Answer:
Step-by-step explanation:
Let's start with the equation of the volume of a cylinder:
![V=\pi r^{2}*h](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E%7B2%7D%2Ah)
Where:
- r is the radius of the cylinder (r=D/2=24/2=12 cm)
- h is the high of the cylinder (h = 60 cm)
We can us partial derivatives to find the differential of this volume. So we will have:
(1)
Now:
![\frac{\partial V}{\partial r}=2\pi r*h=2\pi 12*60=4523.9 cm^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%20V%7D%7B%5Cpartial%20r%7D%3D2%5Cpi%20r%2Ah%3D2%5Cpi%2012%2A60%3D4523.9%20cm%5E%7B2%7D)
![\frac{\partial V}{\partial h}=\pi 12^{2}=452.4 cm^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%20V%7D%7B%5Cpartial%20h%7D%3D%5Cpi%2012%5E%7B2%7D%3D452.4%20cm%5E%7B2%7D)
dr is a differential of the radius, so in our case it is 0.1 cm and dh, differential of the high, is 0.1*2 cm. We multiply by 2 because we need to consider the top and the bottom of the cylinder.
Now we just need to put all of this definitions in the equation (1).
I hope it helps you!
Answer:
the number would be the same
Step-by-step explanation:
<u>Answer:
</u>
x = 5 and y = 0 is correct solution of 2x + y -10 = 0 and x – y – 5 =0
<u>Solution:
</u>
Two given equations which needs to be solve are
2x + y – 10 = 0 ------ (1)
x– y – 5 = 0 ------ (2)
Let’s modify equation (1)
2x + y – 10 = 0
y =10 - 2x ------ (3)
On substituting value of y from equation (3) in equation (2) we get
x – (10 – 2x) -5 = 0
x – 10 + 2x – 5 = 0
3x -15 = 0
x = 5
Substituting x = 5 in equation (3) to get value of y.
y = 10 – 2
5 = 10 – 10 = 0
So on solving given equation we get x = 5 and y = 0.
Lets substitute value of x = 5 and y = 0 in equation (1) and equation (2) to check whether these calculated values satisfies given equations or not.
For equation (1), 2
5 + 0 – 10 = 10 – 10 = 0
For equation (2), 5 – 0 – 5 = 0
On solving, in both cases LHS = RHS for calculated values of x = 5 and y = 0.
Hence x = 5 and y = 0 is correct solution of two given equation.
B, because the constant is on the bottom and the values are correct.
Answer:
-8/5
Step-by-step explanation:
Slope is calculated as the change in y over the change in x, or the rise over the run.
Two points on this line are (2, -4) and (3, 4) The rise between these two points is 8, and the run between these two points is -5.
Therefore, the slope is just 8/-5, or -8/5.
Let me know if this helps!