An equation of a parabola is given  (x-4)^2= 8(y+3) Find the vertex, focus, and directrix of the parabola.  Sketch a graph showing the parabola and its directrix

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A: Topic - Definite integral we are given, ∫116sinx4x34dxFormulas usedddxxn=nxn-1∫sin(x)dx=-cos(x)+C

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A: Use the definition of the derivative of a function.

Q: - Find dy dr (4x² + 2 cos(x)) dy d.x 7 Type sin(x) for sin(x), cos(x) for cos(x), Use x^2 to square…

A: The given function is; y=(4x2+cos(x))7

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A: f(x)=1(x+2)2for f(3) put x=3 in f(x)

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A: Need to find out the solution of the given differential equation.

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A: A television camera is positioned 4000 ft from the base of a rocket launching pad. The angle of…

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A: Solve the following

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A: dlnxdx=1xdcosxdx=-sinxdtanxdx=sec2xsinx cosx=tanx

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A: The answer is given below:

Q: Q. A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 7…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Solve the initial-value problem Select one: O a. y = -cos x+8 O b. y = -cos x + 5) O c. y = -cos x +…

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A: Given :164-x2=1622-x2

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Q: 1. For each problem, find f(x): A. f"(x)=20x³-12x² +6x

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A: Since two triangle are  symmetrical h36=180-160180h36=20180h36=19h=369h=4

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A: Topic:- application of calculus

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A: Topic:- application of algebra

Q: The half-life of cesium-137 is 30 years. Suppose we have a 160 mg sample. (a) Find the mass (in mg)…

A: Topic - Exponential function We are given The half life of cesium-137 = 30 years initial mass of a…

Q: A large snowball is melting so that its radius is decreasing at the rate of 4 inches per hour. How…

A: given radius decreasing rate is 4 inches per hour radius is 5 inches v=43πr3drndr=nrn-1

Q: Question 10 Solve the differential equation. y' + y tan x = cos X, -π/2<x</2 (A) y=xsin x + c sin x,…

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Q: Find the solution to the differential equations sec3xdy = csc2ydx y(π) = π/4

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Q: Let f(x)=√4x² + 4x + 6 f'(x) = f'(5) =

A: To find f'(x)

Q: (a) Find the average rate of change of the area of a circle with respect to its radius r as r…

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Q: (1 point) Find the curvature (t) of the curve r(t) = (4 sin t)i + (4 sin t)j + (5 cost) k

A: we will find the required solution.

Q: Let (in radians) be an acute angle in a right triangle and let x and y, respectively, be the lengths…

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Q: If f(x) = sin² x, find f'(x) f'(x) = Find f'(2) f'(2) =

A: d dx(sinx)=cosxddx(cosx)=-sinxsin2x=2sinxcosx

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A: According to question,Given Functionfx = x53-5x23

Q: Use the tabular method to find the indefinite integral. (Use C for the constant of integration.)…

A: Given integral:- ∫x+82sinxdx

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Q: Let s(t) = 8t³ - 12t²-144t be the equation of motion for a particle. Find a function for the…

A: NOTE: Refresh your page if you can't see any equations. . the given position function is  to find…

Q: 40. *3 dx o 5x + 1

A: We will use substitution method to solve the definite integral

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Q: Evaluate the following limit. Enter an exact numeric answer. To enter ∞o in your answer field, .…

A: limx→-4x+4x2-16∂ xn∂x=nxn-1when we put x=-4  it is 00  form use l'hospital rule to find limit

Q: Determine the limit given that A, B, C, a, b, c ER (they are elements of the set of real numbers).…

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Q: Use the Shell Method to find the volume of the solid obtained by rotating region under the graph of…

A: According to question,Given Functions,fx = x2 + 20≤x≤5,Rotation about x =5

Q: a If the nth partial sum of a series Σ n = 1 00 Σ n = 1 m 2₁ a a = = = Submit Answer (for n > 1) is…

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