Answer:
Volume = 16 unit^3
Step-by-step explanation:
Given:
- Solid lies between planes x = 0 and x = 4.
- The diagonals rum from curves y = sqrt(x) to y = -sqrt(x)
Find:
Determine the Volume bounded.
Solution:
- First we will find the projected area of the solid on the x = 0 plane.
A(x) = 0.5*(diagonal)^2
- Since the diagonal run from y = sqrt(x) to y = -sqrt(x). We have,
A(x) = 0.5*(sqrt(x) + sqrt(x) )^2
A(x) = 0.5*(4x) = 2x
- Using the Area we will integrate int the direction of x from 0 to 4 too get the volume of the solid:
V = integral(A(x)).dx
V = integral(2*x).dx
V = x^2
- Evaluate limits 0 < x < 4:
V= 16 - 0 = 16 unit^3
For this case we have the following inequality: y < 3x + 1 < br/ >
What we must do is to evaluate a point of the Cartesian plane and verify if it is in the shaded region.
The shaded region represents the solution of the system of equations.
For the point (0, 0) we have:
0 < 3(0) + 1 < br / >
0 < 0 + 1 < br / >
0 < 1 < br / >
Therefore, the point (0, 0) is in the shaded region because it satisfies the inequality.
Then, the points that are on the line, are not part of the solution because the sign is of less strict.
Hope I helped ~~Laurel
Point +10.
(-2)*(-1) gives +2 (a negative number multiplied for another negative gives a positive number).
2*5 = +10
At the time of her grandson's birth, a grandmother deposits $12,000.00 in an account that pays 2% compound monthly. What will be that value of the account at the child's twenty-first birthday, assuming that no other deposits or withdrawls are made during the period.
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A(t) = P(1+(r/n))^(nt)
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A(21) = 12000(1+(0.02/12))^(12*21)
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A(21) = 12000(1.5214)
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A(21) = #18,257.15