Marley loves to draw and color. She bought 6 boxes of crayons. There are 8 crayons in each box. What is the total number of cray
2 answers:
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Answer:
8 in
Step-by-step explanation:
volume of a cube is found by multiplying three sides or finding the third power of a side
, where V is volume and s is side length
we are given that V = 512, so
s=8
Given a complex number in the form:
![z= \rho [\cos \theta + i \sin \theta]](https://tex.z-dn.net/?f=z%3D%20%5Crho%20%5B%5Ccos%20%5Ctheta%20%2B%20i%20%5Csin%20%5Ctheta%5D)
The nth-power of this number,
, can be calculated as follows:
- the modulus of is equal to the nth-power of the modulus of z, while the angle of is equal to n multiplied the angle of z, so:
![z^n = \rho^n [\cos n\theta + i \sin n\theta ]](https://tex.z-dn.net/?f=z%5En%20%3D%20%5Crho%5En%20%5B%5Ccos%20n%5Ctheta%20%2B%20i%20%5Csin%20n%5Ctheta%20%5D)
In our case, n=3, so
is equal to
![z^3 = \rho^3 [\cos 3 \theta + i \sin 3 \theta ] = (5^3) [\cos (3 \cdot 330^{\circ}) + i \sin (3 \cdot 330^{\circ}) ]](https://tex.z-dn.net/?f=z%5E3%20%3D%20%5Crho%5E3%20%5B%5Ccos%203%20%5Ctheta%20%2B%20i%20%5Csin%203%20%5Ctheta%20%5D%20%3D%20%285%5E3%29%20%5B%5Ccos%20%283%20%5Ccdot%20330%5E%7B%5Ccirc%7D%29%20%2B%20i%20%5Csin%20%283%20%5Ccdot%20330%5E%7B%5Ccirc%7D%29%20%5D)
(1)
And since
and both sine and cosine are periodic in
, (1) becomes
![z^3 = 125 [\cos 270^{\circ} + i \sin 270^{\circ} ]](https://tex.z-dn.net/?f=z%5E3%20%3D%20125%20%5B%5Ccos%20270%5E%7B%5Ccirc%7D%20%2B%20i%20%5Csin%20270%5E%7B%5Ccirc%7D%20%5D)
The nth-power of this number,
- the modulus of
In our case, n=3, so
And since
and both sine and cosine are periodic in
So for this, this can be written into the equation 
(x = number of months, y = total cost).
To solve this problem, we need to plug in 1325 into the y-variable and solve from there.
Subtract 35 on each side to get
Then just divide by 50 on each side, and your answer should be
And because we cannot go past budget, we will have to round down to 25. In context, the maximum amount of months Abbey can do is 25 months.
To solve this problem, we need to plug in 1325 into the y-variable and solve from there.
Subtract 35 on each side to get
Then just divide by 50 on each side, and your answer should be
And because we cannot go past budget, we will have to round down to 25. In context, the maximum amount of months Abbey can do is 25 months.