A bush fire is burning a circular area whose radius is increasing at a rate of 3 ft/min. How fast is the area of fire increasing in ft²/min when its radius is 25 ft? O 150m O 225r O 625π O 75m

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A: We have to find area of given region.

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Q: II. Anti differentiate the following. D. (ANTIDERIVATIVES by Substitutions) 1. Evaluate [(x + 4)5…

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A: Here we have to find the slope of the tangent line.

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A: Here we have to find the limits and then state whether it diverges or not.

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A: Here we have to check whether the statement is true or false.

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Q: 4. Use the bisection method to approximate the root of f(x) = 2x² [0, 1]. Let € = 0.1 be the margin…

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Q: Use the Comparison Test to determine whether the series converges. Σ k=1 1 8 5k° +6

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Q: x(t) = L−1 (5s² — 22s +24) s(s² - 4s+8)

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Q: Write the first five terms of the geometric sequence. a 1 =  -5; r = -3

A: We can find the first five terms as below.

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A: Since you have posted multipart questions. As per guidelines we"ll solve only first three parts.. If…

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Q: At what points is the following function continuous? 5 cos 0 0+1 y = OA. The function is continuous…

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Q: he method of variation of parameters to determin on of the given differential equation. y"" — y'′ =…

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Q: Using Taylor Series, what is the value of yo(4) if y'=x+y² for y(0)=1?

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Q: e the figure to answer the questions. point A point B B point C point D point E y C D (a) At each…

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Q: Integrate ze da Select one: O A. ex (2x-1) + C OB. e (x-2) + C O C. e* (x-1) + C O D. ex (x-3) + C

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A: We are asked to find which is represented for shaded area between the curves

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A: Let's find minimum cost and it's dimensions.

Q: Consider the following function. f(x) = (x - 3)ex (a) Find the critical numbers of f. (Enter your…

A: We have to find the critical points, monotone intervals and relative extremum.

Q: Integrate O √25 - 2² 2 ▶ X 25 - x² O. + C V6-ਏ 25 - x² 2 dx. +C 25 - x² + C 25 - x² + C

A: topic- indefinite integral ∫xn dx=xn+1n+1+C

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Q: Question 35 If z = x arctan 0 - 4 OFF O undefined ◄ Previous (²).find əz əx at x = 0, y = 1, z = 1.

A: To find the partial derivative of z with respect to x.

Q: Choose the normal vector of the tangent plane to the surface defined by at the point (-4, 2, e88). O…

A: Given problem:- Find the normal vector of the tangent plane to the surface defined by…

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Q: Sy²sin (2y) dy

A: Integration by parts.

Q: Find the limit of the following sequence or determine that the sequence diverges. {tan - 1 (₁ -1…

A: Here we have to find the limit of a sequence.

Q: C What is f" (x) of f(x) = x Arc sin(x) + √1 − x²? Arc sin(x) 2 √1-2² √1-7² ◄ Previous + Arc sin(x)

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Q: Which of the following are the tangent lines perpendicular to y = x, to the curve x + y² = 8? Oy=x+8…

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Q: Work Problems ( your works 1) Let F(t)=(4t — t²)i+t² j+sin(5t — 10) k - - - You need to show all a)…

A: Given: Ft=4t-t2 i+t2 j+ sin5t-10 k

Q: Solve the following triangle. B = 70°, C = 50°, b = 8 O A (Simplify your answer.) a≈ (Type an…

A: We will use law of sines to solve this question.

Q: The admission fee at an amusement park is $1.50 people entered the park, and the admission fees…

A: Given: The admission fee at an amusement prk is $1.50 for children and $4 for adults.On centrain…