrices A = [a b] in R2×2 with a+d=0 is 4. (4) The coordinate vector of p(x) = 2-x+x² in P3 relative to the basis S = {1, 1+x, x + x2} is [4 -2 1]. (5) If a 6×4 matrix A has a rank 3, then the dimension of N(A) is 3.arrow_forward
- 5. (20%) The linear transformation L: P3 → P2 defined by L(f(x)) = f'(x)+ f(0). (a) Find the representing matrix A of L with respect to the ordered basis {x2, x, 1} for P3, and the ordered basis {2,1 - x} for P2. (b) Find the coordinates of the f(x) = 2x² +2 in P3 with respect to the ordered basis {x2,-x, 1}, and find the coordinates of L(f(x)) with respect to the ordered basis {2,1-x}arrow_forwardFor the spinner below, assume that the pointer can never lie on a borderline. Find the following probabilities. (enter the probabilities as fractions)arrow_forwardQuestions 1. Identify and describe potential bias in the study. 2. Identify and describe the way in which the selected participants may or may not represent the population as a whole. 3. Identify and describe the possible problems with the end results since the majority will be from females rather than an even split. 4. Identify and describe the possible problems with identifying females as possibly more vulnerable based on the data collected. 5. Identify a possible null hypothesis and problems in how the study might address this null hypothesis. 6. Identify one possible method of improving the study design and describe how it would improve the validity of the conclusions. 7. Identify a second possible method of improving the study design and describe how it would improve the validity of the conclusions.arrow_forward
- The Course Name Real Analysis please Solve questions by Real Analysisarrow_forwardpart 3 of the question is: A power outage occurs 6 min after the ride started. Passengers must wait for their cage to be manually cranked into the lowest position in order to exit the ride. Sine function model: where h is the height of the last passenger above the ground measured in feet and t is the time of operation of the ride in minutes. What is the height of the last passenger at the moment of the power outage? Verify your answer by evaluating the sine function model. Will the last passenger to board the ride need to wait in order to exit the ride? Explain.arrow_forward2. The duration of the ride is 15 min. (a) How many times does the last passenger who boarded the ride make a complete loop on the Ferris wheel? (b) What is the position of that passenger when the ride ends?arrow_forward
- 3. A scientist recorded the movement of a pendulum for 10 s. The scientist began recording when the pendulum was at its resting position. The pendulum then moved right (positive displacement) and left (negative displacement) several times. The pendulum took 4 s to swing to the right and the left and then return to its resting position. The pendulum's furthest distance to either side was 6 in. Graph the function that represents the pendulum's displacement as a function of time. Answer: f(t) (a) Write an equation to represent the displacement of the pendulum as a function of time. (b) Graph the function. 10 9 8 7 6 5 4 3 2 1 0 t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 -1 -5. -6 -7 -8 -9 -10-arrow_forwardA power outage occurs 6 min after the ride started. Passengers must wait for their cage to be manually cranked into the lowest position in order to exit the ride. Sine function model: h = −82.5 cos (3πt) + 97.5 where h is the height of the last passenger above the ground measured in feet and t is the time of operation of the ride in minutes. (a) What is the height of the last passenger at the moment of the power outage? Verify your answer by evaluating the sine function model. (b) Will the last passenger to board the ride need to wait in order to exit the ride? Explain.arrow_forwardThe Colossus Ferris wheel debuted at the 1984 New Orleans World's Fair. The ride is 180 ft tall, and passengers board the ride at an initial height of 15 ft above the ground. The height above ground, h, of a passenger on the ride is a periodic function of time, t. The graph displays the height above ground of the last passenger to board over the course of the 15 min ride. Height of Passenger in Ferris Wheel 180 160 140- €120 Height, h (ft) 100 80 60 40 20 0 ך 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time of operation, t (min) Sine function model: h = −82.5 cos (3πt) + 97.5 where h is the height of the passenger above the ground measured in feet and t is the time of operation of the ride in minutes. What is the period of the sine function model? Interpret the period you found in the context of the operation of the Ferris wheel. Answer:arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Elements Of Modern Algebra
Algebra
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Cengage Learning,
Finite Math: Markov Chain Example - The Gambler's Ruin; Author: Brandon Foltz;https://www.youtube.com/watch?v=afIhgiHVnj0;License: Standard YouTube License, CC-BY
Introduction: MARKOV PROCESS And MARKOV CHAINS // Short Lecture // Linear Algebra; Author: AfterMath;https://www.youtube.com/watch?v=qK-PUTuUSpw;License: Standard Youtube License
Stochastic process and Markov Chain Model | Transition Probability Matrix (TPM); Author: Dr. Harish Garg;https://www.youtube.com/watch?v=sb4jo4P4ZLI;License: Standard YouTube License, CC-BY