Find the distance from the point (-5,1,2) to the line a(t) = (-5,0, 3)t + (-7, 1, 5) -

Q: Use spherical coordinates to integrate f(x, y, z) = x² + y² + z² = 81. (Give an exact answer. Use…

A: Calculation of above requirement are as follows

Q: Prove by strong induction that root of 2 is irrational.

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Q: Find a plane containing the point (1,4,3) and the line of of the planes 7x + 5y - 8z = 27 and 5x +…

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Q: Use the Chain Rule to find dw/dt. w = xeylz, dw dt = e y 91²2 x = tº, y = 5-t, 6xy 2² Z X Z X z = 7…

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Q: Real Estate The following table shows the cost of 1,000 square feet of luxury real estate in three…

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Q: Write the equation of the ellipse 36. x² + 25 · y² : = 900 in 2 standard form (2²) a + (²2) ² b = 1

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Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = 2x² - 4xy+3y² -…

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Q: Find the distance from the point (5,-6,-8) to the plane x - y - 5z = - 37

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Q: Calculate the double integral. Sk [[[x sec²(y) dA, R = {(x, /1105x58,0sys X y) y) | ≤ ≤ ≤ R 2}

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Q: The point x = 0 is a regular singular point of the given differential equation. Find the equation…

A: To solve the following problem

Q: Find the points on the ellipse 3x² + y² = 3 that are farthest away from the point (1, 0).

A: For the Given Ellipse 3X2+y2=3 ,Points that are  Farthest away from the point (1,0) is calculated as…

Q: For the function f(x)=√²+25, find f'(x). Then find f'²(0) and f’(3).

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Q: Evaluate the integral. (Use C for the constant of integration.) [Car dx (arcsin(x))²

A: Please see the below picture for detailed solution.

Q: Find the directional derivative of the function at P in the direction of v. g(x, y) = √√√√x² + y²,…

A: Given: gx,y=x2+y2, p7,24, v=3i-4j   As we know the expression for the directional derivative of the…

Q: Consider the function on the interval (0, 2π). f(x) = 4 sin²(x) + 4 sin(x) (a) Find the open…

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Q: Consider the initial value problem given below. 3 dy y dx x += x³y²₁ y(1.2) = 1.8 =X The solution to…

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Q: Evaluate the integral. (Use C for the constant of integration.) 5 sin(8x) cos(5x) dx

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Q: interval notation of -292<x<308 not including -67 and 83

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Q: The figure shows the power consumption in San Francisco for a day in September (P is measured in…

A: Here

Q: Find the volume of a square pyramid with a base having a side length of 2 and a height of

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Q: Use an algebraic method to eliminate the parameter and identify the graph of the parametric curve.…

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Q: 9 For the function f(x)=x, find f''(x), f''(0), f''(1), and f’’( − 1). f''(x) = Select the correct…

A: Derivative

Q: K For the cost and price functions below, find a) the number, q, of units that produces maximum…

A: Given: The cost and price functions are C(q)=80+19qp=71-2q To determine:  a. the number, q, of units…

Q: Use cylindrical coordinates. Evaluate x² dv, where E is the solid that lies within the cylinder x2 +…

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Q: Express the limit as a definite integral on the given interval. Do not evaluate the integral. (a)…

A: Given,

Q: The latitude and longitude of a point P in the Northern Hemisphere are related to spherical…

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Q: Consider the following power series. Let a = lim LIM R 11 (-1)*(x-8)* ku 11k (-1)* 11k (x-8)*. Find…

A: Solution will be given below

Q: (a) Write a function of the form P (t) = Poe to model each population P(t) (in millions) years after…

A: We need to write the population function.

Q: 1 5. x = x = (v² + 2 77 find the area of the surface obtained by rotating the curve about the +2)…

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Q: Find the linearization L(x) of f (x) = In(1 + x) at a = 0. Use this linearization approximate…

A: Solving the following problem

Q: Find the critical numbers for the following g(x) = x² - 2x² +5

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Q: find the equation of the line 9. Through (2, –50) with equal intercepts 10. Through (–7, –4) with…

A: Coordinate geometry

Q: Find 1 x²√x² + 16 J Solution Let x = 4 tan(0), - Thus, we have sec(0) tan²(0) dx. -<6 2 = << . Then…

A: According to question,Given Integral,∫1x2x2+16dx

Q: A triangle with area 30 cm^2 is cut from a corner of a square with side 10 cm, as shown in the…

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Q: If f is differentiable and f'(c) = 0, then f has a horizontal tangent line at x = c. True False

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Q: Express the limit as a definite integral on the given interval. Do not evaluate the integral. (b)…

A: Given:- limn→∞∑i=1nsinπin·πn

Q: A beverage company manufactures 2-liter pineapple juice to be packaged in cylindrical cans made of…

A: Given :The surface area of this cylinder = 2πrr+hV=πr2h

Q: C) Convert the equation 5x² + 2y² = 3z to spherical coordinates.

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Q: 19. f(x) = sin²: x cos 2x, 0<x<T

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Q: The concentration C of a chemical in the bloodstream t hours after injection into muscle tissues is…

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Q: If the marginal cost of producing x units of a commodity is given by  C'(x) = 0.3x2 + 2x and the…

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Q: Use the equation to find dy dx dy dx 1 ƏF |ð öð Əx ду 1 utlu cos(xy) = 6 + sin(y)

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Q: True or false: If f is a differentiable function, then True False de [f(x³²)] = f'(3x²) dx

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Q: (d) Use the given information to write an equation that relates the variables x and y. (e) Use part…

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Q: does not exist, enter DNE.) f(t) = t3 − 9t2 + 24t   e) Draw a diagram to illustrate the motion of…

A: Note : according to our guidelines i can solve only first 3 subparts of the given question, please…

Q: Consider the following. u = (-5, 2, 4) v = (0, 1, 7) Find u x v. Determine if u x v is orthogonal to…

A: Use the formula for the cross product of two vectors.

Q: Find the mass of a ball of radius 4 if the mass density of the sphere is proportional to the square…

A: To find the mass of a ball of radius 4 if the mass density of the sphere is  proportional to the…

Q: - d the absolute maximum and minimum values of f(x) = x³ − 3x² − 9x + 10 on the interval 41.

A: we will find the required.

Q: There are 64,000 subscribers to an online fashion magazine. Due to competition from a new magazine,…

A: Given that, There are 64,000 subscribers to an online fashion magazine. Due to competition from a…

Q: Use the graph of f(x) -7 -6 -5 -4 -3 -2 -1 O a) Find f(-2) 4 O + esc 3 Submit 2 -1 d) Find lim f(x)…

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