INTRODUCTION TO MATRICES Answer the following questions: Given the Matrix A below. 12 15 10 5 3 21 16 14 5 11 A= 17 35 45 12 10 6 7 8 17 1 2 3 4 5 1. What is the size of the matrix? 2. Name the elements: a. aas b. a c. au 3. What is the transpose of matrix, A?

Q: Find curl(7z i + 8x j+ 5y k). curl (7z i + &x j+ 5y k) = ( i )i + (i )j + ( )k

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Q: Find the exact area under the curve between the indicated values of x. y = between x = 1 and x = 4…

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Q: Using appropriate substitution 9x2 – 4 dx X is equal to

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Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). 3 ||r(t)||³ r(t) = 3 cos(2t)i+ 3 sin(2t)j + tk…

A: The given formula is: κt=r't×r''tr't3 And rt=3cos2ti+3sin2tj+tk   As we know that; The Chain rule;…

Q: each of the following functions determine dr

A: Given query is to find the derivative of the expression.

Q: Use the formula «(t) = F () ×F (51 to find k(t). ||r(t)||* r(t) = t²i+t°j K(t) = %3D

A: We have t find κ(t) for the given vector r(t) = t2i + t5j The given formula is κ(t) =…

Q: The rate of growth dP/dt of a population of bacteria is proportional to the square root of t, where…

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Q: Find dy for dx 6) In y = In xe*

A: Topic:- derivatives

Q: [y sxy dy is equal to -y cony - J cony A (B у сoly - coty dy Scory dy C у coly + -y coty + J coty D…

A: Solution is given below..

Q: Find the rate of change of w with respect to t at i = 1 by using the chain rule. You can check your…

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Q: Find the domain of the vector-valued function. (Enter your answer using interval notation.) r(t) =…

A: The domain of a vector valued  function r(t) = f(t) i + g(t) j + h(t) k  is the set of all possible…

Q: Describe the graph of the equation. r = (5 – 21) i + 71j O It is a line in 2-space through the point…

A: This is a problem related to vector. Based on the general formula and concept we will answer the…

Q: Let 7(t) = Find a parametric equation of the line tangent to 7(t) at the point (7, 5, 1.386) x(t) =…

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Q: Evaluate the integral / (2x + 12y)dx + (24x – y)dy along the parabolic arc y = x² from (0,0) to…

A: For the arc y = x2 and the range of x from 0 to 1. So, dy = 2x dx. Now,…

Q: Describe the graph of the equation. r = 10 sin 6t í – 10 cos 6t j

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Q: The following table gives the sunrise and sunset times for various dates of the year in Lincroft,…

A: Note: There are multiple questions. Few questions has multiple subparts.No specific question has…

Q: Find curl (6z i + 7x j+ 9y k). curl(6z i + 7x j + 9y k) = ( i )i + ( i )j + ( )k

A: Explanation of the answer is as follows

Q: 3/2 dy The order and degree of the differential equation (). - 4 = 0 dx - dx2

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Q: dx 2. Find the integral x²(x+1) In (***) + C b. In (***) - +C 1+ C c. In (***) ++ c d. None of the…

A: Here we have to find the integral

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: Follow the procedure given below.

Q: Which type of discontinuity does the function exhibit at x = 3? -x2 + 1, -1 sx <0 2х, f(x) = { -4,…

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Q: (a) If f(x)dx = 11 and F(9) = 17, find F(5). F(5) eTextbook and Media 300 (b) If f(x)dx = 0, what is…

A: We have to find the value and the relationship.

Q: Determine the nature of convergence of the following improper integrals +00 1 X A = dx 1+x4 x 2 dx…

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Q: Use the given conditions to write an equation for the line in point-slope form and in…

A: we have the parallel line equation y=-5x+4 comparing with y=mx+c m=-5 is the slope point slope form…

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 8 1 lim t→+o\ 9t2 + 10' 3t (?, ?)

A: We have to find the limit

Q: 5xdx 3. Find the integral (x-1)3 -5 5 а. 2(x-1)2 + C x-1 -5 b. 2(x-1)2 + C x-1 c. In (7DE) – in () +…

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Q: dx tan x +sin x+1

A: Solution of the problem as follows

Q: Which integral corresponds to the area of the shaded region between the curves y = -x? + 3x and y =…

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Q: xdx 1. Find the integral (x+2)3 a. -l +c b. l x+1 а. L(x+2)²! x+1 + C L(x+2)2] x+1 + C |(x+2)3_ с.…

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Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(1) = i – 26j + %3D (a) r(t) 3ti- 2j + 2 k (b)…

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Q: Find the general solution 5. (D² – 1)y = 0

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Q: Verify Green's Theorem by evaluating both integrals an_ am | v² dx + x² dy = dA ây for the given…

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Q: A publisher for a promising new novel figures fixed costs (overhead, advances, promotion, copy…

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Q: Find the general solution 1. (D² – D – 2)y = 0 2. (D² + 3D)y = 0 3. (D2 – 5D) + 4y = 0 4. (D² – 9)y…

A: 1. D2-D-2y=02. D2+3Dy=03. D2-5D+4y=0 Note:    Multiple sub parts are given, we are answer only three…

Q: 1- cos4x lim→0 5x e N – 1 O 1

A: This is 0/0 form so use L hospital rule and Solve.

Q: Let F(t) = < 5t + 5, t - 2t, 2 In < 5t' + 5,f – t, a. Determine the coordinates of the point on the…

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Q: I. Find the derivatives of the following 1. f(x) = 2x2 + 3x - 7 %3D

A: We know that ddxxn = nxn-1               and                    ddxpxn = p ddxxn = p× nxn-1 = pnxn-1

Q: nd and of the following equation then simplify whenever possible. dx dx2 x = 3em y = 2mem

A: Given query is to find derivative of the expression.

Q: A box with a square base and open top must have a volume of 415292 cm. We wish to find the…

A: topic - application of derivatives

Q: Evaluate the integral (12x + 12y)dx + (9x - y)dy along the parabolic arc y = x from (0,0) to (1, 1).…

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Q: Determine whether the series converges or diverges. Make sure to clearly state the test that you're…

A: Given,  ∑n=0∞2xnn!

Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

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Q: y" + 9y = 9 sec² 3t, 0<t < T/6

A: To solve the following differential equation

Q: Evaluate the integral. 2 (3u - 5)(u + 2) du -1

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Q: A stone is thrown vertically upward from the ground with an initial velocity of 128 ft/sec. How long…

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Q: y" - 2у/ + у 3 tet + 4, y(0) — 1, у (0) — 1 || %3D

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Q: 2. Determine the area of the region bounded by the curve y = x3 – x2 – 2x, and а. the x-axis

A: This is a problem related to finding out are using integration. Please follow the procedure given…

Q: ||r(t) × r"(t)|| Use the formula k(t) to find k(t). r(t) = t'i+ t°j K(t)

A: The given formula is; κt=r't×r''tr't3 And rt=t2i+t9j

Q: **. . AY .. ... Use the shell method to write and evaluate the definite integral that represents the…

A: A detailed solution is given below

Q: (x² + 1)3 y = (x3 – 1)

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