Answer:
x = 47 degrees.
Step-by-step explanation:
Note that the angle x + the angle 133 are on the same straight line DPC. So they add up to 180 degrees.
Therefore x + 133 = 180
x = 180 - 133
= 47 degrees.
The radius and height, in two decimal places are mathematically given as
r=10.60
<h3>What is the radius and height, in two decimal places?</h3>
Generally, the equation for the volume is mathematically given as
![V=\pi r^{2} h+\frac{2}{3} \pi r^{3}](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E%7B2%7D%20h%2B%5Cfrac%7B2%7D%7B3%7D%20%5Cpi%20r%5E%7B3%7D)
Therefore
![5000 &=\pi 0^{2} h+\frac{2}{3} \pi r^{3}](https://tex.z-dn.net/?f=5000%20%26%3D%5Cpi%200%5E%7B2%7D%20h%2B%5Cfrac%7B2%7D%7B3%7D%20%5Cpi%20r%5E%7B3%7D)
![V(r, h) &=\pi r^{2} h+\frac{2}{3} \pi r^{3}-5000 \\\nabla V &=\left\langle 2 \pi r h+2 \pi r^{2}, \pi r^{2}\right\rangle \\](https://tex.z-dn.net/?f=V%28r%2C%20h%29%20%26%3D%5Cpi%20r%5E%7B2%7D%20h%2B%5Cfrac%7B2%7D%7B3%7D%20%5Cpi%20r%5E%7B3%7D-5000%20%5C%5C%5Cnabla%20V%20%26%3D%5Cleft%5Clangle%202%20%5Cpi%20r%20h%2B2%20%5Cpi%20r%5E%7B2%7D%2C%20%5Cpi%20r%5E%7B2%7D%5Cright%5Crangle%20%5C%5C)
![\cos t &=100\left(2 \pi r^{2}\right)+75(2 \pi r h) \\\\\cos t &=200 \pi r^{2}+150 \pi r h \\\\\nabla C(r, h) &=\langle 400 \pi r+150 \pi h, 150 \pi r\rangle](https://tex.z-dn.net/?f=%5Ccos%20t%20%26%3D100%5Cleft%282%20%5Cpi%20r%5E%7B2%7D%5Cright%29%2B75%282%20%5Cpi%20r%20h%29%20%5C%5C%5C%5C%5Ccos%20t%20%26%3D200%20%5Cpi%20r%5E%7B2%7D%2B150%20%5Cpi%20r%20h%20%5C%5C%5C%5C%5Cnabla%20C%28r%2C%20h%29%20%26%3D%5Clangle%20400%20%5Cpi%20r%2B150%20%5Cpi%20h%2C%20150%20%5Cpi%20r%5Crangle)
Using Lagrange method
![$\langle 400 \pi \gamma+150 \pi \gamma h, 150 \pi \gamma\rangle=\lambda\left\langle 2 \pi \gamma h+2 \pi \gamma^{2}, \pi r^{2}\right\rangle$](https://tex.z-dn.net/?f=%24%5Clangle%20400%20%5Cpi%20%5Cgamma%2B150%20%5Cpi%20%5Cgamma%20h%2C%20150%20%5Cpi%20%5Cgamma%5Crangle%3D%5Clambda%5Cleft%5Clangle%202%20%5Cpi%20%5Cgamma%20h%2B2%20%5Cpi%20%5Cgamma%5E%7B2%7D%2C%20%5Cpi%20r%5E%7B2%7D%5Cright%5Crangle%24)
![$400 \pi r+150 \pi r=\left(2 \pi r h+2 \pi r^{2}\right) \lambda$](https://tex.z-dn.net/?f=%24400%20%5Cpi%20r%2B150%20%5Cpi%20r%3D%5Cleft%282%20%5Cpi%20r%20h%2B2%20%5Cpi%20r%5E%7B2%7D%5Cright%29%20%5Clambda%24)
![$400 \pi \gamma+150 \pi h=300 \pi h+300 \pi r \\\\](https://tex.z-dn.net/?f=%24400%20%5Cpi%20%5Cgamma%2B150%20%5Cpi%20h%3D300%20%5Cpi%20h%2B300%20%5Cpi%20r%20%5C%5C%5C%5C)
