company produces a spherical object of radius 23 centimeters. A hole of radius 5 centimeters if drilled through the center of the object. Find the volume of the object (in cm3) and the outer surface area of the

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A: Given that the integrand of the definite integral is a difference of two functions. Here we have to…

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A:

Q: Write the complex conjugate of the complex number. 6 + 5i Multiply the number by its complex…

A: Given: Complex number 6+5i

Q: e xp: (1+ e=)² 0.

A:

Q: Consider the following function. g(x, y) = e2x - 5y² + 10\6 v (a) Find the critical point of g. If…

A:

Q: Consider the function whose graph is the surface shown at the right. Which traces go with which…

A: y=-1.9 C x=1.9 E y=-0.5 F x=-1.9 D

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A:

Q: x*+1 dx = 0 y

A:

Q: An equation and, its graph are giiven. Find an inequelity whose sotution ia the shaded region.

A:

Q: |(9x - 5) dx, given the following. Calculate 2 X-dx 3 19 dx = 3 %3D xdx =

A: Property of Definite integration: If the upper and lower limits are the same then the integral is…

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A:

Q: Use long division to divide. (Simplify your answer completely.) (9x – 4) ÷ (3x + 2) 2 3

A: Here we will use long division method,

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A:

Q: Match the indicated conditions with one of the graphs (A)-(D) shown below. 13. f'(x) >0 and f'"(x) >…

A:

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y2 + 1, (1, 4)

A: To find the gradient of the function at the given point.

Q: Solve D.E using Exact from first order (6x² - y+3)dx+(3y² – x- 2)dy

A:

Q: Sketch the graph of the following (free hand with size): d) r = sin20 e) r = cos20 f) r = 0 g) r = 3…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

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A:

Q: Evaluate the integral. 3. [(ax-2-4) dx 2.

A: The given integral,        ∫234x-2-4dx

Q: of of For the function f(x,y) = In (x+ 3y), find and dx df of ду II

A:

Q: Q-5: [5 marks] Find the points at which f(x) = (x – 2)*(x + 1)³ has relative extrema.

A: Solving extreme

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A: Given query is to find the inequality for the solution region.

Q: if fcx) : gex) = X 11 X+ 1 find DE n Dg 2.

A:

Q: Use the Comparison Test to determine whether the series is convergent or divergent. L n4/5 n- 2 1…

A: P-Test: The series ∑n=1∞1np converges iff p>1 and diverges iff p≤1 Comparison Test: Let ∑n=1∞un ,…

Q: The function f(x) = 2x³ – 33x² + 60x + 10 has one local minimum and one local maximum. Use a graph…

A: The given function,      fx=2x3-33x2+60x+10

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Q: In x f(x) (1, 2] 4x

A:

Q: (x'+y' )dx +(2xy+ cos y)dy

A: (x2+y2)dx+(2xy+cosy)dyIt is of the formMdx+Ndy=0where M=x2+y2  ,  N=2xy+cosy∂M∂y=2y  ,…

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A:

Q: Identify the open intervals on which the function is increasing or decreasing. g(x) = x2 - 4x - 12…

A:

Q: Find real numbers a and b such that the equation is true. a + bi 3D 19 — 6і a = %3D

A: We can find the value of 'a' and 'b' as below

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A:

Q: Show that the signum function is discontinuous at x = 0

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A:

Q: TAKE NOTE: KINDLY WRITE IT DOWN ON A WHITE PAPER AND USE THE TEMPLATE BELOW WRITE IT PLEASE ON A…

A: The region is bounded by the graphs,  y=x2-2 and y=6-x2

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Q: (x* +y' )dx+(2xy+ cos y)dy

A: Follow the procedure given below.

Q: Determine the area that lies inside r = 3 + 2 sin 0 and outside r = 2 (the green region below). r =…

A: In this question, we need to find the area of the region that lies inside r = 3+2 sin θ and outside…

Q: Write the complex number in standard form. -18 + V-50

A: (-1)1/2= i

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A: Given function tells us the rate of change in the number of words per minute.

Q: af af Find and ds z when f(x, y) = e*cosy, x= 2s - f and y= 3st. af

A: Given problem:-

Q: Given •7 6. f(x) dx = –10 f(x) dx = 8 %3D g(x) dx = –1 g(x) dx = -8 , %3| compute the following…

A: Integration

Q: How long, in years and months, will it take for an investment of $1,300 to accumulate to $1,561.52…

A:

Q: 7. Given y =x*in*, calculate y'. sinx sinx A) y'=xin* (sin.x Inx + cos x Inx) C) y'=x*inx + cos x…

A: For the solution of the problem follow the next step.

Q: Let A be the given matrix. Find A-1 without a calculator. 00 1 A=100 010 A 1

A: The given matrix is A=001100010

Q: Set up the integral of the volume of the solid formed by revolving the region bounded by y = x² and…

A:

Q: cos*x _8. If S(cos³x · B) dx = A. -sin x + C, what is the B? С. cos x D. secx B. csc x

A:

Q: Use the Quadratic Formula to solve the quadratic equation. (Enter your answers as a comma-separated…

A: Given the quadratic equation is 32x2 - 6x + 9 = 0

Q: Based on the figure below, find the volume of the solid generated by revolving area of the region…

A: Follow the procedure given below.