Answer:
The diameter decreases at a rate of -0.0477 cm/min when it is 10 cm.
Step-by-step explanation:
Surface area of a snowball:
A snowball has a spheric format, which means that it's surface area is given by:
![A = 4\pi r^2](https://tex.z-dn.net/?f=A%20%3D%204%5Cpi%20r%5E2)
In which r is the radius, which is half the diameter. In function of the diameter, the area is given by:
![A = 4\pi(\frac{d}{2})^2 = \pi d^2](https://tex.z-dn.net/?f=A%20%3D%204%5Cpi%28%5Cfrac%7Bd%7D%7B2%7D%29%5E2%20%3D%20%5Cpi%20d%5E2)
Solving the question:
To solve this question, we have to implicitly derivate the area in function of t. So
![\frac{dA}{dt} = 2d\pi\frac{dd}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%20%3D%202d%5Cpi%5Cfrac%7Bdd%7D%7Bdt%7D)
Snowball melts so that its surface area decreases at a rate of 3 cm2/min
This means that ![\frac{dA}{dt} = -3](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%20%3D%20-3)
Find the rate at which the diameter decreases when the diameter is 10 cm.
This is
when
. So
![\frac{dA}{dt} = 2d\pi\frac{dd}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%20%3D%202d%5Cpi%5Cfrac%7Bdd%7D%7Bdt%7D)
![-3 = 20\pi\frac{dd}{dt}](https://tex.z-dn.net/?f=-3%20%3D%2020%5Cpi%5Cfrac%7Bdd%7D%7Bdt%7D)
![\frac{dd}{dt} = -\frac{3}{20\pi}](https://tex.z-dn.net/?f=%5Cfrac%7Bdd%7D%7Bdt%7D%20%3D%20-%5Cfrac%7B3%7D%7B20%5Cpi%7D)
![\frac{dd}{dt} = -0.0477](https://tex.z-dn.net/?f=%5Cfrac%7Bdd%7D%7Bdt%7D%20%3D%20-0.0477)
The diameter decreases at a rate of -0.0477 cm/min when it is 10 cm.
Answer:
If you mean |x| and |-x| yes they are equal.
Step-by-step explanation:
Brackets do not exactly specify the meaning of absolute value.
On most keyboards, above the enter button on the main keyboard part (not the keypad one) there is a back slash symbol \ and if you hold shift, there might be another symbol | which more accurately represents absolute value,
If you aren't talking about the absolute value, then no.
Answer:
$77.76
Step-by-step explanation:
80x0.10=72
72x 0.08= 5.76
72+5.76 = 77.76
31,606,577
= 30,000,000 + <span>1,606,577
</span>
= 30,000,000 + 1,000,000 + <span>606,577
= </span>30,000,000 + 1,000,000 + 600,000 + <span>6,577
= </span>30,000,000 + 1,000,000 + 600,000 + <span>6,000 + 577
</span>= 30,000,000 + 1,000,000 + 600,000 + <span>6,000 + 500 + 77
</span>
= 30,000,000 + 1,000,000 + 600,000 + <span>6,000 + 500 + 70 + 7
</span>
The answer is D.