Answer:
1134
Step-by-step explanation:
![\pi \: radius \: 2](https://tex.z-dn.net/?f=%5Cpi%20%5C%3A%20radius%20%20%5C%3A%202)
=1134.114948
9514 1404 393
Answer:
12/x^5
Step-by-step explanation:
The fractions are multiplied in the usual way. The applicable rule of exponents is ...
(x^a)(x^b) = x^(a+b)
__
![\dfrac{3}{x^2}\cdot\dfrac{4}{x^3}=\dfrac{3\cdot4}{x^2\cdot x^3}=\dfrac{12}{x^{2+3}}=\boxed{\dfrac{12}{x^5}}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%7D%7Bx%5E2%7D%5Ccdot%5Cdfrac%7B4%7D%7Bx%5E3%7D%3D%5Cdfrac%7B3%5Ccdot4%7D%7Bx%5E2%5Ccdot%20x%5E3%7D%3D%5Cdfrac%7B12%7D%7Bx%5E%7B2%2B3%7D%7D%3D%5Cboxed%7B%5Cdfrac%7B12%7D%7Bx%5E5%7D%7D)
Answer:
Its d 5/10
Step-by-step explanation:
The correct works are:
.![\frac{Blue(s + h) - Blue(s)}{h} = 4s + 2h](https://tex.z-dn.net/?f=%5Cfrac%7BBlue%28s%20%2B%20h%29%20-%20Blue%28s%29%7D%7Bh%7D%20%3D%204s%20%2B%202h)
<h3>Function Notation</h3>
The function is given as:
![Blue(s) = 2s^2 + 3](https://tex.z-dn.net/?f=Blue%28s%29%20%3D%202s%5E2%20%2B%203)
The interpretation when Steven is asked to calculate Blue(s + h) is that:
Steven is asked to find the output of the function Blue, when the input is s + h
So, we have:
![Blue(s + h) = 2(s + h)^2 + 3](https://tex.z-dn.net/?f=Blue%28s%20%2B%20h%29%20%3D%202%28s%20%2B%20h%29%5E2%20%2B%203)
Evaluate the exponent
![Blue(s + h) = 2(s^2 + 2sh + h^2) + 3](https://tex.z-dn.net/?f=Blue%28s%20%2B%20h%29%20%3D%202%28s%5E2%20%2B%202sh%20%2B%20h%5E2%29%20%2B%203)
Expand the bracket
![Blue(s + h) = 2s^2 + 4sh + 2h^2 + 3](https://tex.z-dn.net/?f=Blue%28s%20%2B%20h%29%20%3D%202s%5E2%20%2B%204sh%20%2B%202h%5E2%20%2B%203)
So, the correct work is:
![Blue(s + h) = 2s^2 + 4sh + 2h^2 + 3](https://tex.z-dn.net/?f=Blue%28s%20%2B%20h%29%20%3D%202s%5E2%20%2B%204sh%20%2B%202h%5E2%20%2B%203)
<h3>Simplifying Difference Quotient</h3>
In (a), we have:
![Blue(s + h) = 2s^2 + 4sh + 2h^2 + 3](https://tex.z-dn.net/?f=Blue%28s%20%2B%20h%29%20%3D%202s%5E2%20%2B%204sh%20%2B%202h%5E2%20%2B%203)
![Blue(s) = 2s^2 + 3](https://tex.z-dn.net/?f=Blue%28s%29%20%3D%202s%5E2%20%2B%203)
The difference quotient is represented as:
![\frac{f(x + h) - f(x)}{h}](https://tex.z-dn.net/?f=%5Cfrac%7Bf%28x%20%2B%20h%29%20-%20f%28x%29%7D%7Bh%7D)
So, we have:
![\frac{Blue(s + h) - Blue(s)}{h} = \frac{2s^2 + 4sh + 2h^2 + 3 - 2s^2 - 3}{h}](https://tex.z-dn.net/?f=%5Cfrac%7BBlue%28s%20%2B%20h%29%20-%20Blue%28s%29%7D%7Bh%7D%20%3D%20%5Cfrac%7B2s%5E2%20%2B%204sh%20%2B%202h%5E2%20%2B%203%20-%202s%5E2%20-%203%7D%7Bh%7D)
Evaluate the like terms
![\frac{Blue(s + h) - Blue(s)}{h} = \frac{4sh + 2h^2}{h}](https://tex.z-dn.net/?f=%5Cfrac%7BBlue%28s%20%2B%20h%29%20-%20Blue%28s%29%7D%7Bh%7D%20%3D%20%5Cfrac%7B4sh%20%2B%202h%5E2%7D%7Bh%7D)
Evaluate the quotient
![\frac{Blue(s + h) - Blue(s)}{h} = 4s + 2h](https://tex.z-dn.net/?f=%5Cfrac%7BBlue%28s%20%2B%20h%29%20-%20Blue%28s%29%7D%7Bh%7D%20%3D%204s%20%2B%202h)
Hence, the correct work is:
![\frac{Blue(s + h) - Blue(s)}{h} = 4s + 2h](https://tex.z-dn.net/?f=%5Cfrac%7BBlue%28s%20%2B%20h%29%20-%20Blue%28s%29%7D%7Bh%7D%20%3D%204s%20%2B%202h)
Read more about function notations at:
brainly.com/question/13136492