The rate a which the surface area, S, decreases is
![\frac{dS}{dt} =-8 \pi \, cm^{2}/s](https://tex.z-dn.net/?f=%20%5Cfrac%7BdS%7D%7Bdt%7D%20%3D-8%20%5Cpi%20%5C%2C%20cm%5E%7B2%7D%2Fs)
The surface area is
S = 4πr²
where r = the radius at time t.
Therefore
![\frac{dS}{dt} = \frac{dS}{dr} \frac{dr}{dt} =8 \pi r \frac{dr}{dt} \\\\ -8 \pi = 8 \pi r \frac{dr}{dt} \\\\ \frac{dr}{dt} =- \frac{1}{r}](https://tex.z-dn.net/?f=%20%5Cfrac%7BdS%7D%7Bdt%7D%20%3D%20%5Cfrac%7BdS%7D%7Bdr%7D%20%20%5Cfrac%7Bdr%7D%7Bdt%7D%20%3D8%20%5Cpi%20r%20%20%5Cfrac%7Bdr%7D%7Bdt%7D%20%5C%5C%5C%5C%20-8%20%5Cpi%20%20%3D%208%20%5Cpi%20r%20%20%5Cfrac%7Bdr%7D%7Bdt%7D%20%5C%5C%5C%5C%20%20%5Cfrac%7Bdr%7D%7Bdt%7D%20%3D-%20%5Cfrac%7B1%7D%7Br%7D%20)
When r = 3 cm, obtain
![\frac{dr}{dt}]_{r=3} = - \frac{1}{3} \, cm/s](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdr%7D%7Bdt%7D%5D_%7Br%3D3%7D%20%3D%20-%20%5Cfrac%7B1%7D%7B3%7D%20%5C%2C%20cm%2Fs%20%20)
Answer: -1/3 cm/s (or -0.333 cm/s)
Answer:
A). y > x – 2 and y < x + 1
Step-by-step explanation:
Answer:
X=7
Step-by-step explanation:
Since area of a rectangle is 294
Area of a rectangle=length×breadth
Let's the width be x
Since length is 6 times of width=6x
Area=l×w
294=x×6x
294=6x^2
Divide both sides by 6
x^2=49
Square root both sides
x=7
Therefore x is 7
If you can multiply or divide the original triangle to equal the second triangle, and if the angles are the same, then it is a dilation
Answer:
10 =x
Step-by-step explanation:
-90 = -100 + x
Add 100 to each side to isolate x
-90+100 = -100+100 + x
10 =x