The length of a rectangle is given by 8t + 7 and its height is √t, where t is time in seconds and the dimensions are in centimeters. Find the rate of change of the area with respect to time

Q: Factor. 7c²-7t² 7c²-7²2² = (Factor completely.)

A: Given expression 7c2 - 7t2

Q: Find the extrema of the following function on the given interval, if they are any, and determine the…

A: Follow the procedure given below.

Q: Q3/Evaluate: ff(x + y) dy dx for the region bounded by the x = 0, x = 2, y=x and y=x+2

A: Given

Q: A) e-2 Β) e2 Σε e=2n =? 71=0 C) CADEMI Ε)

A:

Q: Find the cumulative density function for the given probability density functio k(x) = 1.4 e 1.4x,…

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Q: xe5x dx (5x-1) i 51 e³z B.5 (5x-1)+c C. 5x+ E

A: We will solve the problem.

Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y = 2rsine

A: Here, the total derivative rule used is: z=f(x,y)=x2y2 & x=2rcos θ , y=2rsin θ

Q: Problems: Solve the following differential equations: 3- (2x+y)dx+(x-2y)dy=0

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: 5 4(x²+y²) Qu/ If w = f(u, v) = cos uv, u = xyz , v = aw Prove that = 0 at the this point (x,y,z) =…

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Q: In the Figure 1, if Q= 40 N, P = 50 N, and B = 145°, then R is equal to (in N): Figure 1: C R A Q B…

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Q: B/ Find the value of lim,-.. 1. ²/2 O 1 O 2 7x²+x-100 2x²-5x N NIN

A: To evaluate: limx→∞7x2+x-1002x2-5x

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A:

Q: a2e-a dir?

A: Given problem:- ∫ x2e-xdx

Q: 3 use the definition of latlace transforms to find £{+²H (E-5) } JINO

A:

Q: Use the Laplace transform to solve the given initial-value problem. y" + 4y = sin tu(t - 2π), y(0) =…

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Q: We have that 10 177 g (17x + 7) dx O a) 4 O b) O c) 17 Od) -4 24 17 g (t) dt = 4 I so what's the…

A:

Q: 1 50° || 5 1191 10% what is

A: Here we have to find the value a→·b→=?

Q: Verify that the indicated function y = y(x) is an explicit solution of the given first-order…

A:

Q: Use the graph of f to find the largest open interval on which f is increasing, and the largest open…

A: Given,

Q: Confirm that the integral test is applicable and use it to determine whether the series converges.…

A: a)  ∑k=1∞17k+2b) ∑k=1∞11+16k2

Q: Do not use calculators. Approximated decimals are not accepted. k=3 Let j=8 Evaluate and Simplify…

A:

Q: 3. Given u =(3, 10,-8) and v = (-1,6,4), a) find 3v--u

A:

Q: 5) (6: -1). Find f'(x) if f(x) = (4x² + 5) ( 6x - f'(x) =

A:

Q: Find the plane determined L1: x=-1+t 12: x=1-4s by the intersecting lines: y=2+t y=1+2s 2=1-1-3-1-00…

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Q: A load W = 400 lb. is attached to the beam. The tension force, T., in the cable is given by: T=…

A: MATLAB code: % Defining the constants W = 500; % (in lb) L = 120; % (in inch) h = 50; % (in inch) 1…

Q: Evaluate /1-(y-1)² by first changing it to polar coordinates. 219 dx dy

A:

Q: Find the directions of maximum and minimum change of fat the given point, and the values of the…

A: Given:      fx,y=9y2e6x The gradient of a function z=Fx,y is denoted by ∇Fx,y The direction of the…

Q: ³√x²e²²\ Which of the following is the most appropriate technique to use in evaluating O Integration…

A: The given integral is x2e-x.

Q: Find when y = cos(sin 2x). ay dx dy dx

A:

Q: 2. Line I has the equation y = 3x - 4. Line m has the equation y = 3x + 2. a. Graph each line on the…

A: Given line equation is in form of :               y=mx+c              where m= slope of line…

Q: (x + 2) sin ydx + x cos ydy = 0

A: Solve by variable separable

Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

A: Topic = Derivative

Q: Q3. Use the integral test to determine whether the series, n=1 divergent. 1 (n+1)√n+1 is convergent…

A:

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A:

Q: Derive the Maclaurin and Taylor Series of the function below:

A:

Q: Find the derivative of f(x) = 2x3 + 12x² +18x + 9. f'(x) =

A: To Find : Derivative of f(x)=2x3+12x2+18x+9     Note that : Derivative of xn is nxn-1

Q: 3) Find equations for the lines: h the no e. The line through (1,1,1) parallel to the z-axis. f. The…

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Q: - 6x + 2 on the domain [-7,2]. Find the absolute extrema if they exist, as well as all values of x…

A:

Q: A number x is selected at random from the interval [4,20]. The probability density function for x is…

A:

Q: Q4/ A/If x² (y - 4z) - y²(2x + 3z) + z²(3x - 4y) = xyz Find Zx

A:

Q: Use Simpson's Rule with n = 10 to estimate the arc length of the curve. (Round your answer to six…

A:

Q: et J ((et + 4)²-9)³/2 9)³3/2 dt.

A: See the details solution in below

Q: Find the extrema of the following function on the given interval, if they are any, and determine the…

A: Since you have asked multiple questions,as per our guidelines we are supposed to answer only one…

Q: 2. Which of the following is correct in solving [2.xv 2x√√/2+x dx? (a) Substitution technique can be…

A:

Q: Example: If w = f(x,y), find d²w dr² x = et, and y = 2t - 1

A: Here, w=f(x,y), x=et, y=2t-1

Q: 7. Determine the area bounded by y = x² - 6x + 10, x = 1, x = 5 and the x-axis.

A: Above question is solved.

Q: (c) Find the Inverse Laplace transform of the function. 1 s² + s-5 H (s) = (s−2)² +3 s (s² + 2s + 5)…

A: Given H(s)=1(s-2)2+3+s2+s-5s(s2+2s+5)To find Inverse Laplace Transform.

Q: 5. lim, A.7 Oi O о O. +D T 7x²+x-100 2x²-5x B 712 NIT D.2

A:

Q: Write the equation for a cosecant function satisfying the given conditions. period: 5x; range: (-∞,…

A:

Q: -πl-π" ㅠㅠ Using the technique of substitution with u = • ITT -T, the terms of u as 1 -1 -1- du (a)…

A: This question can be solved using the concept of integration by substitution.