Differential Equations and Linear Algebra (4th Edition)
4th Edition
ISBN: 9780321964670
Author: Stephen W. Goode, Scott A. Annin
Publisher: PEARSON
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Chapter 4.2, Problem 27P
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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 4 Solutions
Differential Equations and Linear Algebra (4th Edition)
Ch. 4.1 - True-False Review For items a-I, decide if the...Ch. 4.1 - Prob. 2TFRCh. 4.1 - For items a-I, decide if the given statement is...Ch. 4.1 - For items a-I, decide if the given statement is...Ch. 4.1 - For items a-I, decide if the given statement is...Ch. 4.1 - For items a-I, decide if the given statement is...Ch. 4.1 - Prob. 7TFRCh. 4.1 - Prob. 8TFRCh. 4.1 - For items a-I, decide if the given statement is...Ch. 4.1 - Prob. 10TFR
Ch. 4.1 - Prob. 11TFRCh. 4.1 - Prob. 12TFRCh. 4.1 - If x=(1,4) and y=(5,1), determine the vectors...Ch. 4.1 - If x=(3,1) and y=(1,2), determine the vectors...Ch. 4.1 - If x=(5,2,9) and y=(1,6,4), determine the additive...Ch. 4.1 - If x=(3,1,2,5) and y=(1,2,9,2), determine...Ch. 4.1 - If x=(1,2,3,4,5) and z=(1,0,4,1,2) and y is 5 such...Ch. 4.1 - Prob. 6PCh. 4.1 - If x=(2+i,3i) and y=(5,22i) in 2 find a vector z...Ch. 4.1 - If x=(5+i,0,12i,1+8i) and y=(3,i,i,3) in 4 find a...Ch. 4.1 - Verify the commutative law of addition of vectors...Ch. 4.1 - Prob. 10PCh. 4.1 - Prob. 11PCh. 4.1 - Prob. 12PCh. 4.1 - Show with example that if x in the first quadrant...Ch. 4.2 - For Questions a-j, decide if the given statement...Ch. 4.2 - True-False Review For items a-j, decide if the...Ch. 4.2 - For Questions a-j, decide if the given statement...Ch. 4.2 - For Questions a-j, decide if the given statement...Ch. 4.2 - For Questions a-j, decide if the given statement...Ch. 4.2 - For Questions a-j, decide if the given statement...Ch. 4.2 - For Questions a-j, decide if the given statement...Ch. 4.2 - PROBLEMS For Problems 1-14, determine whether the...Ch. 4.2 - PROBLEMS For Problems 1-14, determine whether the...Ch. 4.2 - PROBLEMS For Problems 1-14, determine whether the...Ch. 4.2 - PROBLEMS For Problems 1-14, determine whether the...Ch. 4.2 - Problems For Problems 1-14, determine whether the...Ch. 4.2 - PROBLEMS For Problems 1-14, determine whether the...Ch. 4.2 - PROBLEMS For Problems 1-14, determine whether the...Ch. 4.2 - PROBLEMS For Problems 1-14, determine whether the...Ch. 4.2 - PROBLEMS For Problems 1-14, determine whether the...Ch. 4.2 - PROBLEMS For Problems 1-14, determine whether the...Ch. 4.2 - PROBLEMS For Problems 1-14, determine whether the...Ch. 4.2 - PROBLEMS For Problems 1-14, determine whether the...Ch. 4.2 - PROBLEMS For Problems 1-14, determine whether the...Ch. 4.2 - PROBLEMS For Problems 1-14, determine whether the...Ch. 4.2 - We have defined the set 2={(x,y):x,y}, together...Ch. 4.2 - Determine the zero vector in the vector space...Ch. 4.2 - Generalize the previous exercise to find the zero...Ch. 4.2 - Determine the zero vector in the vector space...Ch. 4.2 - Generalize the