well without exact answer choices i have narrowed it down to these numbers
-37
-36
-35
-34
-33
-32
sorry about my lack of knowing this exact answer but that should narrow it down unless i went about this question wrong
82°
7x+4 = 88°
7x = 84°
7x-2 = 82°
Answer:
Step-by-step explanation:
a.
An implicit expression is a relation of the form y = f(x) where f is a a function with x as a variable.
On integrating both sides, we get
We know that 
.
Therefore,
![\int \frac{dy}{y(4-y)}=\int \frac{1}{2}\,dt\\\frac{1}{4}\int \frac{1}{y}+\frac{1}{4-y}\,dy=\int \frac{1}{2}\,dt\\\frac{1}{4}\left [ \ln y-\ln (4-y) \right ] =\frac{t}{2}+C](https://tex.z-dn.net/?f=%5Cint%20%5Cfrac%7Bdy%7D%7By%284-y%29%7D%3D%5Cint%20%5Cfrac%7B1%7D%7B2%7D%5C%2Cdt%5C%5C%5Cfrac%7B1%7D%7B4%7D%5Cint%20%5Cfrac%7B1%7D%7By%7D%2B%5Cfrac%7B1%7D%7B4-y%7D%5C%2Cdy%3D%5Cint%20%5Cfrac%7B1%7D%7B2%7D%5C%2Cdt%5C%5C%5Cfrac%7B1%7D%7B4%7D%5Cleft%20%5B%20%5Cln%20y-%5Cln%20%284-y%29%20%5Cright%20%5D%20%3D%5Cfrac%7Bt%7D%7B2%7D%2BC)
As 
,
So, ![\frac{1}{4}\left [ \ln y-\ln (4-y) \right ] =\frac{t}{2}-\frac{\ln 3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%5Cleft%20%5B%20%5Cln%20y-%5Cln%20%284-y%29%20%5Cright%20%5D%20%3D%5Cfrac%7Bt%7D%7B2%7D-%5Cfrac%7B%5Cln%203%7D%7B4%7D)
b.
![\frac{1}{4}\left [ \ln y-\ln (4-y) \right ] =\frac{t}{2}-\frac{\ln 3}{4}\\\ln y-\ln (4-y)=2t-\ln 3\\\ln \left ( \frac{y}{4-y} \right )=2t-\ln 3\\\frac{y}{4-y}=e^{2t-\ln 3}\\y=(4-y)e^{2t-\ln 3}\\y\left ( 1+e^{2t-\ln 3}\\ \right )=4e^{2t-\ln 3}\\y=\frac{4e^{2t-\ln 3}}{1+e^{2t-\ln 3}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%5Cleft%20%5B%20%5Cln%20y-%5Cln%20%284-y%29%20%5Cright%20%5D%20%3D%5Cfrac%7Bt%7D%7B2%7D-%5Cfrac%7B%5Cln%203%7D%7B4%7D%5C%5C%5Cln%20y-%5Cln%20%284-y%29%3D2t-%5Cln%203%5C%5C%5Cln%20%5Cleft%20%28%20%5Cfrac%7By%7D%7B4-y%7D%20%5Cright%20%29%3D2t-%5Cln%203%5C%5C%5Cfrac%7By%7D%7B4-y%7D%3De%5E%7B2t-%5Cln%203%7D%5C%5Cy%3D%284-y%29e%5E%7B2t-%5Cln%203%7D%5C%5Cy%5Cleft%20%28%201%2Be%5E%7B2t-%5Cln%203%7D%5C%5C%20%5Cright%20%29%3D4e%5E%7B2t-%5Cln%203%7D%5C%5Cy%3D%5Cfrac%7B4e%5E%7B2t-%5Cln%203%7D%7D%7B1%2Be%5E%7B2t-%5Cln%203%7D%7D)
Answer:
I believe the volume is 80 cubic centimeters.
Step-by-step explanation:
V = volume
B = base
H = height
V = BH
V = (4) 20
V = 80
