The answer is: Two possible solutions which are (0.53, 37.19)
Explanation:
Given:
A = 30°
<span>a = 20 </span>
<span>b = 16 </span>
Now use the law of Cosines:
a² = b² + c² - 2bc*cos(A)
Plug in the values:
20² = 16² + c² - (2*(16)*c*cos(30))
<span>400 = 256 + c² - 32c(0.866) </span>
<span>400 = 256 + c² - 27.71c </span>
<span>c² - 27.71c = 400 - 256 </span>
<span>c² - 27.71c = 144 </span>
<span>c² - 27.71c + 191.96 = 144 + 191.96 </span>
<span>(c - 18.86)² = 335.96 </span>
<span>c - 18.86 = √336.95 </span>
<span>c - 18.86 = ± 18.33 </span>
<span>c = 18.86 ± 18.33 </span>
<span>If c = 18.86 + 18.33, then </span><span>c = 37.19 </span>
<span>If c = 18.86 - 18.33, then </span><span>c = 0.53 </span>
<span>c = (0.53, 37.19) Two solutions!</span>
A=p(1+rt)
3514=3500(1+(1/12)r)
Solve for r
r=0.048*100=4.8%
Answer:
x = -15/2
Step-by-step explanation:
For this problem, we will simply use equation properties to solve for x.
2x - 5 = -20
2x - 5 + 5 = -20 + 5
2x = -15 ( Add positive 5 to both sides )
2x * (1/2) = -15 * (1/2)
x = -15/2 ( Multiply both sides by 1/2)
Hence, the solution to x is -15 / 2.
Cheers.
Answer:
Radius of sphere = 3 feet
Step-by-step explanation:
The volume of sphere is 36 π ft³.
We need to find the radius of sphere.
The formula used is: 
Putting value of volume and finding radius
![Volume\:of\:sphere=\frac{4}{3}\pi r^3\\36\pi =\frac{4}{3}\pi r^3\\r^3=36 \pi \times \frac{3}{4\pi} \\r^3=9 \times 3\\r^3=27\\Taking\:cube\;root\:on \:both\:sides\\\sqrt[3]{r^3}=\sqrt[3]{27}\\r=3](https://tex.z-dn.net/?f=Volume%5C%3Aof%5C%3Asphere%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3%5C%5C36%5Cpi%20%3D%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3%5C%5Cr%5E3%3D36%20%5Cpi%20%5Ctimes%20%5Cfrac%7B3%7D%7B4%5Cpi%7D%20%5C%5Cr%5E3%3D9%20%5Ctimes%203%5C%5Cr%5E3%3D27%5C%5CTaking%5C%3Acube%5C%3Broot%5C%3Aon%20%5C%3Aboth%5C%3Asides%5C%5C%5Csqrt%5B3%5D%7Br%5E3%7D%3D%5Csqrt%5B3%5D%7B27%7D%5C%5Cr%3D3)
So, Radius of sphere = 3 feet
Answer:
D
Step-by-step explanation:
y<2
y<x+2
y>-1/4-3
if you plug in one of the points in the included grey area the equations should be true
