Answer:
Step-by-step explanation:
Given
Represent the height of the smaller cylinder with h and its radius with r.
The height (H) of the larger cylinder is
And the radius (R) is;
Required
Determine the volume of the larger cylinder
Volume of the smaller cylinder is:
Substitute 16 for V1
While the volume of the larger cylinder is:
We have that:
and
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Simplify both expressions
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Substitute values for R and H in
Collect Like Terms
Recall that:
<em>Hence, the volume of the larger cylinder is 37.5</em>
Recall that the component form of a vector that goes from point (x,y) to point (v,w) is:
Therefore the component form of the vector that goes from point A to point B is:
Simplifying the above result we get:
Answer:
Answer:
10√2
Step-by-step explanation:
If x=1+√2, evaluate x³+1/x³
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- x³+1/x³= (x+1/x)(x²-x*1/x+1/x²)=(x+1/x)(x²+1/x²+2-3)= (x+1/x)((x+1/x)²-3)
- x+1/x= 1+√2 + 1/(1+√2)= 1+√2+(1-√2)/(1-√2)(1+√2)= 1+√2 - (1-√2)= 2√2
- x³+1/x³= 2√2((2√2)²-3)= 2√2(8-3)= 10√2
Answer:
960 ft^2
Step-by-step explanation:
There are 9 surfaces forming the solid.
5 of them are congruent squares and 4 of them are congruent triangles.
area of square = (side)^2
area of triangle = (base)(height)/2
total surface area = 5 * area of square + 4 * area of triangle
A = 5 * (12 ft)^2 + 4 * (12 ft * 10 ft)/2
A = 5 * 144 ft^2 + 4 * 60 ft^2
A = 720 ft^2 + 240 ft^2
A = 960 ft^2
