Multiply the amount she puts in the account every week by the number of weeks (w) and add that to what she already has saved:
20w + 600 >= 2000
For the derivative tests method, assume that the sphere is centered at the origin, and consider the
circular projection of the sphere onto the xy-plane. An inscribed rectangular box is uniquely determined
1
by the xy-coordinate of its corner in the first octant, so we can compute the z coordinate of this corner
by
x2+y2+z2=r2 =⇒z= r2−(x2+y2).
Then the volume of a box with this coordinate for the corner is given by
V = (2x)(2y)(2z) = 8xy r2 − (x2 + y2),
and we need only maximize this on the domain x2 + y2 ≤ r2. Notice that the volume is zero on the
boundary of this domain, so we need only consider critical points contained inside the domain in order
to carry this optimization out.
For the method of Lagrange multipliers, we optimize V(x,y,z) = 8xyz subject to the constraint
x2 + y2 + z2 = r2<span>. </span>
Answer:
Step-by-step explanation:
Given
--- interval
Required
The probability density of the volume of the cube
The volume of a cube is:
For a uniform distribution, we have:
and
implies that:
So, we have:
Solve
Recall that:
Make x the subject
So, the cumulative density is:
becomes
The CDF is:
Integrate
![F(x) = [v]\limits^{v^\frac{1}{3}}_9](https://tex.z-dn.net/?f=F%28x%29%20%3D%20%5Bv%5D%5Climits%5E%7Bv%5E%5Cfrac%7B1%7D%7B3%7D%7D_9)
Expand
The density function of the volume F(v) is:
Differentiate F(x) to give:
So:
Answer:
36.88
Step-by-step explanation:
6.1 + 6.3 = 12.4
3.2 x 12.4 = 39.68
39.68 - 2.8 = 36.88
Answer:
It will be worth $1732.30.
Step-by-step explanation:
After 1 year : 6000 x .78 = 4680
2 yr - 4680 x .78 = 3650.4
3 yr - 3650.4 x .78 = 2847.312
4 yr - 2847.312 x .78 = 2220.90336
5 yr - 2220.90336 x .78 = 1732.304621
1732.30
I think this is what it was asking
