Find the centroid of the region bounded by the parabola y= 8x and the line y=2x. O (0.8,2) O (1,4) O (2,0.8) O (0.5, 1.75)

Q: Find an equation of the plane through (4, 1, –4) that is perpendicular to the line x – 2 = 5t, y+3 =…

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Q: Evaluate the definite integrals

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Q: Q2) Convert the polar function r tan20 to cartesian.

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Q: 3. Find the area of the band cut from the paraboloid x² + y? – z = 0 by the planes z = 2 and z = 6.…

A: Let's find.

Q: Find f"(3) if Ax) = X-2.

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Q: 1 Evaluate: xInx In Oc -In 6 O d. In 6 l3.

A: The given problem is solved below in detail.

Q: –6x-'dx

A: Follow the procedure given below.

Q: Evaluate the following double integral over the region R. 7 x-y') dA; R= {(x,y): 0<xS1, -1sys1}…

A: Here we have to evaluate the given double integral over the region R .

Q: 1 lim X0-x23

A: Given,limx→ 0-1x23We know that,For x approaching 0 from the left, x&lt;0  ⇒   x23&lt;0The…

Q: Step 1 In pert (a), it was found that the two planes were 200 miles apart and getting closer at the…

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Q: -6x-'dx

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Q: Question A 5-foot ladder is leaning against a wall. If we push the ladder toward the wall at a rate…

A: let x be the distance of bottom of ladder from the wall andy be the distance between top of the…

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: Consider z=e (*3+y2) Evaluate dx2 O (6r2+ 3x)e (*3+y2) (9x4+6x)e (x³+y²) (6x4+ 9x) e (x³+y²)

A: Topic = Derivative

Q: Cha invests Php5,000 in an investment that earns 6% per annum. How many complete years does it take…

A: Given Cha invested(P)= Php5,000Rate of interest (R)=0.06Time (t)=?Amount (A)=Php 10,000We know that…

Q: Find the volume of the following solid. The tetrahedron bounded by the coordinate planes (x-0, y= 0,…

A: Given problem:- Find the volume of the following solid.   The tetrahedron bounded by the…

Q: 8. (5x'-4x +8x) dx

A: Topic = Integration As per guidelines , At a time only one question can be answered out of different…

Q: Differentiate the following function and factor fully. g(x) = (2x – 1)*(2 – 3x)“ |

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Q: [ sec" x (Vtan' x+ 1) +1) dx 2. 4 sec'x 3

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Q: a ) Σ-1 (-1)"-1 Zn=1 2n+1

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Q: xist enter DNE.

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Q: Evaluate the following limit: x² + x- 2 lim- x-1x2- 2x + 1 If it does not exist enter DNE. Round to…

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Q: Note Answer One Question Q1 The following data is provided for the velocity of an object as a…

A: Let's find.

Q: Is this series convergent or divergent?

A: This question can be solved using the concept of root test.

Q: Write each complex number in complex polar notation: 21) - 4.053 +2.042.

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Q: Consider the parametric curve defined by x=3+5t and y=1+3t Over which values of does the curve has a…

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Q: g(x) - tan(x)

A: The functions given are fx=x,gx=tanx. Formula used: Newton's Formula xn+1=xn-fxnf'xn

Q: Question For the equation given below, one could use Newton's method as a way to approximate the…

A: This question is related to numerical methods, we will solve it using given information.

Q: Evaluate: / yº sech(eThy ) tanh (e "hy ) dy 7Iny -mch(v^) + C None -ech"(,?) + C

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Q: For the functionf(x) given below, evaluate lim f(x) and lim f(x). x00 X→ー0 f(x) = -5x - 3x + 2 cos…

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Q: An object moves with acceleration function a(t) = 5 + 2t – 9t². Its initial velocity is v(0) = 6 m/s…

A: Find out the position after t seconds.

Q: Q2) Solve the D.E dy - (2x/1– y²)dx = 0

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Q: Q2) Solve the D.E dy – (2x/1- y²)dx = %3D

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Q: Find the Area bounded by the curves y = x and x = 2y – y?.

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Q: Q2) Evaluate the following integral using Trigonometric Substitutions Method: dx y 9x² + 16

A: To evaluate: I=∫dx9x2+16 Substitute x=4sec u3⇒dx=43sec u tan u du

Q: Sx³e** dx

A: To evaluate: ∫x3e4x dx

Q: 3-x Q1) Evaluate the integral * dy dx using polar coordinate

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Q: The graph of g consists of two straight lines and a semicircle. Use it to evaluate each integral. y…

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Q: Find the equation of the tangent line for x=t^3+1, y=t^2-t at t=1

A: x=t3+1  y=t2-t To be found - Tangent line equation at t=1

Q: Q5/ Use Linear Regression to fit the following data: 1 2 3 4 6 Y 4 6. 10 10 8

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Q: Evaluate: / sech[in cosr Janx dx A -2 tan-1(e cosx) +c cOsx B) None 2 tan -(e cOx) + C COSA D - 2…

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Q: Question Using Rolle's theorem for the following function, find all values c in the given interval…

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Q: Find the distance between the parallel planes 10х — 5у — 52z — 26 — 0. 2х + у + 2 %3 0 and - - NOTE:…

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Q: Q3) Evaluate triple integral (x2 - y?)dz dx dy.

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Q: 2 Vy x+j Q3) Evaluate triple integral S dz dx dy х-у

A: We can solve this as follows:

Q: SVx+3(x+ 1)dx r64 dt ap 2 +-2^)

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Q: X+ 1 Evaluate lim x→1* ** - 5x +4• | O-1 OO OO

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Q: Solve

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Q: -бх + 9 3. V6x – x² хр

A: We have to find the given integral.