previous exercise to find the zero...Ch. 4.2 - On +, the set of positive real numbers, define the...Ch. 4.2 - On 2, define the operations of addition and scalar...Ch. 4.2 - On 2, define the operations of addition and scalar...Ch. 4.2 - Prob. 23PCh. 4.2 - On M2(), define the operation of addition by...Ch. 4.2 - For Problems 2627, verify that the given set of...Ch. 4.2 - For Problems 2627, verify that the given set of...Ch. 4.2 - Is 3 a real vector space? Explain.Ch. 4.2 - Prob. 29PCh. 4.2 - Prob. 30PCh. 4.2 - Prob. 31PCh. 4.2 - Prove that Pn() is a vector space.Ch. 4.3 - For the problems a-h, decide if the given...Ch. 4.3 - Problems Let S={x3:x=(r2s,3r+s,s),r,s} aShow that...Ch. 4.3 - Problems Let S={x2:x=(2k,3k),k} aShow that S is a...Ch. 4.3 - Problems For Problems 322, express S in set...Ch. 4.3 - Problems For Problems 322, express S in set...Ch. 4.3 - Problems For Problems 322, express S in set...Ch. 4.3 - Problems For Problems 322, express S in set...Ch. 4.3 - Problems For Problems 322, express S in set...Ch. 4.3 - Problems For Problems 322, express S in set...Ch. 4.3 - Problems For Problems 322, express S in set...Ch. 4.3 - Problems For Problems 322, express S in set...Ch. 4.3 - Problems For Problems 322, express S in set...Ch. 4.3 - Problems For Problems 322, express S in set...Ch. 4.3 - Problems For Problems 322, express S in set...Ch. 4.3 - Problems For Problems 322, express S in set...Ch. 4.3 - Problems For Problems 322, express S in set...Ch. 4.3 - Problems For Problems 322, express S in set...Ch. 4.3 - Problems For Problems 322, express S in set...Ch. 4.3 - Problems For Problems 322, express S in set...Ch. 4.3 - Problems For Problems 322, express S in set...Ch. 4.3 - Problems For Problems 322, express S in set...Ch. 4.3 - Problems For Problems 322, express S in set...Ch. 4.3 - Problems For Problems 322, express S in set...Ch. 4.3 - Problems For Problems 2329, determine the null...Ch. 4.3 - Problems For Problems 2329, determine the null...Ch. 4.3 - Problems For Problems 2329, determine the null...Ch. 4.3 - Problems For Problems 2329, determine the null...Ch. 4.3 - Problems For Problems 2329, determine the null...Ch. 4.3 - Problems For Problems 2329, determine the null...Ch. 4.3 - Problems For Problems 2329, determine the null...Ch. 4.3 - Problems Show that the set of all solutions to the...Ch. 4.3 - Problems Let S1 and S2 be subspaces of vector...Ch. 4.4 - Prob. 1TFRCh. 4.4 - For question (a)(l), decide if the given statement...Ch. 4.4 - Problems For Problems 1-4, determine whether the...Ch. 4.4 - Problems For Problems 1-4, determine whether the...Ch. 4.4 - Problems For Problems 1-4, determine whether the...Ch. 4.4 - Problems For Problems 1-4, determine whether the...Ch. 4.4 - Problems Recall that three vectors . in 3 are...Ch. 4.4 - Problems Recall that three vectors . in 3 are...Ch. 4.4 - Problems Recall that three vectors . in 3 are...Ch. 4.4 - Problems Recall that three vectors . in 3 are...Ch. 4.4 - Problems Show that the set of vectors...Ch. 4.4 - Problems Show that the set of vectors...Ch. 