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Q: Question 1: F(t)= -{³ (a) 5. 2t+1 (b) 500-1500 t-1 The amount of money raised during a fund-raising…

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Q: A. Find all the partial derivatives of f(x,y) = 12x²y + 2xy + 5y²

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Q: Solve the initial value problem.. (tan (@y) - 4)dx + (8x sec ²(By) + -] dy = 0, y(0) = 1 The…

A: Given differential equation ( tan( 8y ) - 4 )dx + ( 8xsec2( 8y ) + 1y )dy = 0 Mdx + Ndy = 0

Q: what is -16 IT 3 52" ST 5² p²rin & dp dp de 0

A: Recall the formula:

Q: Use the information given below to find cos (a −ß). 8 17' 3 tan B with B in quadrant III 4 sin a =…

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Q: For the curve given by r(t) = (3t, -5t, 1 + 7t²), Find the derivative r' (t) = ( Find the second…

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Q: 2. The limit of the sequence {cos cos an n+1 is

A: The given sequence is: an=cos(πn)n+1

Q: 3 Let f(x) = (x³ + 4x + 7)³. Compute each of the following. f'(x) = ƒ'( − 2) =

A: given  f(x)=(x3+4x+7)3  we know  d(xn)dx=nxn-1d dx(constant)=0

Q: 7. Determine the y-intercept of the exponential function j(x) = a(b)*, if a > 0, b>0. A. 0 B. 1 C. a…

A: To determine the y‐intercept of the following exponential function. jx=abx, if a>0, b>0

Q: If it takes someone t minutes to drive, run, or walk a mile, then their average speed s(t), in miles…

A: We will put the value of t to find s(t)

Q: Find an equation of the sphere that passes through the origin and whose center is (−2,1,3) Be sure…

A: Given that the sphere passes through the origin and whose center is (-2,1,3).

Q: Question 2 A y B Hence, calculate the size of the shaded area R X Diagram not to scale- The above…

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Q: 1) Find the domain: A]f(x)=√x B)g(x) == C₁h(x)=; D) x(x) = log₂ (2x + 1)

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Q: 口 4. Find the vertex of the given function: y=x² + 3x-4 O (-1.5, 6.25) O (-1.5, -6.25) O (1.5,…

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

Q: Use the information given below to find tan (a+ß). 5 12 3 5' tan a = cos B with a in quadrant III…

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Q: h(t) = t 5t 24

A: h(t) = t2 + 5t + 24 The above equation represents the height at any time t. The rate of…

Q: Let f be the function given by f(x)=√x4 - 9x² Find f'(x).

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Q: The marginal revenue derived from producing q units of a certain commodity is R(q) = 6q- 1.5q2…

A: given  R'(q)=6q-1.5q2we know ∫qndq=qn+1n+1+cgiven  revenue for 22 units is 35000

Q: 14. A rectangular garden is to be planted against the side of a barn. The gardener has 80 metres of…

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Q: ——— For the function f(x) = 3 − (x + 1)³, at the point (0, 2) – O a. f has a relative maximum. O b.…

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Q: 3. The rate of change of the number of people who knows a certain rumor is proportional to the…

A: The rate of change dNdtof the number of persons who have heard a certain dt rumor over time is…

Q: Solve the differential equation given below. 77-2 141H

A: The given differential equation is: dydx=7y-24x-1

Q: Determine the distance from the line y = x + 1 to the parabola y2 = x. (Hint: Let (x, y) be a point…

A: The shortest distance from the line y = x + 1 to the parabola y2=x. Equation of line y = x + 1is…

Q: Prove the identity. cot²x (sec²x - 1) = 1

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Q: Find the velocity, acceleration, and speed of a particle with position function r(t) = (-3t sint,…

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Q: 7. Find the surface area generated by revolving y = x² from x = 0 to x 2 about the x-axis. = a.…

A: To find the surface area generated by revolving y=x2 from x=0 to x=2 about the  x-axis.

Q: Find the arclength of the curve r(t) = (3√/2t, e³, e-³), 0≤t≤1

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Q: Given the function f(x) = 5x each of the following. Give your answer as an integer or a simplified…

A: Let's evaluate the following function.

Q: Which of these is an equation of the tangent line to the curve (t² + 2t + 3, 4t cost, 2 e³t) 0? at…

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Q: After t hours on the job, a factory worker can produce 145te-0.8t units per hour. How many units…

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Q: Consider the following linear equations: 7x + 6y + 5z = −7 7x +(18-k)y + 4z = -5 7x + 6y + (9- k)z…

A: Let's solve given linear equations for no solution and infinite number of solution.

Q: F If f(3) = 5 and f'(x) ≤ 2 for 3 ≤ x ≤7, how large Use Mean Value Theorem) can f(7) possible be?…

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Q: Find the equation of the sphere centered at (-3, 1, -3) with radius 8. Normalize your equations so…

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Q: Use the 2 solutions Bernoulli's equation y y' + √y=0

A: Given differential equation y' + yx - y = 0

Q: Use the 2 solutions Bernoulli's equation dy y + = x²y² dx x

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Q: 05 If |a+31/2=1 and 2|b+1|=6, then la +b] could equal any of the following EXCEPT * O A.1 B.3 C.5…

A: Topic:- algebra

Q: If ƒ(x) = 7x² − 7x − 24, find ƒ'(x).

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Q: 3 a)Find the area of the parallelogram with vertices: P(0,0,0), Q(4,-3,-1), R(4,-2,-2), S(8,-5,-3).…

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Q: 1. Find by double integration the volume of the solid generated by revolving about the x- axis the…

A: According to our guidelines , we can answer only first question. Kindly re-post other remaining…

Q: 3. Consider the functions f: R → R defined by f(0) = 4 + sin 0 and g: R → R defined by g(0) = sin…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: (1)=2x+5 y(2)=x^2-8x+17   1. find the value of y(2) at its minimum, and the rate of change of…

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Q: a. If a polynomial f (x) is divided by 2x - 1, what is remainder?

A: Solution ⇒    Given polynomial is  =f(x)    Divided by  (2x−1)    Remainder =?    If…

Q: For subject to F(x, y) = 4x y-24(x + y) 2 X 2 + y² = 36,

A: Given, Fx,y=4xy-24x+yFx,y=4xy-24x-24y Subject to x2+y2=36 ⋯⋯⋯⋯ 1 To find: Stationary point = ?

Q: Sketch the following graphs show how if possible thanks y an(6 1 -tan 2 0+ T 4 y = 3 cos(20+6)

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Q: factor each number correctly 62 30

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Q: False True 3. Start the process of completing the square by converting the quadratic function into…

A: given statement Start the process of completing the square by converting the quadratic function into…

Q: (a) (b) d'y 3. +2dy dx --y=0 y"-2y = y'

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Q: A painting is purchased as an investment for $175. If its value increases continuously so that it…

A: A painting is purchased as an investment for $175.If its value increases continuously so that it…

Q: Solve the initial value problem. dy 5x²- 5x^ - x- 2 dx (x + 1)(y +1) ' y(1)=3 The solution is. (Type…

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Q: When an object is dropped on a certain earth-like planet, the distance it falls in t seconds,…

A: The function is  s(t)=17t2 a) At t= 3 second S(2)=17×(2)2 S(2)=68 ft so , the the hammer will fall…