In how many ways can a committee of 5 people be chosen out of 9 people?

Q: lim X→+∞ 5 In³ x 2 X²

A: Let's evaluate limit.

Q: Evaluate the integral. 8t 8 e S dt 1+ e 8t 8e 1+e 8t 8t dt =

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Q: Find the inverse of the function on the given domain. f(x) = (x-5)^2, [5,00) f-1(x): =

A: The solution is given in the next step.

Q: Find the equation of the tangent line to the graph of the function f(x) = sin (3/7) at the point…

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Q: 1. Evaluate the given integral Q. J[(y - 2x) dA, R where is the region bounded by x = 0, y = x, x =…

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Q: x==2t X 1 1-y = Given: line ₁ = -8 and ₂ = = y = 2+2t. 3 2 z = 6 + 2t 1. If the given lines…

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Q: 1) Find a power series representation for the function and determine the interval of convergence.…

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Q: x² dx -1 (2x²+2x+1)² sº₁

A: We have to evaluate the integral. ∫dxa2+x2=1atan-1(xa)+c

Q: Find the critical points and sketch the graph of the function. 1. f(x) = √5 + x

A: We need to find critical point and graph.

Q: Assuming 8x³ - 10y² - 2xy = 0 defines y as a differentiable function of x, use the theorem dx dy dx…

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Q: If sec2A = Select one: a. 3 deg O b. 5 deg O c. 7 deg d. 6 deg 1 sin13A' determine the angle A in…

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Q: 2 2 dx 2x (V2x + 9)

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Q: 2) Given the vectors a-[4, 2, -6], b-[6, -3, 2], and c-[-5, 0, 4], simplify the following vector…

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Q: 4x+8 (x+2) ³ 3). D. Ba -dx

A: This is a problem related to integration. Based on the general formula and concept we will evaluate…

Q: Given: f(x) = 10-X g(x)=x² + 4x-2 Find and simplify (9°F)

A: Given query is to find indicated composite function.

Q: A boy released a balloon vertically in the middle of a hemispherical dome at a velocity of 5 m/s.…

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Q: The instantaneous velocity of a particle is defined as the derivative of some functions. Select one:…

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Q: 32/5 y=x² 32 Find the area of the region bounded by the graphs of y = x² and y = 4x. 64/3 32/3 64

A: The area between curves is the area between a curve fx and a curve gx on an interval a, b given…

Q: Andrew is an ecologist investigating a pond. He notices that an algal bloom is growing in the pond.…

A: To find out the rate of area.

Q: 3. Find the member of the curve whose slope at any point is and passes through the point (1, 1)

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Q: clnx Find the integral of ²x ye²dzdxdy

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Q: find the inflection point to the right of y-axis of the curve defined by the equation, y=x^2/2 +…

A: Given problem :- find the inflection point to the right of y-axis of the curve defined by the…

Q: 4. Given that f'(x) = −6x² + x + 12 and f(1) = 7, find f(x).

A: Given : f'(x)=-6x2+x+12f(1)=7   To Find : f(x)

Q: 3. A spherical balloon is inflated at a rate of 100 cm3 /sec. How fast is the radius changing when…

A: We know that volume of the balloon is V=43πr3                          (1) Given that Spherical…

Q: a and simplify (fºg) d 4x-2 + ₂X = + ₁2x = (x)6 X-01 = (x)} = ₂

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Q: 2. Use integration to find the volume of the solid generated which is bounded by x + y = 2 and the x…

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Q: Solve the following equations: (D³ + 3D² + 3D + 2)y = 0

A: We can solve this as follows:

Q: Suppose each matrix below represents the augmented matrix for a system of linear equations. For…

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Q: 3 If f *¸9 (2) dx = -5 g(x) dx = -2 and Find the value of 3 15 -5 g(x) dx 15 g(x) dx = 9

A: Solution of given question is written in below steps.

Q: 3. h(x) == 4. p(x) = 5. f(x) = ਜ 2- x+3 (6x+5)(2x-1) (3x+5)

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Q: A. Evaluate the follow 1. S dy 3+√y+3

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Q: Solve the following problems showing detailed solutions. Draw the complete figures for each…

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Q: Find the derivative of cos-¹(sin x)

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Q: Given cost and price (demand) functions C(q) = 150q+46,400 and p(q) = -2.4q+880, if the company sets…

A: Given that cost and price (demand) function C(q)=150q+46,400 and p(q)=-2.4q+880.Also, if the company…

Q: Find Ans= dy dx for y = 3x + ex x² - 5

A: Using formula of d/dx(U/V)

Q: x³ +7x X-00 √4x³+5 Find the lim

A: A detailed solution is given below.

Q: Find the area of the surface obtained by rotating the curve y=1+3x² from 0 to x = 9 about the…

A: Let's find area of surface obtained by given curve.

Q: Suppose the functions f(x) and g(x) satisfy the following: f(2)= g(2) = g(0) = 4 3 2 f'(2) = g'(2) =…

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Q: Find the differential dy: y = sin(x√³). Ody = COS cos (T√²³) [2√T™- 2 O 0 O (E) None of these…

A: A detailed solution is given below.

Q: Find the second derivative of f(t) = [(1+)¹ +1]¹

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Q: 2 √₁² √√x² - 4x + 8

A: The solution is given in the next step.

Q: 1. Evaluate the given integral Q. Q • S S (² (x - y) dx dy -

A: Evaluating the given integral

Q: Find the derivative of f(w) = √3w²

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Q: Find the derivative of the function at Po in the direction of A. f(x,y,z) = 2 e* cos (yz),…

A: We can solve this as follows:

Q: If zs² + yt²= 1 and 2²s+y³t = ry - 4, find 0x/0s, az/at, Əy/08, Əy/ot, at (x, y, s. t) = (1, -3,2,…

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Q: √x³√1-x² 2

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Q: Suppose the functions f(x) and g(x) satisfy the following: f(2)= g(2) = g(0) = 4 3 2 = ƒ'(2) = g'(2)…

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Q: Find the area bounded by the line y = x+2 and parabola y = x².

A: We can solve this as follows:

Q: 4 -3 -2 -1 5 4+ 3 2 1 -1- ea -3- 4+ -5- 3 4 domain range = =

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Q: Evaluate the following integrals: (show solution) a x² +2 b.) 1 x+1 x+√x c) f(sec x d.) e 4x 4x+1 x…

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