4.4 - Problems Show that v1=(2,1), v2=(3,2) span 2 and...Ch. 4.4 - Problems Show that v1=(1,5), v2=(6,3) span 2, and...Ch. 4.4 - Problems Show that v1=(1,3,2), v2=(1,0,1),...Ch. 4.4 - Problems Show that v1=(1,3,2), v2=(1,2,1),...Ch. 4.4 - Problems Show that v1=(1,1), v2=(1,2), v3=(1,4)...Ch. 4.4 - Problems Let S be the subspace of 3 consisting of...Ch. 4.4 - Problems Let S be the subspace of 4 consisting of...Ch. 4.4 - Problems Let S be the subspace of M2() consisting...Ch. 4.4 - Problems Let S be the subset of M2() consisting of...Ch. 4.4 - Problems Let S be the subspace of M2() consisting...Ch. 4.4 - Let S be the subspace of M3() consisting of all 33...Ch. 4.4 - Problems Let S be the subspace of M3() consisting...Ch. 4.4 - Problems Let S be the subspace of 3 consisting of...Ch. 4.4 - Problems Let S be the subspace of P3() consisting...Ch. 4.4 - Problems For Problems 2533, determine a spanning...Ch. 4.4 - Problems For Problems 2533, determine a spanning...Ch. 4.4 - Problems For Problems 2533, determine a spanning...Ch. 4.4 - Problems For Problems 2533, determine a spanning...Ch. 4.4 - Problems For Problems 2533, determine a spanning...Ch. 4.4 - Problems For Problems 2533, determine a spanning...Ch. 4.4 - Problems For Problems 2533, determine a spanning...Ch. 4.4 - Problems For Problems 2533, determine a spanning...Ch. 4.4 - Problems For Problems 2533, determine a spanning...Ch. 4.4 - For Problems 3435, determine span {v1,v2} for the...Ch. 4.4 - For Problems 3435, determine span {v1,v2} for the...Ch. 4.4 - Problems Let S be the subspace of 3 spanned by the...Ch. 4.4 - Problems For Problems 3739, determine whether the...Ch. 4.4 - Prob. 38PCh. 4.4 - Problems For Problems 3739, determine whether the...Ch. 4.4 - Problems If p1(x)=x4 and p2(x)=x2x+3, determine...Ch. 4.4 - Problems Consider the vectors A1=[1120],...Ch. 4.4 - Problems Consider the vectors A1=[1213], A2=[2111]...Ch. 4.4 - Prob. 43PCh. 4.4 - Prob. 44PCh. 4.4 - Prob. 45PCh. 4.4 - Prob. 46PCh. 4.4 - Prob. 47PCh. 4.4 - Prob. 48PCh. 4.4 - Prove that span{v1,v2,v3}=span{v1,v2} if and only...Ch. 4.5 - For problem 1-10, determine whether the given set...Ch. 4.5 - For problem 1-10, determine whether the given set...Ch. 4.5 - For problem 1-10, determine whether the given set...Ch. 4.5 - For problem 1-10, determine whether the given set...Ch. 4.5 - For problem 1-10, determine whether the given set...Ch. 4.5 - For problem 1-10, determine whether the given set...Ch. 4.5 - For problem 1-10, determine whether the given set...Ch. 4.5 - For problem 1-10, determine whether the given set...Ch. 4.5 - For problem 1-10, determine whether the given set...Ch. 4.5 - For problem 1-10, determine whether the given set...Ch. 4.5 - Let v1=(1,2,3), v2=(4,5,6,), v3=(7,8,9), determine...Ch. 4.5 - Determine all the values of constant k for which...Ch. 4.5 - For Problem 14-15, determine all the values of...Ch. 4.5 - For Problems 14-15, determine all the values of...Ch. 4.5 - For Problem 16-18, determine whether the given set...Ch. 4.5 - For Problem 16-18, determine whether