I can help you with #20. For example, lets say 3/5, this fraction would be made up of 5 parts and 3 are covered, which doesn't make it full, if it was 5/5 it would be full. When you do something with a reciprocal you turn it over, so 3/5 would be turned over to 5/3, thus making it a whole number
Answer: 36 shirts and costs $432
step by step:
first make an equation with the amount of sold shirts being equal to cost of making them -
12x=10x+72 where x is the number of shirts
then, subtract 10x from 12x to get the variable on the same side -
2x=72
finally, divide by 2 to isolate x
x=36 shirts
to figure out the cost, substitute 36 for x in 10x+72
10(36)+72= 360+72= $432
Answer:
![\mathbf{r^{\to} (t) = ti^{\to} + 5t^2^{\to} j+(6t^2 + 25t^4) k ^{\to}}](https://tex.z-dn.net/?f=%5Cmathbf%7Br%5E%7B%5Cto%7D%20%28t%29%20%3D%20ti%5E%7B%5Cto%7D%20%2B%205t%5E2%5E%7B%5Cto%7D%20j%2B%286t%5E2%20%2B%2025t%5E4%29%20k%20%5E%7B%5Cto%7D%7D)
Step-by-step explanation:
Given that:
The paraboloid surface z = 6x² + y² and the parabolic cylinder y = 5x²
Let assume that:
x = t
then from y = 5x², we have:
y = 5t²
Now replace y = 5t² and x = t into z = 6x² + y²
z = 6t² + (5t²)²
z = 6t² + 25t⁴
Hence, the curve of intersection is illustrated by the set of equations:
x = t, y = 5t², and z = 6t² + 25t⁴
As a vector equation:
![\mathbf{r^{\to} (t) = ti^{\to} + 5t^2^{\to} j+(6t^2 + 25t^4) k ^{\to}}](https://tex.z-dn.net/?f=%5Cmathbf%7Br%5E%7B%5Cto%7D%20%28t%29%20%3D%20ti%5E%7B%5Cto%7D%20%2B%205t%5E2%5E%7B%5Cto%7D%20j%2B%286t%5E2%20%2B%2025t%5E4%29%20k%20%5E%7B%5Cto%7D%7D)