Part 1 Find the binomial coefficient. 7C5 20C15   Part 2 (Use the binomial theorem to expand and simplify the expression). (x + 2)4  (1 - 4x)3 (x2 + 2)4

Q: Evaluate by complete u -substitution x+1 (x-1)² dx

A: Use u-subsituation method

Q: An investment worth $1 million in 2005 has been growing at a rate of f(t) 0.14(1.18) million dollars…

A: An investment worth $1 million in 2005 has been growing at a rate of ft=0.141.18t millions dollars…

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A: We have to find the antiderivative of the given function. On the basis of formula of integration of…

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A: We are required to find: Two unit vectors that make an angle of 60° with  v = 3i + 4j.

Q: Sketch a graph of the function f(x) = 3sin x. Please state the range.

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Q: В (9,-8)

A: We know that the vector= Terminal point -initial point

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Q: At two points on the curve y = x3 − 6x2 + 8x − 1, the slope of the tangent line is −1. Find these…

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Q: 2. For each problem, find the length of the curve. (a) y = (e+ e-*) on the closed interval 0 ≤ x ≤…

A: Solving the problem

Q: 2π A sector of a circle has a diameter of 8 feet and an angle of Round your answer to four decimal…

A: We have, θ = 2π/3  Diameter (2r) = 8 r = 8/2 = 4

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A: gx=ln3x+21+1.1

Q: (b) x = on the interval 0 ≤ x ≤ 9; about y-axis. ² X=

A: The surface area of rotatint the curve about y axis⇒S=2π∫cdgy1+gy2dy

Q: 2x cos(x²) esin(x2-

A:

Q: f(1) = 1 ƒ'(1) = 2 ƒ'(3) = -5 (a) Chain Rule: h(x) = f(g(x)) ⇒ (b) Product Rule: h(x) = f(x) · g(x)…

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Q: The marginal profit is given by MP= P'x = x(90x+2x^2). Find the total profit function.

A: To find the total profit function, we need to integrate the marginal profit function with respect to…

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A: We know that the integral of x^n dx= x^(n+1)/(n+1)

Q: Section 4.3 #48 Determine the value of the logarithm without using a calculator loga =>

A: Given,

Q: A lake initially contains 5000 fish. Suppose that in the absence of predators or other causes of…

A: A lake initially contains 5000 fish. Suppose that in the absence of predators or other causes of…

Q: Question 4 Given that sin() = 0.73, match each trigonometric function with its value. cos(8) csc (8)…

A:

Q: Find the value of k such that the limit exists x² kx + 4 lim x-1 - x - 1 The k value is The limit is…

A: We have  function (x2-kx+4)/(x-1) We have to find value of k for limit existence when x tends to 1…

Q: Show all steps to prove the statement is true. Neatly show each step of your work to earn full…

A: Given Trigonometric expression  ( 1 - sinx )( 1 + cscx ) = cscx - sinx

Q: Evaluate the integral. (Use C for the constant of integration.) 3 sin(t) dt cos³ (t)

A: NOTE: Refresh your page if you can't see any equations. . ......................(1)

Q: he graph of f(x) = ax² +bx+c where a, b, and c are constants, passes through the (0,1) and is…

A:

Q: Determine the derivative of the following exponential function d. f(x)= 10* (sin sin x)

A: We have to find the derivatives of the function.

Q: What is the area of the region bounded by the curves y = x and y = x³ in the first quadrant ?

A: We are required to find: The area of the region bounded by the curves y=x and y=x3 in the first…

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A: The given differential equation is;  9y''-16y=sin(x)

Q: What is the polar form of the equation? (x+6)² + y² = 36 O² 12r cos 0 Or(r+ 12 cos 0) = 0 ○r (r + 12…

A: x+62 + y2 = 36

Q: f(3) = lim f(x)= x-3 f(5) lim f(x)= x-5 lim f(x)= lim f(x)= x-3° lim f(x) = x-5 lim f(x)= 1-5 M lim…

A: When function continuous at x=1⇒limx→afx=faOR⇒limx→a-fx=limx→a+fx=fx

Q: Calculate the integral, if it converges. If it diverges, enter diverges for your answer. e³x √-3 da…

A: If the integral valu finite then the integral is convergence And integral valu not finite then…

Q: How many petals does the graph of the rose curve r=4sin(3θ) have? Enter your answer in the box

A: For the function, r=asinnθ    or    r=acosnθ If n is odd then there are n number of petals. If n is…

Q: Consider the following. x = ln(t), y = 2t, z = t², (0, 2, 1)

A:

Q: - Consider the surface F(x, y, z) = x626 + sin(y³z6) — 10 = 0. Find the following partial…

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Q: Given the function f and the point Q, find all points P on the graph of f such that the line tangent…

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Q: x² c² and y=c²x² is 2 C - 2 Find c> 0 such that the area of the region enclosed by the parabolas y =…

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Q: 1a Differentiate the following functions with respect to t and simplify your answer as far as…

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Q: PART III: Solve the following problems. 2. The sum of two positive numbers is 2. Find the smallest…

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Q: Evaluate the integral. (Use C for the constant of integration.) [tan²(x) cos³(x) dx

A: let B=∫tan2xcos3xdx

Q: A CD has diameter of 130 millimeters. When playing audio, the angular speed varies to keep the…

A:

Q: The total U.S. personal income I (in billions of dollars) can be approximated by I=535.6(1.054)t  ,…

A:

Q: 10. for fx fx xy f₂ y f(x,y)=3x³y² + 4(3x+2y)³ find

A: The given function is;  f(x,y)=3x3y2+4(3x+2y)5 Find the fx, fxy, fy, fyx.

Q: The federal tax rate for heads of household is given in the graph shown to the right. Use the graph…

A: We are given a graph of a function rx.We need to find the following limits:limx→8297-rx,…

Q: Evaluate the integral. (Use C for the constant of integration.) [₁ 7 tan²(x) dx

A: We have, ∫  7 tan2xdx

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A: A sphere is given having a hole and we need to find out the volume of the resulted solid.

Q: What is the reference angle of θ if θ = –137°? A 43° B 47° C 137° D 223°

A: Explanation of the answer is as follows

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A: To find the dot product of given line and find the line is parallel or not.

Q: Find a formula for a cubic function f if f(3) = 24 and f(−1) = f(0) = f(4) = 0.

A:

Q: fees

A: Solving the problem

Q: company has revenue function R(x)=8000x-40x2-x3 (in dollars) wehre x is the number of items sold. A…

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Q: F(t )=100,000t for the next 9 years. What is the Present Value of this income stream over the 9…

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Q: Compute the improper integral 1 x ln(x) -dx if it exists. If not, select DNE.

A: We have to find the improper integral.