the given set...Ch. 4.5 - For Problem 16-18, determine whether the given set...Ch. 4.5 - For problem 19-22, determine whether the given set...Ch. 4.5 - For problem 19-22, determine whether the given set...Ch. 4.5 - For problem 19-22, determine whether the given set...Ch. 4.5 - For problem 19-22, determine whether the given set...Ch. 4.5 - Show that the vectors p1(x)=a+bx and p2(x)=c+dx...Ch. 4.5 - If f1(x)=cos2x, f2(x)=sin2x, f3(x)=cos2x,...Ch. 4.5 - For Problems 25-31, determine a linearly...Ch. 4.5 - Prob. 26PCh. 4.5 - For Problems, 25-31, determine a linearly...Ch. 4.5 - For Problems, 25-31, determine a linearly...Ch. 4.5 - For Problems, 25-31, determine a linearly...Ch. 4.5 - For Problems, 25-31, determine a linearly...Ch. 4.5 - For Problems 32-36, use the Wronskian to show that...Ch. 4.5 - Prob. 35PCh. 4.5 - Prob. 36PCh. 4.5 - For Problems 37-39, show that the Wronskian of the...Ch. 4.5 - Prob. 38PCh. 4.5 - Prob. 39PCh. 4.5 - Prob. 41PCh. 4.5 - a. Show that {1,x,x2,x3} is linearly independent...Ch. 4.5 - Prob. 45PCh. 4.5 - Problems If v1andv2 are vectors in a vector space...Ch. 4.5 - Prove from Definition 4.5.4 that if {v1,v2,...,vn}...Ch. 4.5 - Prob. 49PCh. 4.5 - Problems Generalizing the previous exercise prove...Ch. 4.5 - Problems Prove Theorem 4.5.2. Theorem 4.5.2.Let...Ch. 4.5 - Problems Prove Proposition 4.5.8. Let V be a...Ch. 4.5 - Problems Prove that if {v1,v2,......,vk} spans a...Ch. 4.5 - Prob. 54PCh. 4.6 - For Questions a-k, decide if the given statement...Ch. 4.6 - For Problems 1-7, determine whether the given set...Ch. 4.6 - For Problems 1-7, determine whether the given set...Ch. 4.6 - For Problems 1-7, determine whether the given set...Ch. 4.6 - For Problems 1-7, determine whether the given set...Ch. 4.6 - For Problems 1-7, determine whether the given set...Ch. 4.6 - For Problems 1-7, determine whether the given set...Ch. 4.6 - For Problems 1-7, determine whether the given set...Ch. 4.6 - Determine all values of the constant k for which...Ch. 4.6 - For Problems 9-14, determine whether the given set...Ch. 4.6 - For Problems 9-14, determine whether the given set...Ch. 4.6 - For Problems 9-14, determine whether the given set...Ch. 4.6 - For Problems 9-14, determine whether the given set...Ch. 4.6 - For Problems 9-14, determine whether the given set...Ch. 4.6 - For Problems 9-14, determine whether the given set...Ch. 4.6 - For Problems 15-18, determine whether the given...Ch. 4.6 - For Problems 15-18, determine whether the given...Ch. 4.6 - For Problems 15-18, determine whether the given...Ch. 4.6 - For Problems 15-18, determine whether the given...Ch. 4.6 - For Problems 19-23, find the dimension of the null...Ch. 4.6 - For Problems 19-23, find the dimension of the null...Ch. 4.6 - For Problems 19-23, find the dimension of the null...Ch. 4.6 - For Problems 19-23, find the dimension of the null...Ch. 4.6 - For Problems 19-23, find the dimension of the null...Ch. 4.6 - Let S be the subspace of 3 that consists of all...Ch. 4.6 - Let S be the subspace of 3 consisting of all...Ch. 4.6 - Determine