A stone is dropped from the edge of a roof, and hits the ground with a velocity of -175 feet per second. How high (in feet) is the roof? ft Note: the acceleration of an object due to earth's gravity is 32 sec2

Q: Find the general solution: dy + ycotx = 3eCosx dx y = 3cscx(ecosx) - ccosx b. y = -3cscx(ecosx)+…

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Q: Evaluate the following rational function with the following (a, b, c, and d). 1.…

A: Please see the answer below.

Q: Find the equation of the tangent to the function f(x) = -4 sin’x at the point where x = (use EXACT…

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A: A line will lie in a plane if any two points on the line also lies in that plane. As we know between…

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Q: Approximate / 1+r² dr using four rectangles and the left endpoint method (L4).

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Q: Find the interval of convergence. 00 (x + 6)" (n In(n))2 n=2 (Use symbolic notation and fractions…

A: limn→∞ an+1an <1limn→∞ (x+6)n+1(n ln n)2(n+1)ln(n+1)2 (x+6)n<1limn→∞ (x+6)n ln nn+1…

Q: Calculus Question

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Q: Evaluate the integral if it converges and enter the exact value. If the integral diverges, indicate…

A: Given: I=∫08dxx3   As we know that; The Power rule: ∫xndx=xn+1n+1+C  ; n≠-1

Q: (k +3)! kk Consider the series ak k=1 a) What is ak+1? ak-1= ak+12 b) What is ak ak-1/a = ak+1 c)…

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Q: Find the general solution of the differential equation y" + 3y' – 18y = -66t + 36t?. NOTE: Use t as…

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Q: Describe how to use the second derivative test to classify critical numbers. You must state 3 steps.

A: Describe how to use the second derivative test to classify critical numbers. You must state 3 steps.

Q: 6)Let f ( x ) = x4 + x3 - 3x2 + 1 a)Find all the hypercritical values. b)Determine the intervals…

A: The given function is f(x) = x4+x3-3x2+1 ............................ (1) We have to a)Find all the…

Q: Derive the derivative function for secx and express your answer in product form.

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Q: Using an appropriate lineař appratimation, Feel free to leave fractions in answer.

A: The given approximation 35

Q: 12. f (x) = xe -x

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Q: Consider the function f(t) = 3 sec?(t) – 4t². Let F(t) be the antiderivative of f(t) with F(0) = 0.…

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Q: In each part, use a scalar triple product to determine whether the vectors lie in the same plane.…

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Q: Find the absolute maximum and absolute minimum of f (x) = 2x^3 −6x + 1 on [0, 3].

A: Find first derivative and equate to zero. And find interval at which function is increasing or…

Q: Use THIS standard form for a tangent plane: - fz (x1, yı) * (x – x1) – fy (x1, yı) * (y – y1) + (z –…

A: Given

Q: If f (z, y) — е"у, then fr (1, In (3)) —??? (а) е (b) e³ (с) 1/3 (а) 3 (е) 3ln (3)

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Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: Explanation of the answer is as follows

Q: Choose the correct speed and direction of a plane with a velocity of (5,-12). 13,113° 17,293°…

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Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does…

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Q: 8)Suppose the total cost of a certain product is C(x) = 0.001 x2+ 5x + 300. The product can be sold…

A: Find your answer below

Q: ind a function F(x) satisfying the given conditions. . F'(x) = 2x ; F(1) = 2 2. F'(x) = 4x +1; F(2)…

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

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Q: Find the area of the curve r²=16cos(theta)

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Q: Wheat is poured through a chute at the rate of 10 ft/min and falls in a canonical pile whose bottom…

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Q: SOLVE THE FOLLOWING INDETERMINATE FORMS x' -x? - 8x +12 Lim 1. X→2 3x' -10x² +4x + 8

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Q: Solve the ff first order DE using integration method, by substitution, or bernoulli's equation. show…

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Q: x² – 4x – 5 lim z-5 x2 – 25 lim (3x² – ) x-2 5x + 2

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Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Answer the following True or False. dt sec 't |', \_ 1 = 27. |t|VE2 - 1 O True O False

A: sec-11=0 and sec-1(-1)=π

Q: Given: -8 17 cose = 15/17 -8/17 8/17 -15/17

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Q: Consider the one-parameter family of linear systems depending on the parameter a. dY This family…

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Q: 3. S

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Learning Task 1: Directions: Solve for y in terms of x (isolate y on one side of the equation and…

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Q: 4. Given f(x) = x +-: a) Find all asymptotes and state their equations. b) Find all local max/min…

A: Find your answer below

Q: 34. f (г) — 1 ; с34

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Q: Find the exact length of the cur x =t sin t y =t cos t for 0 <t < 1.

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Q: Find parametric equations for the line whose vector equation is given (а) (г, у) — (6, —5) + t(1,…

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Q: Find the x values of all the horizontal tangents to the function f(x) = cos.x + /3 sinx on the…

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Q: Direction: Find the first derivative of the following functions: 1. y = sin (2x) - cos (2x) 2. y =…

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Q: Consider the function f(r) 10r 10 + 9x° 2x2 6. Enter an antiderivative of f(x). Do not enter +c as…

A: Solve for the antiderivative

Q: Given f''(x) = 4x – 5 and f'(– 3) = 3 and f( – 3) = 6. Find f'(x) = and find f(3)

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Q: coordinates

A: We have to choose the correct option according to the given information

Q: Find the volume of the parallelepiped with the given vertices . (0, 0, 0), (0, 4, 0), (-3, о, 0),…

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