Find the volumes of the solids generated by revolving the regions bounded by the graphs of the given equations y=6-2x-x² and y=x+6 about the x − axis.

Q: S (e7z +8) dæ

A: LetI=∫ (e7x+8)dxWe apply the Sum RuleI=∫ e7xdx+∫ 8dxI= e7xddx(7x)+ 8xdx+CI=17e7x+8x+C∫…

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A: answer is in next step

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A: This question can be solved using the concept of augmented matrix.

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A: Sketch a 30 – 60 – 90 triangles below. Include the angle measures. The shorter leg measures 1/2 cm…

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A: topic - dot product and derivative of a function

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Q: Given the vectors v and u, answer a. through d. below. v = 2i + 3j – 6k u = 5i + 12j

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Q: Consider f(x, y) = 3a² – 4y² and U = cosn î + sin }r î. %3D %3D Find the directional derivative of f…

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Q: .2 1 27 36

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Q: Find the area of the regien bounded by the following curves y? = 3- x and y = -4x. %3D

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Q: III. Find the Inverse Laplace of the following a. s²+6s+25 b. (s-1)³ 7 C. s4 2s-9 d. s²+2 1 е.…

A: This is a problem related to laplace transform of the function. Based on the general formula and…

Q: Evaluate using a table of integration formulas. 5 dx 24) XV36 - x2 X-6 +C X +6 A) In +C B) In 12 6 -…

A: Solve the following

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A: This question can be solved using the concept of nature of graphs.

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A: We have to find force as per given conditions.

Q: timear

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A: Let's find.

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Q: Let f(r, y) = - 4

A: This is a problem related to function calculation. Based on the formula and concept we will find the…

Q: Évaluate the integral of 2xdx /(2x²+4) if the upperlimit is G and the lower limit is 3.

A: Given,             The integral of 2x/(2x2+4) dx if the upper limit is 9 and the lower limit is 3.

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Q: Show that the function f defined by 1, (x, y) = (1, –1) f(x, y) = x2 + Y (x, y) # (1, –1) x +y is…

A: Here, the given function is: f(x,y)=1;   (x,y)=(1,-1)x2+yx+y; (x,y)≠(1,-1) lim(x,y)→(1,-1)

Q: Find the area of the region bounded by the following curves y = 3 - x and y = -4x. %3D %3D

A: y2=3-x  and y2=-4xSolve both the equations:3-x=-4x3x=-3x=-1Substitute x=-1 in y2=-4xy2=-4(-1)y=±2The…

Q: Multeplero Selve using Lagrange final 4 decimal placia . o have anQwere phould Find the maximum and…

A: Here, the given function is: f(x,y)=3x-6y To find a maximum and minimum subject to the constraint…

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A: A hot cup of tea has temperature T1=198°F, one minute after it has been sitting on the dining table.…

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: L(sinh at)

A:

Q: Q/ Find the Surface area generated by revolving y = 1 - 2² around the y-axis, ?0 <x <1 where

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Q: 1 - x dx. e + x Evaluate:

A: We have to find the given integral.

Q: u = 6i - 2j - 7k, v= 7i - 7k

A: Here I am providing my handwritten solution

Q: sin:

A: This question is based on Partial diffrentiation.

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Q: Given the graph of f, determine the signs of f(a), f'(a), and f"(a). + + + a b d. /f(x) f(a) is […

A: Given the graph. Determine the sign of f(a), f'(a) and f"(a).

Q: Solve the system -8 6 dx dt -4 2 with the initial value 14 x(0) = x(t) =

A: Let's find.