Find a such that the line x = a divides the region bounded by the graphs of the equations into two regions of equal area. (Round your answer to two decimal places.) y2 = 64 - x, X = 0

Q: -6w + x + 3y + 6z = -6 -7w - x – 9y – 2z = -33 -4w – 9x + 8y + 9z = -94 -w – 6x – 10y + 9z = -202…

A:

Q: Evaluate the line integral-ydx + xdy along the curve C: y? = 21x from (21, 21) to (0,0). NOTE: Enter…

A:

Q: Find V (V x F) if F(x, y, z) = 5 sin xi + 9 cos(x – 2y)j+ zk. V. (V × F) =

A:

Q: Let f(x) = 9x* + xx² + e2*. Compute f©(x). (Use symbolic notation and fractions where needed.) f9(x)…

A: Compute 5th derivative of f(x)

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A:

Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

A: Given

Q: Find div F and curl F if F(x, y, z) = x°i – 2j + yzk. div F= curl F=

A:

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

A:

Q: Find r'(t). r(t) = 6 cos (t)i + 3 sin3(t)j + k r'(t) =

A: Let's find.

Q: Find T(t) and N(t) at the given point. = e' cos t, y = e' sin t, z = e'; t= 0

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Q: 1- Show that the following subset is a subgroup. H = {o e S, lo(n) = n}cS,

A: Explanation of the answer is as follows

Q: Determine the area of the region bounded by y=2x^2+10 and y = 4x+16

A: To find the area of the region bounded by the given curves.

Q: Find the area of the region bounded by the equations y= x and Y3D6X-x². Note: theses are conics.

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Q: (x + 1) f' (x) = f(1) = 5 x,

A: Solution is given below:

Q: Use a double integral to find the volume of the indicated solid. 4아 2 30 z = 25 - xy 20 10 3. 2 y=x…

A:

Q: 1. Find the equation of the tangent line to the curve x = e', y = et att = 1. 2. Find all values of…

A: tangent property

Q: Find the Laplace transform of f(t) ={0, 0 ≤t ≤1         7t −7, t ≥1 .}

A: Given :f(t)=00≤t≤17t-7t≥1

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A:

Q: Directions: Evaluate the derivatives of the following functions with respect to x and simplify the…

A:

Q: ||r'(t) x r"(t)|| Use the formula k(t) to find k(t). 13 r(t) = t’i+t5j K(t) =

A: We have to find k(t)

Q: Find div F and curl F if F(x, y, z) = x°i – 9j + yzk. - div F= curl F=

A: Divergence of a vector function F(x,y,z) is given by, div(F)=i∂∂x+j∂∂y+k∂∂zF and curl of vector…

Q: V4-x? 3-x2-y² Evaluate the iterated integral. x dz dy dx -5+x2+y? A 128/15 16/89 23/6

A:

Q: 12. Find an equation for the tangent plane to the surface given by 2xy? = 2z2 – ryz at the point (2,…

A: We know that the equation of the tangent plane is: nxx-x0+nyy-y0+nzz-z0=0 Where n→-nxi+nyj+nzk is…

Q: Sketch the region in the plane consisting of points whose polar coordinates satisfy the given…

A:

Q: Use the arc length formula to find the length of the curve  y = 3x − 5,   −2 ≤ x ≤ 3.  Check your…

A: Given : y=3x-5 ,   -2≤x≤3   To Find : Arc length

Q: If f is continuous at a number, x, then f is differentiable at x. True False

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Q: For each of the following series determine if the series converges or diverges. In(n) Σ n=2

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy -180 J-120

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Q: -Ive the derivative dy for the function: x dx = e'sint ; y = ecost %3D

A: To find dy/dx.

Q: Question 9 1 2 1 Evaluate the iterated integral. J, J. J. (x²+ y2 + z?) dx dy dz -1°0 0, А) 5 В) з 8…

A: The solution is given in the next step.

Q: Find V · (F × G), if F(x, y, z) = 2xi+j+14yk and G(x, y, z) = xi + yj – zk. | V · (F x G) =

A:

Q: Find the center of mass of the given system of point masses lying on the x-axis. m = 8, m, = 3, m, =…

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Q: Calculate the (f(g(x)))' and (g(f(x)))' derivatives if f(x) = x8 1 g(x) 5x + 1 (Express numbers in…

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy = -72

A: To evaluate: ∫02∫-72y2∫-48zyz dx dz dy

Q: 13. Calculate the divergence of the vector field F = x1e1 + 2x1e2 + +nx1en. ...

A:

Q: Use double integration to find the volume of the solid. ... 3 3x + 2y + 4z = 12 А) 6 в) 9 c) 12 D)…

A: Volume

Q: Find the directional derivative of the function at P in the direction of v f(x, y) = x³ - y³, P(6,…

A: we have to find directional derivative.

Q: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t att-0. x =…

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Q: [r(t)xu(t)] , in two dilferent ways Find CHE).t)] and rt)- costi + sintj +tk, u(t)=j+Ek dt (i) Find…

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Q: dy Compute the derivative y dx y = 5x4 – x-4 (Express numbers in exact form. Use symbolic notation…

A: Given,y=5x4-x-4  Formula: If, y=xn then, y'=nxn-1

Q: Directions: Evaluate the derivatives of the following functions with respect to x and simplify the…

A:

Q: Question 13 Evaluate JJ xy dA , where R is the region in fa, 3) (1, (5, 3) R (2, 1) (4, 1) x A 56 В)…

A: A detailed solution is given below.

Q: Use double integration to find the volume of the solid. ... 3x + 2y + 4z = 12

A:

Q: Evaluate the integral by choosing a convenient order of integration: « сos(хy) сos1"(тӕ) dA; R —D |…

A: Given

Q: Find div F and curl F if F(x, y, z) = 13y*z'i – 11a'2®j – 5xy*k. div F= curl F=

A: We can solve as follows

Q: Find the centroid of the region. NOTE: Enter the exact answers. (7, g) = |(?, ?) y = 1

A:

Q: Find the area of the region(s) enclosed by the curve y= |2x-6|, the x-axis, and the lines x =0 and x…

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Q: Evaluate the double integral over the rectangular region R. | 8xy'dA; R = {(x, y): -1<xs 1, - 8 syS…

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Q: 2 2 3 Y= (4x3 - 4a3 ) 2

A:

Q: Find div F and curl F if F(x, y, z) = 7e*i – 6 cos yj+ 6 sin? z k. div F= curl F=

A: DivF  and curl F are evaluated.