Answer:
<h2>$4.7</h2>
Step-by-step explanation:
step one:
Let the cost be y
to solve for the cost of a movie ticket, we need to solve the expression
y=2.75+0.10x
step two:
given that x is the number of years between 1980-2000
the number of years is 20years
put x= 20 in the expression for the cost we have
y=2.75+0.10(20)
y=2.7+2
y=$4.7
Angle UTV is basically given: it's 138°.
Moreover, since UTV is isosceles, the other two angles have the same measure x. We thus have
![138+x+x=180 \iff 2x=42 \iff x=21](https://tex.z-dn.net/?f=138%2Bx%2Bx%3D180%20%5Ciff%202x%3D42%20%5Ciff%20x%3D21)
So, TUV is 21°, and VUW is complementary, so it must be 69° so that they sum up to 90°
Answer:
w<-6
Step-by-step explanation:
11w+99<33
-99
11w<-66/11
Answer:
bottom side (a) = 3.36 ft
lateral side (b) = 4.68 ft
Step-by-step explanation:
We have to maximize the area of the window, subject to a constraint in the perimeter of the window.
If we defined a as the bottom side, and b as the lateral side, we have the area defined as:
![A=A_r+A_c/2=a\cdot b+\dfrac{\pi r^2}{2}=ab+\dfrac{\pi}{2}\left (\dfrac{a}{2}\right)^2=ab+\dfrac{\pi a^2}{8}](https://tex.z-dn.net/?f=A%3DA_r%2BA_c%2F2%3Da%5Ccdot%20b%2B%5Cdfrac%7B%5Cpi%20r%5E2%7D%7B2%7D%3Dab%2B%5Cdfrac%7B%5Cpi%7D%7B2%7D%5Cleft%20%28%5Cdfrac%7Ba%7D%7B2%7D%5Cright%29%5E2%3Dab%2B%5Cdfrac%7B%5Cpi%20a%5E2%7D%7B8%7D)
The restriction is that the perimeter have to be 12 ft at most:
![P=(a+2b)+\dfrac{\pi a}{2}=2b+a+(\dfrac{\pi}{2}) a=2b+(1+\dfrac{\pi}{2})a=12](https://tex.z-dn.net/?f=P%3D%28a%2B2b%29%2B%5Cdfrac%7B%5Cpi%20a%7D%7B2%7D%3D2b%2Ba%2B%28%5Cdfrac%7B%5Cpi%7D%7B2%7D%29%20a%3D2b%2B%281%2B%5Cdfrac%7B%5Cpi%7D%7B2%7D%29a%3D12)
We can express b in function of a as:
![2b+(1+\dfrac{\pi}{2})a=12\\\\\\2b=12-(1+\dfrac{\pi}{2})a\\\\\\b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a](https://tex.z-dn.net/?f=2b%2B%281%2B%5Cdfrac%7B%5Cpi%7D%7B2%7D%29a%3D12%5C%5C%5C%5C%5C%5C2b%3D12-%281%2B%5Cdfrac%7B%5Cpi%7D%7B2%7D%29a%5C%5C%5C%5C%5C%5Cb%3D6-%5Cleft%28%5Cdfrac%7B1%7D%7B2%7D%2B%5Cdfrac%7B%5Cpi%7D%7B4%7D%5Cright%29a)
Then, the area become:
![A=ab+\dfrac{\pi a^2}{8}=a(6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a)+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a^2+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}-\dfrac{\pi}{8}\right)a^2\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right)a^2](https://tex.z-dn.net/?f=A%3Dab%2B%5Cdfrac%7B%5Cpi%20a%5E2%7D%7B8%7D%3Da%286-%5Cleft%28%5Cdfrac%7B1%7D%7B2%7D%2B%5Cdfrac%7B%5Cpi%7D%7B4%7D%5Cright%29a%29%2B%5Cdfrac%7B%5Cpi%20a%5E2%7D%7B8%7D%5C%5C%5C%5C%5C%5CA%3D6a-%5Cleft%28%5Cdfrac%7B1%7D%7B2%7D%2B%5Cdfrac%7B%5Cpi%7D%7B4%7D%5Cright%29a%5E2%2B%5Cdfrac%7B%5Cpi%20a%5E2%7D%7B8%7D%5C%5C%5C%5C%5C%5CA%3D6a-%5Cleft%28%5Cdfrac%7B1%7D%7B2%7D%2B%5Cdfrac%7B%5Cpi%7D%7B4%7D-%5Cdfrac%7B%5Cpi%7D%7B8%7D%5Cright%29a%5E2%5C%5C%5C%5C%5C%5CA%3D6a-%5Cleft%28%5Cdfrac%7B1%7D%7B2%7D%2B%5Cdfrac%7B%5Cpi%7D%7B8%7D%5Cright%29a%5E2)
To maximize the area, we derive and equal to zero:
![\dfrac{dA}{da}=6-2\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right )a=0\\\\\\6-(1-\pi/4)a=0\\\\a=\dfrac{6}{(1+\pi/4)}\approx6/1.78\approx 3.36](https://tex.z-dn.net/?f=%5Cdfrac%7BdA%7D%7Bda%7D%3D6-2%5Cleft%28%5Cdfrac%7B1%7D%7B2%7D%2B%5Cdfrac%7B%5Cpi%7D%7B8%7D%5Cright%20%29a%3D0%5C%5C%5C%5C%5C%5C6-%281-%5Cpi%2F4%29a%3D0%5C%5C%5C%5Ca%3D%5Cdfrac%7B6%7D%7B%281%2B%5Cpi%2F4%29%7D%5Capprox6%2F1.78%5Capprox%203.36)
Then, b is:
![b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a\\\\\\b=6-0.393*3.36=6-1.32\\\\b=4.68](https://tex.z-dn.net/?f=b%3D6-%5Cleft%28%5Cdfrac%7B1%7D%7B2%7D%2B%5Cdfrac%7B%5Cpi%7D%7B4%7D%5Cright%29a%5C%5C%5C%5C%5C%5Cb%3D6-0.393%2A3.36%3D6-1.32%5C%5C%5C%5Cb%3D4.68)