A spherical tank with a radius of 3 meters is half-full sitting on the ground. Set up an integral that computes the work needed to pump all the water to the top of the tank.

Q: Evaluate lim (10x³ – 7x + 14). 21 (1023 lim (10x3 7x+14) = x→-1 = Number

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Q: A force of 4 pounds is required to hold a spring stretched 0.3 feet beyond its natural length. How…

A: We solve the given problem by using integration techniques.

Q: Find the derivative of the function. f(z) = earcsin(25)

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Q: A piece of cardboard measuring 10 inches by 8 inches is formed into an open-top box by cutting…

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

Q: Using the given graph of the function f, find the following. (a) the intercepts, if any (b) its…

A: As we can see that the graph has two x intercepts and no y intercept as it not cross y axis other…

Q: f(x,t)=x²+14x+y²-4y+3. Pls find maxima, minima, & saddle points. Thank you & I will give thumbs up.

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Q: Find the derivative of the function. y = tan-¹(√x- X-8 y' = 1 X

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Q: 3. Write the equation of the tangent to x² + y² + 2xy = 4 at the point (1,1).

A: x ^ 2 + y ^ 2 + 2xy = 4

Q: (c) h(y) = 754 h'(y) = * ( = 7 (5(~²))* = 7 @y= √√x + √x + √ (d) dy dx

A: The given function,

Q: Let C be the curve y=x for -1 ≤x≤ 3, Evaluate [8xds с 3 A. 3 (17 ³ - 5 ² ) 1₁ B.3 (37 ² - 5*) c. ²²…

A: Let C be the curve .To evaluate .

Q: Let A be a 3 x 4 matrix with reduced row echelon form given by [10 5 1 3 --- U = 0 1 1 1 If a₁ find…

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Q: Represent the plane curve by a vector-valued function. (There are many correct answers.) 3x + 8y −…

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Q: The compound interest formula is given by A = P(1 + 7)". Round solutions to the nearest cent. If…

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Q: Determine Duf (3,-10) for F(X, Y, Z) = 4x - y² ³ 2 3x2 of ✓² = (-1₁4, 2) in the direction

A: Given function have to find the directional derivative in the direction of vector .As we know -

Q: 3. Differentiate the following functions and state whether they have maxima or minima. a) y =…

A: Note:-Since you asked multiple questions which are not interlinked, according to our policy we can…

Q: Let f(x) = In(x). State if the following statement is true or false (a) The graph of f(x) has a…

A: According to bartleby guidelines we are supposed to do only one question.  If you want more to be…

Q: The population of Vero Beach can be modeled by the function P = 17234e0.01921t where t is the number…

A: where t is the number of years since 2020

Q: v² dv (1 — v²) 5/²

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Q: Find the indefinite integral. (Use C for the constant of integration.) J 4 16 – (In(x))² dx

A: To find the following indefinite integral.

Q: For the formula Dûƒ(P) = Vƒ(P) · û to hold, what must be true of û?

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Q: 2. Find the angle of intersection between the curves y=x² +5x-8 and y=x²-2x+6 to three significant…

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Q: Use properties of exponential functions to solve each equations. Show all steps and give the exact…

A: The given equations (a) (b)

Q: Evaluate lim f(x) for f (x) shown here: x→1° If the limit does not exist, enter DNE. lim f(x) = x-1…

A: To evaluate  shown here.

Q: Write the given expression as a SINGLE logarithmic term. log(x + 6) - / log(x + 3) + log(x - 1), x>…

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Q: 100 dk=1 le -2k

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Q: Use the Chain Rule to find dz dt 1 where z = 3x siny, x = t², and y = 2t4.

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Q: The gas law for an ideal gas at absolute temperature T (in kelvins), pressure P (in atmospheres),…

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Q: converging on a single point as they fly at right angles to each other. One plane is 304 miles away…

A: Air traffic control detects two airplanes at the same altitude converging on a single point as they…

Q: 1. Suppose that a population develops according to the logistic equation = 0.5P 0.0025P2 where t dt…

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Q: Find the derivative of the function at P0 in the direction of u. f(x,y)=4x2+3y, P0(7,10), u=3i-4j

A: f(x,y)=4x2+3y, P0(7,10), u=3i-4j

Q: question 3

A: Figure

Q: Evaluate integral using integration by parts 2 3+ ((1²+ 41²+5) e" d It

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Q: Find three positive numbers whose sum is 160 and whose product is a maximum.

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Q: Let f(x) = 2x + 11 - 13e. Then the equation of the tangent line to the graph of f(x) at the point…

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Q: A particle moves according to a law of motion s= = tª — 2t² + 1, t > 0, where t is measured in…

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Q: Evaluate SS x JA, R = R y² {(x₂x): 1 ≤ x ≤ 2, 4 ≤ Y ≤ 6)

A: given integration

Q: Answer using the following polynomial using remainder theorem. Show your solutions. f(x) = 4x5 -…

A: To answer the following polynomial by using remainder theorem.

Q: Solve the initial value problem. dr/dt=-5ti+5tj+9tk. Initial condition r(0)=-4i+5k

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Q: The median home value in Ohio and Wyoming (adjusted for inflation) are shown below. Ohio Wyoming…

A: The median home value in Ohio and Wyoming YearOhioWyoming 19505030041300200010370096600Let x be the…

Q: Concavity and points of inflection. Answer the following questions using the function f(x) The…

A: The given function .The aim is to find the concavity intervals of the given function.

Q: The length that a hanging spring stretches varies directly as the weight placed at the end of the…

A: The length that a hanging spring stretches varies directly as the weight placedat the end of the…

Q: Fill in the blanks and evaluate the following indefinite integral. 2x / ₁ x 2² x ₁1² dx = [( (x +…

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Q: 8 3 Evaluate S -dx. 10 9x 4

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Q: Using a telescope, you track a rocket that was launched 6 km away recording the angle between the…

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Q: Find the maximum rate of change of f(x, y, z) = x+y/z at the point (3, 4, 5) and the direction in…

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Q: 4. A weather balloon rising from the ground at 120 ft/min is tracked by a range finder located 350…

A: A weather balloon rising from the ground at 120 ft/min is tracked by a range finder located 350 feet…

Q: Kindly provide, using the graph: a.) domain and range in interval notation. b.) the interval for…

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Q: dw dt ne derivative where w = xyz, x = 5t³, y = 3t¯1, and z = 6 |z=6t-2 1

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Q: Let f(x) = (x-3)-2. Find all values of c in (2,5) such that f(5)-f(2) = f'(c)(5-2). (Enter your…

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Q: Find the first 4 nonzero terms of the Maclaurin series for h(x) C₁x + C₂x² + 3x³ +…... = COS X = Co…

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