Find the volume of the solid whose base is the region enclosed by y = x² and y = 1, and the cross sections perpendicular to the y-axis are squares. V =

Q: Determine the exact value of the following expression. tan 137) 8

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Q: 18. A company makes $1000 on the first 100 widgets sold. The rate of change for profit is given by…

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Q: Determine the open intervals on which the graph of the function f(x)= x²+64 is concave upward or…

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Q: What is the median of the following list of numbers? [4, 12, 12 6, 10, 3] Number

A: given numbers  4,12,12,6,10,3first step is to find median is to sort our dataset from lowest to…

Q: Use the following information to determine cos(2x). Answer cos(x) = cos(2x) = 2 √6 and tan(x) is…

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Q: Find the dimensions of the largest rectangle that can be inscribed in a circle of radius r.

A: Answer in step 2.

Q: 4. Trace the curve: y² = x²−4x−12 x²-2x-3

A: for x intercept put y=0for y intercept put x=0y2=x2-4x-12x2-2x-3

Q: 10- You want to invest €1000. What interest rate is required to make this investment grow to €2000…

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Q: The roots of the auxiliary in y (4) + 3y"- 4y=0_ Om= ±2 Om=+1,i Om= + 2i Om= ± 1, ± 2i

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Q: 18) The graph of f(x) is shown. fox A) I only 4 B) 1:4 f¹=0 at X = ? c) 1; 4; 5: D) 143536

A: As per guideline only one question is allowed to solve if multiple question is asked in single…

Q: Differentiate. f'(t) = f(t) = 8t t³t-1

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Q: b) (x + 2y - 3)dx + (2x + 4y - 9)dy = 0

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Q: v = {3,k,-2} and w = {-2,1,2k} What value(s) of k are the vectors v and w perpendicular?

A: To determine the value of k for which the vectors v and w are perpendicular.v=3, k, -2 and w=-2, 1,…

Q: An equation of an ellipse is given. ²+12²=1 (a) Find the vertices, foci, and eccentricity of the…

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Q: 3x 16x³ +24x² - 9. Find: 10. Given f(x) = a) All maximum and minimum points b) All intervals wher

A: given that ;- f(x)=3x4-16x3+24x2-9now ,  f'(x)=ddx3x4-16x3+24x2-9f'(x) = 12x3-48x2+48xand…

Q: Evaluate the integral 4x3 x² +1 - dx.

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Q: Differentiate. y' = y = 3 sec(x) - csc(x)

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Q: 2- Say whether each given sequence is an arithmetic sequence. Find the common difference and the…

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Q: The farmer knows that the area of the rectangular enclosure must be at least 400 square meters. This…

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Q: A) O B) i C of 4) Given g@=2, g'(3)=3, * P(x) = [90] 2, then P'(3) equals; A) 4 B) 6 c) 9 D) 12 E)…

A: Given; g(3)=2, g'(3)=3, p(x)=[g(x)]2.

Q: Simplify the following expression: O sin²(u) O 1 - sec²(u) O sin(u) O cos² (u) Ⓒ 1 - cos(u) cos(u)…

A: formula used is  secu=1cosusin2u+cos2u=1

Q: 23. lim 848 5√√x+3 1 - 17x²

A: Solve limit

Q: 16) Sinx-cosy-2=0; dy = ? A) -cot X c) CosX siny B) -cot y d) -cscy cos X E) 2-COS X siny

A: given 16) sinx - cosy - 2 = 0

Q: Find the distance between the points with polar coordinates (6, π/3) and (8, 2π/3).

A: formula for distance is  D=(x2-x1)2+(y2-y1)2in rectangular coordinates  x=rcosθ and y=rsinθgiven…

Q: The average cost per item to produce q items is given by a(g) 0.01g²-0.6q+17, for q>0. What is the…

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Q: Write Sk k: 4+8+12+...+ -0-0 Do not simplify.) Write SK+1. k+1:4+8+12+...+4(k+ 1) = Simplify your…

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Q: (b) Given the graph of f (x) below (blue), select the correct graph of the transformation y = 2f (x)…

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Q: Find the length of the curve x = t³, 312 y = ²2² ²²₁ 0 ≤ t ≤ √3 t²,

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Q: If A and B are constants, find where f''(x) = 0 I= f(x) = 9 Ar² + 7. Bx³

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Given f(x) = 19x - 3| +2 25. f'(²-) = If f(x)=(√3x-2)5 then f'(9) = Given f(x) = sin(3x)² 26. f'() =

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Q: Find f sin ¹xdx -

A: Given query is to find the integral.

Q: * Your answer is incorrect. Consider each function to be in the form y = k xP, and identify k or p…

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Q: Find the area of the region bounded by the graphs of the algebraic functions. f(x)=x² +34x+289 g(x)…

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Q: The number of bacteria in a culture is given by the function, n(t) 930e0.5t, where t is measured in…

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Q: Solve the initial value problem dy € + ² = 5x√ỹ, _y(1) = 2.

A: standard form is dydx+p(x)y=q(x)given  dydx+yx=5xydivide by y  both sides 1ydydx+1x×yy=5xwe know…

Q: (D7 + 2D6 + 7D5 + 14D4 + 8D³ + 16D² - 16D - 32) y = 0

A: The given differential equation D2+2D6+7D5+14D4+8D3+16D2-16D-32y=0. We have to find the general…

Q: Given the graph below, solve the following inequality: k(t) < 0 +10 +RVEY 9 8 7 6 5 4 3 2 1…

A: To solve the given inequality

Q: Find F'(x) given F(x) = f ³² z S³ z³ dz. <-3x ○ F¹(x)= 54x³ ○ F'(x)=0 ○ F'(x)=81x³ ○ F'(x) = 162x³

A: fiven  F(x)=∫-3x3xz3dzwe know  ∫zndz=zn+1n+1+cdxndx=nxn-1

Q: Write the sum without sigma notation. Then evaluate. 6 Σ sin kn k=2 Write out the sum. 6 Σ sin kn =…

A: Given series ∑k=26sinkπ

Q: A closed box with a square bottom has a total surface area (all 6 sides) of 400 square inches.…

A: We have given a box with a square bottom length = width = w inches Surface area = 400 in2 Surface…

Q: Use the summation formulas to rewrite the expression O O 4 8 71 72 6 8 6 S I I I + n 8 4 72 8 S…

A: 12+22+...+n2 = n(n+1)(2n+1)6. 1+2+...+n = n(n+1)2

Q: Differentiate the function. F(t) = (3t - 5)² F'(t) =

A: Let's differentiate given function.

Q: 1 cm?

A:

Q: 11. -log/2x+3

A: To graph the given function. To state the domain and range. To identify the parent function and to…

Q: 4) Evaluate 2 √x√x² +1 dx

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Q: 12. Find f x √(1-x²)³ dx

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Q: -X xy' + (1 + x)y = e¯* sin(2x)

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Q: : You need to provide a clear and detailed solution for the following Questions: Question 1 Given…

A: Solution: Given data, y"-7y'+10y = -2e3t

Q: Determine whether Rolle's Theorem can be applied to the function f(x)=x²- 10x + 16 on the closed…

A:

Q: Suppose c is inversely proportional to the square of d. If c = 8 when d = 2, find the constant of…

A: Function