![$400 \pi r-300 \pi r=150 \pi h$](https://tex.z-dn.net/?f=%24400%20%5Cpi%20r-300%20%5Cpi%20r%3D150%20%5Cpi%20h%24)
![$160 \pi r=150 \pi h \quad \\\\\\](https://tex.z-dn.net/?f=%24160%20%5Cpi%20r%3D150%20%5Cpi%20h%20%5Cquad%20%5C%5C%5C%5C%5C%5C)
with
![h=\frac{2}{3} r $](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B2%7D%7B3%7D%20r%20%24)
![$\pi r^{2} h+\frac{2}{3} \pi r^{3}=5000$](https://tex.z-dn.net/?f=%24%5Cpi%20r%5E%7B2%7D%20h%2B%5Cfrac%7B2%7D%7B3%7D%20%5Cpi%20r%5E%7B3%7D%3D5000%24)
![\pi r}\left(\frac{2}{3} r \right)+\frac{2}{3} \pi^{3}=5000$](https://tex.z-dn.net/?f=%5Cpi%20r%7D%5Cleft%28%5Cfrac%7B2%7D%7B3%7D%20r%20%5Cright%29%2B%5Cfrac%7B2%7D%7B3%7D%20%5Cpi%5E%7B3%7D%3D5000%24)
![$\frac{4 \pi \gamma^{3}}{3}=5000 \quad](https://tex.z-dn.net/?f=%24%5Cfrac%7B4%20%5Cpi%20%5Cgamma%5E%7B3%7D%7D%7B3%7D%3D5000%20%5Cquad)
![r^{3}=\left(\frac{5000 \times 3}{4 \pi}\right)$](https://tex.z-dn.net/?f=r%5E%7B3%7D%3D%5Cleft%28%5Cfrac%7B5000%20%5Ctimes%203%7D%7B4%20%5Cpi%7D%5Cright%29%24)
r=10.60
In conclusion, the radius and height, in two decimal places is
r=10.60
Read more about radius
brainly.com/question/13449316
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The answer is 7 14/15. How do I get it? You add 1/3+4/5; which equals 1 2/15. Then you multiply 7, and you get your answer.
Answer:
area of circle having radius 3
is πr²=π*3²=9π square units
area of circle having radius 2
=πr²=π×2²=4π square units
again
area of big circle having radius [3+2]=5 units
=πr²=π×5²=25π square units
Now
<u>area</u><u> </u><u>of</u><u> </u><u>shaded</u><u> </u><u>region</u><u>=</u><u>2</u><u>5</u><u>π</u><u>-</u><u>4</u><u>π</u><u>-</u><u>9</u><u>π</u><u>=</u><u>1</u><u>2</u><u>π</u><u> </u><u>or</u><u> </u><u>3</u><u>7</u><u>.</u><u>7</u><u>s</u><u>q</u><u>u</u><u>a</u><u>r</u><u>e</u><u> </u><u>units</u><u>.</u>
Answer:
106
Step-by-step explanation:
![3^4+5*5](https://tex.z-dn.net/?f=3%5E4%2B5%2A5)
Apply PEMDAS:
In this scenario we will solve the exponent part first, followed by the multiplication part and then we add them up.
![\rightarrow3^4=3*3*3*3=81\\\\81+5*5\\\\\rightarrow5*5=25\\\\81+25\\\\\boxed{106}](https://tex.z-dn.net/?f=%5Crightarrow3%5E4%3D3%2A3%2A3%2A3%3D81%5C%5C%5C%5C81%2B5%2A5%5C%5C%5C%5C%5Crightarrow5%2A5%3D25%5C%5C%5C%5C81%2B25%5C%5C%5C%5C%5Cboxed%7B106%7D)
Hope this helps!