<span>Given
number: Two hundred billion in half, how to write this one in standard form
let us first simplify each statement:
=> two hundred billion = 200 000 000 000
=> in half meaning = half of the given number or divide the given number by
2 to get the answer
=> 200 000 000 000 / 2
Show, the ½ of two hundred billion in standard form
=> Thus, two hundred billion in half
is equals to 100 000 000 000
</span>
Answer:
0.13 ft/min
Step-by-step explanation:
We are given that
![\frac{dV}{dt}=15ft^3/min](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D15ft%5E3%2Fmin)
We have to find the increasing rate of change of height of pile when the pile is 12 ft high.
Let d be the diameter of pile
Height of pile=h
d=h
Radius of pile,r=![\frac{d}{2}=\frac{h}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7B2%7D%3D%5Cfrac%7Bh%7D%7B2%7D)
Volume of pile=![\frac{1}{3}\pi r^2 h=\frac{1}{12}\pi h^3](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2%20h%3D%5Cfrac%7B1%7D%7B12%7D%5Cpi%20h%5E3)
![\frac{dV}{dt}=\frac{1}{4}\pi h^2\frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B1%7D%7B4%7D%5Cpi%20h%5E2%5Cfrac%7Bdh%7D%7Bdt%7D)
h=12 ft
Substitute the values
![15=\frac{1}{4}\pi(12)^2\frac{dh}{dt}](https://tex.z-dn.net/?f=15%3D%5Cfrac%7B1%7D%7B4%7D%5Cpi%2812%29%5E2%5Cfrac%7Bdh%7D%7Bdt%7D)
![\frac{dh}{dt}=\frac{15\times 4}{\pi(12)^2}](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%3D%5Cfrac%7B15%5Ctimes%204%7D%7B%5Cpi%2812%29%5E2%7D)
![\frac{dh}{dt}=0.13ft/min](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%3D0.13ft%2Fmin)
Okay, let me just make this a little clearer. Hopefully, this is what you meant:
A. y - 8 = -4(x + 4)
B. y - 8 = 4(x + 4)
C. y + 8 = 4(x - 4)
D. y + 8 = -4(x - 4)
--
This can also be written as y2 - y1 = m(x2 - x1).
Your M is your slope.
Both A and D have their m as a negative 4. Because you are looking for a positive slope, immediately cancel those answers.
* note that you could have also put them in a more standard form and discovered m which is the x in bx.
Now, you are looking for an equation that contains (4,-8).
Because it is written as y2-y1, your y's are actually points if you were to find another slope or something. This part is a bit hard to explain, but -8 is only found in the y coordinate place in answer B. Your answer would be B. For more explanation on that, there's this great site called coolmath.com and if you search for finding the equation of two points, it explains it much better on there, but I would not want to plagiarize.
The answer is B.
I got a different answer..
and i don't see it as one of your choices, also your question is confusing since you're repeating it .-.
But anyways i got