Use the Shell Method to find the volume of the solid obtained by rotating region above the graph of f(x) = x² + 2 and below y = 6 for 0 ≤ x ≤ 2 about the y-axis. -1 V=I 20 -1

Q: IV. The dimensions of a closed rectangular box are measured as 10cm, 11cm, and 18 cm with a possible…

A: Closed rectangular box has dimension 10cm , 11 cm ,18 cm. Let , L=10cm , B=11cm , H=18cm…

Q: The following table gives values of a continuous function. X ave 20 25 30 f(x) 41 38 29 35 40 45 50…

A: The following table gives values of a continuous function. x 20 25 30 40 45 50 fx 41 38 29 26…

Q: f(x, y) = 9 — x² y4

A: To use the second derivative test, we need to find the critical points of the function first. To do…

Q: A particle is moving with the given data. Find the position of the particle, s(t). a(t) = 2t + 5,…

A: a(t)=2t+5, s(0)=4, v(0)=-5 Find s(t).

Q: Evaluate the integral. Lo 6π t² sin(2t) dt

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Q: Evaluate the integral. (Use C for the constant of integration.) [7. 7z³e² dz

A: ∫7z3ezdz

Q: The graphs of f(x) = x²-3x - 4 and g(x) = -2x - 2 intersect at the point (-1,0). The (acute) angle…

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Q: Find the most general antiderivative of the function. antiderivative.) F(x) = f(x): = 2x4 + 6x³ +³ -…

A: To find the most general anti-derivative of the following function. fx=2x4+6x3-xx3, x>0

Q: D. MEAN-VALUE THEOREM & ROLLE'S THEOREM Determine if Rolle's Theorem and the Mean Value Theorem is…

A: Note:- Since you asked multiple question , according to our policy we can solve only first question…

Q: 1) Find the average value of the function f(x) = 3-4x + 5x² over the interval [-1, 3].

A: The function is given by fx = 3-4x+5x2 To determine: The average value of the function over interval…

Q: Optimization 6) A rectanguiar box with an open top is to have 3 a 10m³. The length of its base is…

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Q: (c) Figure 4.1 shows the rough sketch of the function: y = x(x² - 6x + 8) y 0 A Figure 4.1 B X Find…

A: NOTE: Refresh your page if you can't see any equations. . to find the zeros of the function, take…

Q: 2. A mother holds a baby's stroller stationary on a hill with a 20° incline. The stroller and baby…

A: 2) Magnitude of the parallel component = Weight × cosangle of incline…

Q: Use differentials to estimate the amount of metal (in cm³) in a closed cylindrical can that is 26 cm…

A: Volume of the cylinder = πr2h where r is the radius and h is the height of the cylinder.

Q: Practice similar Help me with this First, note that we know how to integrate 7 dx = 1=²+4² 1² da 2 x…

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Q: A waste management company is designing a rectangular construction dumpster that will be twice as…

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Q: (b) 2 1 √2 t√²-1 dt (c)

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Q: Use the standard Maclaurin series for sin(x) to find the first three non- zero terms in the…

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Q: Water flows from the bottom of a storage tank at a rate of r(t) = 300 - 6t liters per minute, where…

A: This is question of calculus  Here rate of change of water flow is given  Further calculation is…

Q: Consider the following. r(t) = (7t)i + (4t − 3)j + 6tk, P(6, 1, 6) (a) Find the arc length function…

A: The arc length of the  vector curve r(t) is given by St=∫abr'tdt

Q: y = x³, y = 0, x = 2 . Find the volume created by revolving about a = = 3. Use washer or disk…

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Q: Find the average value gave of the function g on the given interval. 8 1+ [0, 9] gave = g(t) = =

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Q: A circular swimming pool has a diameter of 18 m, the sides are 3 m high, and the depth of the water…

A: Given: Diameter= 18 m Sides = 3 m  Dept = 3 m  Acceleration = 9.8 Density = 1000

Q: 12-0 dt = + C

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

Q: 7) Refer to the information in Problem 6. Find the object's total distance traveled on the interval…

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Q: Write the following expression as a single definite integral of the form f(x) dx. [²_1(x) dx + [³1x)…

A: Given expression is ∫-22fxdx+∫25fxdx-∫-2-1fxdx

Q: A particle is moving with the given data. Find the position of the particle, s(t). a(t) = 2t + 7,…

A: We have acceleration function, need to find position function using integration.

Q: ons, use your work (a) to help you the generar (Recall that general antiderivative of a function…

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Q: Use the Integral Test to determine whether the infinite series is convergent. 8 n=1 -n² 16ne

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Q: 73. 1 S dx 0(8x² + x4) ¹/3

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Q: PRACTICE ANOTHER Solve the system of linear equations. (Enter your answers as a comma-separated…

A: x1-x2=0...............A 7x1-6x2=-1..........................B

Q: Find the direction angle of the vector. Round to the nearest hundredth of a degree for the angle. p…

A: We have to find the direction angle of the given vector. First as direction angle we will measure a…

Q: 79. Give an example of a divergent sequence {a,} such that lim |an| converges. n→∞

A: To find a divergent sequence whose absolute sequence converges

Q: 17. (8.06)2/3

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Q: 9. Find all the vertical and horizontal asymptotes for the following function and indi- cate the…

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Q: Consider the integral 9 3 1² ( 2²/2 + 5) dz dx X (a) Find the Riemann sum for this integral using…

A: Given integral  ∫59( 3x + 5 )dx

Q: Use the Shell Method to calculate the volume of rotation, V, about the x-axis for the region…

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Q: Subject: calculus  Using integration, find the area of the region enclosed by the lines 2x+y-6=0…

A: Given equation of lines are as following 2x+y-6=0 ; 3x-2y-1=0; x-3y+4=0 To find the area enclosed by…

Q: Two ocean liners leave from the same port in Puerto Rico at 10:00 a.m. One travels at a bearing of N…

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Q: Test (4 Star A... 1. https://lkdsb.elearningont..... E https://pdsb.elearningont....…

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Q: -0.015 16. e

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Q: Evaluate. Use reduced fractions instead of decimals in your answer. 7 sec 6x dx = ² S + C

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Q: Compute the following. Enter your answer as a fraction. 27 ** (-+ ) *- dx = 2

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Q: 4) A region is bounded by the line x = -1, the line y = 2, and the curve y = 2*. Find the area of…

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Q: Given the area bounded by the parabola x2-4x+12y-20=0, the x-axis and the lines x=1 and x=2.…

A: The area bounded by the parabola x2-4x+12y-20=0, the x-axis and the lines x = 1 and x = 2. We have…

Q: Consider the following vector function. r(t) = (8 sin(t), t, 8 cos(t)) (a) Find the unit tangent and…

A: To find unit tangent and unit normal vector and curvature. Given  r( t) =  { 8sin(t), t, 8cos(t) }

Q: If C(x)= 17,000+600x - 2.8x² + 0.004x³ is the cost function and p(x) = 4,200- 7x is the demand…

A: We have given the cost function C(x) = 17,000 + 600x − 2.8x2 + 0.004x3  and demand function p(x) =…

Q: 63. bn = 3-4" 2+7.4" n

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Q: An aircraft (at Z) is spotted by two observers (at X and Y) who are L = 1200 feet apart. As the…

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Q: Given: (x is number of items) Demand function: d(x) 5120 √x Supply function: s(x) = 5√√x Find the…

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