Answer:
142.1π in³
Step-by-step explanation:
Given that:
The radius (r) = 7 in
The slant height (y) = 25 in
Then the height (x) can be determined by using the Pythagoras rule:
y² = x² + r²
25² = x² + 7²
125 = x² + 49
125 - 49 = x²
x² = 76
x = √76
x = 8.7
The formula for the volume of a cone is;
= 1/3 πr²h
where;
height(h) is calculated as "x" from above = 8.7
Then;
= 1/3 × π × (7 in)² × 8.7 in
= 142.1π in³
Answer:
- <u><em>Second option: the graph approaches 0 as x approaches infinity.</em></u>
Explanation:
The function f(x) is:
![f(x)=\frac{2x}{1-x^2}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B2x%7D%7B1-x%5E2%7D)
- When x approach infinity the term x² grows rapidly (more rapid than x), thus 1 - x², which is in the denominator will decrease, become a large negative more rapid than the x in the numerator. Thus you can expect that the function approaches zero.
To prove that in a more analytical way, divide both numerator and denominator by x and simplifiy:
![\lim_{x \to \infty} \frac{2x}{1-x^2}\\\\ \lim_{x \to \infty} \frac{2x/x}{(1-x^2)/x}\\\\ \lim_{x \to \infty} \frac{2}{1/x-x}\\\\\lim_{x \to \infty} \frac{2}{0-x}\\ \\ \lim_{x \to \infty} \frac{2}{-x}\\ \\ \lim_{x \to \infty} -\frac{2}{x}=0](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B2x%7D%7B1-x%5E2%7D%5C%5C%5C%5C%20%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B2x%2Fx%7D%7B%281-x%5E2%29%2Fx%7D%5C%5C%5C%5C%20%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B2%7D%7B1%2Fx-x%7D%5C%5C%5C%5C%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B2%7D%7B0-x%7D%5C%5C%20%20%5C%5C%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20%5Cfrac%7B2%7D%7B-x%7D%5C%5C%20%20%5C%5C%20%5Clim_%7Bx%20%5Cto%20%5Cinfty%7D%20-%5Cfrac%7B2%7D%7Bx%7D%3D0)
Answer:
![f(x) = (x+ 10)(x - 2)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%28x%2B%2010%29%28x%20-%202%29)
Step-by-step explanation:
We want to rewrite
![f(x) = {x}^{2} + 8x - 20](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20%2B%208x%20-%2020)
in the form that would most easily help you identfiy the zeros of the function.
This the same as writing in factored form.
![f(x) = {x}^{2} + 10x - 2x - 20](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%20%7Bx%7D%5E%7B2%7D%20%20%2B%2010x%20-%202x%20-%2020)
Factor by grouping:
![f(x) = {x}(x+ 10)- 2(x + 10)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%20%7Bx%7D%28x%2B%2010%29-%202%28x%20%20%2B%2010%29)
Factor further to get:
![f(x) = (x+ 10)(x - 2)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%28x%2B%2010%29%28x%20-%202%29)
Answer:
1/4 miles.
Step-by-step explanation:
If I want to walk from my house to a clothing store 3/4 of a mile away, this implies that the location is 0.75 miles from my home.
Now, if after walking 1/2 mile I decide to stop, I will have traveled 0.5 miles in total. In this way, when I get back on my way, I will have to travel 0.25 miles to reach my destination (0.75 - 0.50).
Therefore, since 1 divided by 4 equals 0.25, I have to walk 1/4 mile to reach my destination.
Answer:
x = -2
Step-by-step explanation:
Since we know they will have the same output, we can set them equal to each other in an equation. We'll use x to represent the input.
3x + 6 = 8(x + 2) (Given)
3x + 6 = 8x + 16 (Distributed the 8)
6 = 5x + 16 (Subtracted 3x on both sides)
-10 = 5x (Subtracted 16 on both sides)
-2 = x (Divided 5 on both sides)