a basis S for P3(), and hence, prove...Ch. 4.6 - Determine a basis S for P3() whose elements all...Ch. 4.6 - Let S be the subspace of M2() consisting of all 22...Ch. 4.6 - Let S be the subspace of M2() consisting of all 22...Ch. 4.6 - Let S be the subspace of 3 spanned by the vectors...Ch. 4.6 - Let S be the vectors space consisting of the set...Ch. 4.6 - Determine a basis for the subspace of M2() spanned...Ch. 4.6 - Let v1=(1,1) and v2=(1,1). a Show that {v1,v2}...Ch. 4.6 - Prob. 34PCh. 4.6 - Let v1=(0,6,3), v2=(3,0,3), and v3=(6,3,0). Show...Ch. 4.6 - Prob. 36PCh. 4.6 - Let p1(x)=1+x, p2(x)=x+x2, and p3(x)=1+2x2. Show...Ch. 4.6 - Prob. 38PCh. 4.6 - Prob. 39PCh. 4.6 - Prob. 40PCh. 4.6 - Prob. 43PCh. 4.6 - Prob. 44PCh. 4.6 - For Problems 45-47, a subspace S of a vector space...Ch. 4.6 - For Problems 45-47, a subspace S of a vector space...Ch. 4.6 - For problems 45-47, a subspace S of a vector space...Ch. 4.6 - For Problems 48-50, determine a basis for the...Ch. 4.6 - For Problems 48-50, determine a basis for the...Ch. 4.6 - For Problems 48-50, determine a basis for the...Ch. 4.6 - Prob. 51PCh. 4.6 - Prob. 52PCh. 4.6 - Prob. 53PCh. 4.6 - Prob. 54PCh. 4.7 - True-False Review For Questions a h, decide if...Ch. 4.7 - Problems For Problems 1-14, determine the...Ch. 4.7 - PROBLEMS For Problems 1-14, determine the...Ch. 4.7 - PROBLEMS For Problems 1-14, determine the...Ch. 4.7 - Prob. 4PCh. 4.7 - PROBLEMS For Problems 1-14, determine the...Ch. 4.7 - PROBLEMS For Problems 1-14, determine the...Ch. 4.7 - PROBLEMS For Problems 1-14, determine the...Ch. 4.7 - PROBLEMS For Problems 1-14, determine the...Ch. 4.7 - PROBLEMS For Problems 1-14, determine the...Ch. 4.7 - PROBLEMS For Problems 1-14, determine the...Ch. 4.7 - PROBLEMS For Problems 1-14, determine the...Ch. 4.7 - PROBLEMS For Problems 1-14, determine the...Ch. 4.7 - PROBLEMS For Problems 1-14, determine the...Ch. 4.7 - Prob. 14PCh. 4.7 - PROBLEMS
Let v1=(0,6,3), v2=(3,0,3), and...Ch. 4.7 - PROBLEMS
Let p1(x)=1+x, p2(x)=x+x2, and...Ch. 4.7 - PROBLEMS For Problems 17-26, find the...Ch. 4.7 - PROBLEMS For Problems 17-26, find the...Ch. 4.7 - PROBLEMS
For Problems 17-26, find the...Ch. 4.7 - PROBLEMS
For Problems 17-26, find the...Ch. 4.7 - PROBLEMS For Problems 17-26, find the...Ch. 4.7 - PROBLEMS
For Problems 17-26, find the...Ch. 4.7 - PROBLEMS
For Problems 17-26, find the...Ch. 4.7 - PROBLEMS
For Problems 17-26, find the...Ch. 4.7 - PROBLEMS
For Problems 17-26, find the...Ch. 4.7 - PROBLEMS
For Problems 17-26, find the...Ch. 4.7 - PROBLEMS
For Problems 27-32, find the...Ch. 4.7 - PROBLEMS
For Problems 27-32, find the...Ch. 4.7 - Prob. 29PCh. 4.7 - PROBLEMS
