Answer:
![\frac{dy}{dx} =-\sqrt[3]{\frac{y}{x} }](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D-%5Csqrt%5B3%5D%7B%5Cfrac%7By%7D%7Bx%7D%20%7D)
Step-by-step explanation:
Recall that using the chain rule we can state:
and therefore solve for dy/dx as long as dx/dt is different from zero.
Then we find dy/dt and dx/dt,
Given that
And similarly:
Therefore, dy/dx can be determined by the quotient of the expressions we just found:
now notice that we can find ![cos(t) = \sqrt[3]{y}](https://tex.z-dn.net/?f=cos%28t%29%20%3D%20%5Csqrt%5B3%5D%7By%7D)
from the expression for y,
and ![sin(t) = \sqrt[3]{x}](https://tex.z-dn.net/?f=sin%28t%29%20%3D%20%5Csqrt%5B3%5D%7Bx%7D)
from its expression for x.
Therefore dy/dx can be written in terms of x and y as:
![\frac{dy}{dx} =-\frac{cos(t)}{sin(t)}=-\sqrt[3]{\frac{y}{x} }](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D-%5Cfrac%7Bcos%28t%29%7D%7Bsin%28t%29%7D%3D-%5Csqrt%5B3%5D%7B%5Cfrac%7By%7D%7Bx%7D%20%7D)
Answer:
93214.28 cm³
Step-by-step explanation:
The area of the given solid in the front side is = area of the rectangle + area of the semi circle.
= ( 40 × 30 ) + 0.5 × π × r²
= 
{Since radius = 0.5 × Diameter = 0.5 × 30 = 15 cm}
= 1553.57 cm².
Now the volume of the solid is given by (Area of the vertical surface × horizontal length) = 1553.57 × 60 = 93214.28 cm³ (Answer)
Answer:
third option
Step-by-step explanation:
good luck on the rest of it
A would be your answer. 20x-11=5x+11
Answer:
D
Step-by-step explanation:
In order to solve this problem, we simply need to multiply 15 by 4 by 8, which is the equation for volume. Or variably, length times width times height. Our answer will be 480 cm.
