1. Find the centroid of the semicircular area inside x? + y² = a²_with y> 0 Answer:

Q: Evaluate the integral In(x) le2 x[ln4(x)-1] e3

A: The integration of the integral is  ln(x)/[x(ln4x -1)] limit from e2 to e3.

Q: 3. a) Describe the translations applied to the graph of y= x² to obtain a graph of the quadratic…

A:

Q: Find the measures of the angles of the triangle whose vertices are A = (-1,0), B = (2,1), and C= (2,…

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Q: Determine if the function is odd, even or neither * x2-1 x²+1

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Q: Find the length of the arc y =: 8 1 from X = 1 tox = 4. 4x?

A: Graph: Given: y=x48+14x2. So,          y'=x48+14x2' =x32-12x3.

Q: Find the volume generated by the region bounded by the curve y 12X and the line X3 rotated about the…

A:

Q: 1. A boy is blowing a spherical balloon at a rate of 50 cm /s. At what rate is the radius of the…

A: This question is based on application of derivative.

Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the given…

A:

Q: nd the sum of the following series. If it is divergent, type "Diverges" or "D". 3n 5"n! nswer. ote:…

A: To find the sum of the series.

Q: The general antiderivative determined by - x² - 3x +2 is dx

A:

Q: a) Is the series Σ is Vn + n3 + 10 n=1 convergent or divergent? justify your answers. 8.

A: Dear student, As per guidelines if multiple questions are posted we are allowed to solve only ist…

Q: separable 2

A:

Q: Let f (x) = 1(1 2 2 +4. Evaluate f(-8). f(-8) = Number

A: Given f(x) = -½(½)x + 4 We have to find f(-8)

Q: Find the curve's unit tangent vector. T(t) = Di+Dj+Ok

A:

Q: Suppose z is a function of x and y. and tan Vy? + x² = 2"e6y dz dz Solve for and

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Q: Evaluate the integral 7-2x dx /7+12x-4x²

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Q: D) Decreasing on (-00, 0) Determine where the given function is concave up and where it is concave…

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Q: the choices for this question is a. 5x - 3y +19 = 0 b. -5x + 3y -19 = 0 c. 5x +3y -19 = 0 d. 5x…

A: Here is the answer given below

Q: n! 00 is 2.5.8....(3n+2) Zn=1 а. 3 b. 5 с. d. 3.

A: For the following problem,

Q: 2) Consider the function 9 defined by glx, y) - (7x/g)+ COS logs (x-y) la) determine dydx

A: Given: g(x,y)=cos⁡(πxy)+1log3⁡(x−y) To find: ∂2g∂y∂x ∂2g∂y∂x means first partially differentiate…

Q: Find the position function s(t) for an object with acceleration function a(t) = 9sin(3t), whose…

A: We have to find the s(t)

Q: What are all values of x for which the function f defined by f (x) = a+3z2 - 9x +7 is increasing?…

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Q: If L(4sin(3t) + 2cos(9t)) = As"+Bs +Cs+D, (s² +9)(s² +81) the value of C is

A: C = 18

Q: The size of an unborn fetus of a certain species depends on its age. Data for Head circumference (H)…

A: Let's find.

Q: Find the general soultion of the follwoing equations dy cos x + y = cos²x, dx *+ y = xy/3.

A: Differential equation

Q: Find the area of the region that lies outside the circle r = 3 cos and inside the cardioid r = 1+…

A: Given r=3cosθr=1+cosθ

Q: sinh x – 1 dx cosh x

A: The given integral: ∫sinh x-1cosh xdxWe need to find the antiderivatives.

Q: Find the plane determined by the intersecting lines. y = 2+2t y = 1+ 2s z= 1- 4t L1 x= - 1+t L2 x=1-…

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Q: The rectangles in the graph below illustrate a left endpoint Riemann sum for f(x) = on the interval…

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Q: 2 3. Evaluate the integral ||x dx -2 O 2 4

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Q: A sequence is shown. -12, -7, -2, 3, 8, 13, … Which function produces the same sequence? f(n) =…

A: nth term of A.P. f(n)=a+(n-1)d

Q: Which test is most appropriate for In(n+4) series: 2 n =1 n*+2? b) series is convergent or…

A:

Q: The revenue (in millions of dollars) from a manufacturing process is projected to follow the model R…

A: Profit=Revenue-Cost

Q: 4 sec t to evaluate the integral J 2-16 dx Use the substitution x = Note: Use C for an arbitrary…

A:

Q: kindly answer immediately, thanlyou somucchhh Determine the equation that passes through (-2,-3)…

A: Given query is to find the equation of the line.

Q: separable 9-X(2lnX+1) Sin y+ ycosy

A:

Q: 7 1 = xp- Зх-2 du 5. 2 O True O False

A: Given query is to find statement is true or false.

Q: Given the demand function D(p)=150/p Find the Elasticity of Demand at a price of $38

A: Given, Given the demand function Q=150/p At p=38 Q=150/38 Q=75/19 We know that price Elasticity of…

Q: Find L(sin? at)

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Q: Find the arc length of y = +(x + 2)³ + (x + 2)-1 for 1 < x < 2. (Give your answer to three decimal…

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Q: 5. а. ³(1 + t4)³ dt

A:

Q: n-1 1 Given the series 2 n=1 Does this series converge or diverge? converges O diverges If the…

A: A series is of the form  a + ar + ar^2 + ar^3 + . . .  is called an infinite geometric series with…

Q: Graph each parabola. Identify the vertex, focus, directrix, endpoints of the latus rectum, and the…

A: We have to sketch graph of parabola then identify the vertex, focus, directrix, endpoints of the…

Q: -5x- 4 etermine an equation of the inverse of the function y = 6x +4 y = -5 -5x +6 C. リ= -4 6x-4 y =…

A: Given query is to find the inverse function.

Q: FIND THE LENGTH OF THE CURVE y = In sec X from X = 0 to X = - 4

A: Given curve is y= lnsecx .  We have to find the length of the curve from x=0 to x=π4. Length formula…

Q: Consider the curve C on the yz-plane with equation y2- z + 2 = 0 (a) Sketch a portion of the right…

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Q: dx 4e2a -8e+5 e

A: We want to find the integral.

Q: dy The family of curves having * is 1) y=-2x+c 2) y=(2x - x') +e 3) y = 2x - +o O 4) y=(2- x²)³ +c…

A: We have to find solution of the above question

Q: Write the sum using sigma notation: -3+5 + - 7+...+- 17 Σ i = 1

A:

Q: Graph each parabola. Identify the vertex, focus, directrix, endpoints of the latus rectum, and the…

A: The given equation is: y2-12y-16x-28=0⇒y2-12y+36=16x+28+36⇒(y-6)2=16x+64⇒4(4)(x+4)=(y-6)2 which is…