The average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values.
Answer:
![\boxed{r = \frac{h}{3} + \frac{v}{\pi {h}^{2} } }](https://tex.z-dn.net/?f=%20%5Cboxed%7Br%20%3D%20%20%5Cfrac%7Bh%7D%7B3%7D%20%20%2B%20%20%5Cfrac%7Bv%7D%7B%5Cpi%20%7Bh%7D%5E%7B2%7D%20%7D%20%7D%20)
Step-by-step explanation:
![Solve \: for \: r: \\ = > v= \pi {h}^{2}(r - \frac{h}{3} ) \\ \\ v=\pi {h}^{2}(r - \frac{h}{3} )is \: equivalent \: to \: {h}^{2}\pi(r - \frac{h}{3} ) = v: \\ = > {h}^{2}\pi(r - \frac{h}{3} ) = v \\ \\ Divide \: both \: sides \: by \: \pi {h}^{2} : \\ = > r - \frac{h}{3} = \frac{v}{\pi {h}^{2} } \\ \\ Add \: \frac{h}{3} \: to \: both \: sides: \\ = > r = \frac{h}{3} + \frac{v}{\pi {h}^{2} }](https://tex.z-dn.net/?f=Solve%20%5C%3A%20%20for%20%5C%3A%20%20r%3A%20%20%5C%5C%20%20%3D%20%20%3E%20%20%20v%3D%20%5Cpi%20%7Bh%7D%5E%7B2%7D%28r%20-%20%20%5Cfrac%7Bh%7D%7B3%7D%20%20%29%20%5C%5C%20%20%5C%5C%20%20v%3D%5Cpi%20%7Bh%7D%5E%7B2%7D%28r%20-%20%20%5Cfrac%7Bh%7D%7B3%7D%20%20%29is%20%5C%3A%20%20equivalent%20%20%5C%3A%20to%20%20%20%5C%3A%20%20%20%7Bh%7D%5E%7B2%7D%5Cpi%28r%20-%20%20%5Cfrac%7Bh%7D%7B3%7D%20%20%29%20%3D%20v%3A%20%5C%5C%20%20%3D%20%20%3E%20%20%7Bh%7D%5E%7B2%7D%5Cpi%28r%20-%20%20%5Cfrac%7Bh%7D%7B3%7D%20%20%29%20%3D%20v%20%5C%5C%20%20%5C%5C%20Divide%20%20%5C%3A%20both%20%5C%3A%20%20sides%20%20%5C%3A%20by%20%20%5C%3A%20%5Cpi%20%20%7Bh%7D%5E%7B2%7D%20%3A%20%20%5C%5C%20%20%3D%20%20%3E%20r%20-%20%20%5Cfrac%7Bh%7D%7B3%7D%20%20%3D%20%20%5Cfrac%7Bv%7D%7B%5Cpi%20%7Bh%7D%5E%7B2%7D%20%7D%20%20%5C%5C%20%20%5C%5C%20Add%20%5C%3A%20%20%20%5Cfrac%7Bh%7D%7B3%7D%20%20%5C%3A%20%20to%20%20%5C%3A%20both%20%5C%3A%20%20sides%3A%20%20%5C%5C%20%20%3D%20%20%3E%20r%20%3D%20%20%5Cfrac%7Bh%7D%7B3%7D%20%20%2B%20%20%5Cfrac%7Bv%7D%7B%5Cpi%20%7Bh%7D%5E%7B2%7D%20%7D%20)
Answer:
Henry will get $15.77 back.
Step-by-step explanation:
20 - 4.23 = 15.77
Answer:Hello! Here we have a cube, with a mass of 10g and a side length of 2.5cm.
First we want to determine the volume.
The volume of a cube, is equal to his cubic side length, where L is the side length:
So
So the volume of the cube is 15.625 cubic centimeters.
Now we want to calculate te density of the material, as you know:
This means that the density is 0.64 grams per cubic centimeter.
Step-by-step explanation:
Answer:
We have expanded formula of (-4x-1)² = a²+2ab+b².
So, we write the formula in square form as (a+b)².
Since we have a²-b² in step 4. We further write this as (a+b)(a-b). This is the factor formula of a²-b².
As we had two terms in place of in (a+b)(a-b), we multiply the term 'b' with '+' and '-' sign respectively.
Write the second expression given in the question.
Write the terms in the form of cube.
Write the factor formula of a³-b³) in the form of (a-b)(a²+ab+b²).
Write the H.C.F. (Highest Common Factor) of the given expressions by analysing the factors you generated in each expressions. Here, (4x²+2x+1) are the common factors.