Find the area of the plane region bounded by y = x - 4x and y% x(2-x). Answer

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A: Since multiple questions are asked,I am doing first question

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Q: ||r(t) × r"(t)|| ||M(t)|| Use the formula k(t) to find k(t). r(t) = t²i + t'"j 242 t7 K(t) = (4+ 121…

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Q: LI (x + 4)(x +3)dr = 74/3 Select one: O True O False

A: topic- definite integral

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Q: 1. Find the area bounded by the parabola y?=4ax, the x-axis, and the lines x=4a, x=9a. 2. Find the…

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Q: The general solution of the differential equation dy/dx = 12x³ is y = 4x3 + C. Select one: O True O…

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Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution. 1. dx 2. x²/4-x?

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Q: One of the correct steps to evaluate x2Inx dx to yield the correct integral

A: Our Aim is to identify the correct step to evaluate ∫x2 ln (x) dx to yieldthe correct integral.

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A: Given query is to find the time when concentration will be maximum.

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A: Here I am providing my handwritten solution.

Q: The particular solution that satisfies the differential equation and the initial condition of dy/dx…

A: Given , dy/dx = x2+2x-4 We can get y by integrating.

Q: The number N of beavers in a given area after x years can be approximated by the following. N = 5.5…

A: Given  population of beavers in a given area after x area N=5.5×100.23x    ,  0≤x≤10

Q: x³dx is equivalent to Using trigonometric substitution, Vx² –4 A 6/ tan*0 seco do B) None © 8 sec0…

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Q: 3 dy Зу =-sin -1 +C 4- 9y2 3 A True False B.

A: The given integral is 3/sqrt(4-9y2).

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Q: 3. Graph the function f(x) = 1 and estimate the area for -2 <x < 2 1+ x2

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A: The understanding of radioactive decay is required. The explanation part is given below.

Q: If f(2) = 10, f' is continuous, and f'(x) dx = 20, what is the value of f(3)? f(3) =

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Q: The decay of a certain substance is modelled by the function N(t) = 100 (3+ e), where the number of…

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Q: QUESTION 6 Refer to the graph below. When the price of a product is P2, then the consumer surplus…

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Q: i cos r-dt can best be evaluated by: A Trigonometric Transf ormation (B) None © Power Formula D…

A: Solution: ∫t cost2dt

Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integral. | (4x2 + 9) dx…

A: To find the value of definite integral using  fundamental theorem of calculus.

Q: Find V · (V × F) if F(x, y, z) = 3 sin xi + 9 cos(5x – 6y)j+ 10zk.

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Q: Find the speed of the curve F(t) = (4cos (t), 4 sin(t), 6t) at t = 3 %3| Speed =

A: Consider the curve  r(t)=&lt;4cost2,4sint2,6t&gt;

Q: t²dt can best be evaluated by: (A Trigonometric Formula B Integration by Parts (c) Trigonometric…

A: We have to find out

Q: Find the inverse Laplace transform: 1 (s(s² + 1).

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Q: 9+ 5+ g(x) 8 4 7- 6- h(x) 3 5 4 3 1 5 4 5 2 3 x-values 4 2 3 x-values If f(x) = g(x) · h(x), then…

A: Solve the following

Q: The following differential equation is exact. Find the general solution. (7x + 6y) dx + (6x − 8y3)…

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A: Given: f(t)=-16t2+444t+8

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Q: Find V. (V × F) if F(x, y, z) = 7 sin xi + 2 cos(2x – 3y)j+ 6zk. V·(V × F)

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Q: A candy box is made from a piece of cardboard that measures 31 by 17 inches. Squares of equal size…

A: let the cut out square side be "x"length of cardboard is 31 inBreadth of cardboard is 17 inAfter…

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Q: 3. Find the area of one of the sine curve.

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Q: Find the indefinite integral. (Use C for the constant of integration.) tan2 dx secº x

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A: We have to solve