For Problems 27-32, find the...Ch. 4.7 - PROBLEMS For Problems 27-32, find the...Ch. 4.7 - Prob. 32PCh. 4.7 - PROBLEMS For Problems 33-37, verify Equation...Ch. 4.7 - Prob. 34PCh. 4.7 - Prob. 35PCh. 4.7 - Prob. 36PCh. 4.7 - Prob. 37PCh. 4.7 - Prob. 38PCh. 4.7 - PROBLEMS Prove that if every vector v in a vector...Ch. 4.7 - Show that if B is a basis for a finite-dimensional...Ch. 4.8 - Prob. 1TFRCh. 4.8 - For Problem 12, a determine a basis for...Ch. 4.8 - For Problem 12, a determine a basis for...Ch. 4.8 - For Problem 39, a find n such that rowspace(A) is...Ch. 4.8 - For Problem 39, a find n such that rowspace(A) is...Ch. 4.8 - For Problem 39, a find n such that rowspace(A) is...Ch. 4.8 - For Problem 39, a find n such that rowspace(A) is...Ch. 4.8 - For Problem 39, a find n such that rowspace(A) is...Ch. 4.8 - For Problem 39, a find n such that rowspace(A) is...Ch. 4.8 - For Problem 39, a find n such that rowspace(A) is...Ch. 4.8 - For Problem 1013, determine a basis for the...Ch. 4.8 - For Problem 1013, determine a basis for the...Ch. 4.8 - For Problem 1013, determine a basis for the...Ch. 4.8 - For Problem 1013, determine a basis for the...Ch. 4.8 - Let A=[124511213713]. a Find a basis for...Ch. 4.8 - Prob. 15PCh. 4.8 - Give examples to show how each type of elementary...Ch. 4.8 - Let A be an mn matrix with...Ch. 4.8 - Let A be an nn matrix with...Ch. 4.9 - Prob. 1TFRCh. 4.9 - For problem 1-5, determine the null space of A and...Ch. 4.9 - Prob. 2PCh. 4.9 - For problem 1-5, determine the null space of A and...Ch. 4.9 - For problem 1-5, determine the null space of A and...Ch. 4.9 - For problem 1-5, determine the null space of A and...Ch. 4.9 - For problem 6-9, determine the nullity of A by...Ch. 4.9 - For problem 6-9, determine the nullity of A by...Ch. 4.9 - For problem 6-9, determine the nullity of A by...Ch. 4.9 - For problem 6-9, determine the nullity of A by...Ch. 4.9 - For problem 10-13, determine the solution set to...Ch. 4.9 - For problem 10-13, determine the solution set to...Ch. 4.9 - For problem 10-13, determine the solution set to...Ch. 4.9 - Prob. 13PCh. 4.9 - Problems Show that a 37 matrix A with nullity(A)=4...Ch. 4.9 - Problems Prove that a 64 matrix A with...Ch. 4.9 - Problems Prove that if rowspace(A)=nullspace(A),...Ch. 4.9 - Prob. 17PCh. 4.9 - Problems Show that 38 matrix A must have...Ch. 4.9 - Prob. 19PCh. 4.11 - Additional Problems For problem 1-2, let r and s...Ch. 4.11 - Additional Problems For problem 1-2, let r and s...Ch. 4.11 - Additional Problems For problem 3-12, determine...Ch. 4.11 - For Problems 3-12, determine whether the given set...Ch. 4.11 - Prob. 8APCh. 4.11 - Prob. 9APCh. 4.11 - Prob. 10APCh. 4.11 - Prob. 23APCh. 4.11 - Prob. 24APCh. 4.11 - Prob. 25APCh. 4.11 - Prob. 26APCh. 4.11 - Prob. 27APCh. 4.11 - Prob. 28APCh. 4.11 - Prob. 29APCh. 4.11 - Prob. 30APCh. 4.11 - Prob. 31APCh. 4.11 - Additional Problems Prove that if {v1,v2,v3} is...Ch. 4.11 - Let A be an mn matrix. Show that the columns of A...Ch. 4.11 - Let (V,+v,v) and (W,+w,w) be vector spaces and...Ch. 4.11 - Additional Problem Show that a basis for P3() need...Ch. 4.11 - Prob. 38APCh. 4.11 - Prob. 39APCh. 4.11 - Prob. 40APCh. 4.11 - Prob. 41APCh. 4.11 - Prob. 42APCh. 4.11 - Additional Problems For Problem 40-43, find a...Ch. 4.11 - Prob. 44AP
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- 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
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