Let Sbe the solid in the first octant situated between the planes z+y+z=6and 3z +3y+ 2z - 18. Find the volume of S. Enter an exact answer. Provide your answer below:

Q: 2х + у dy 3+ 3у? — х dx 3.

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A: Here, the given vectors are: A(1,-1,2), B(2,-3,0), C(-1,-2,0) & D(2,1,-1) (a) Here, AB=(2,-3,0)-...

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A: a)Area of the box (A)=x.x+2xh+2xhA=x2+4xh75=x2+4xh  [Since A=75 cm2]75-x2=4xhh=14x75-x2Volume of the...

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Q: Let f(x) = /3r – 10. According to the definition, f'(r) = lim h0 (Enter the limit in reduced form)

A: f(x)=3x-10f'(x)=limh→0f(x+h)-f(x)h

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Q: Let f(x) = 5 + 9x -9. According to the definition, f'(x) = lim (Enter the limit in reduced form) h 0

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Q: for power substitution method, next step is * For Sdz 16 – 5(u²)â + u² -(2udu) 4 – u? r6 – 5u² + u? ...

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

A: Volume of a tetrahedron with adjacent edges given by the vectors u,v,w is given by, V= |u.(v×w)|/6

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Q: 3. For what value of x will the slope of the tangent to f(x) = 3*e* +5x +17 be equal to 5?

A: We can solve the given question as follows:

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A: We have to find the value of r' at s=2a.

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Q: 6. Find the minimum surface area of a box that holds 2 cubic meters.

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Q: a. Use integrals to show that the circumference of the circle z2 + y? = a² is 27a. %3D b. Find the l...

A: Given that equation of circle x2+y2=a2center of circle 0,0  and radius =aSolution :x2+y2=a2y=±a2-x2o...

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A: We have to integrate

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A: Solving question (a), 

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A: Given  f(x) = x+1x;  1, 3

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Q: 2 NOT: L..

A: We have to find the value of x such that f(x)bis continuous but not differentiable

Q: 1 Evaluate the following integral. dx X4V9-x2

A: ∫vn dv = vn+1n+1+C

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A: slope m at (2,1)  m = 2(2+5)2 m = 2*49 m = 98 so line equation y - y0 = m(x - x0 ) y -1 = 98(x - 2) ...

Q: (6) Shipping fees (or shipping charges) are often based on a formula that offers a lower charge per ...

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Q: EVALUATE THE INTEGRAL

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A: We have to find the two unit vectors.

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Q: Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the double-...

A: tanu = 5/13 other side of triangle = 194 cosu = 13/194 sinu = 5/194 sin2u = 2*cosu*sinu sin2u = 2*13...

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A: Find your answer below 

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Q: Evaluate the definite integral. Use a graphing utility to verify your result. (x³ + 1)² dx

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A: As per our guidelines we only solve one question and rest of the question will be reposted.

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A: The vector equation of a plane in normal form is   r.n^=d Here r is the position vector of a point l...