3 is not the GCF, 30 is the GCF. The answer is 30(2+3).
Answer:
Step-by-step explanation:
<u>Volume of the prism:</u>
- V = Bh, where B- area of base, h- height
<u>Given:</u>
<u>Volume is:</u>
Use the double angle function sin2x = 2sinxcosx.
2sinxcosx + sinx = 0
For the first part of the problem, consider the solutions on the interval where sinx = 0
x = 0, pi
Now consider the solutions where sinx does NOT equal zero.
2sinxcosx + sinx = 0
2sinxcosx = - sinx
2cosx = - 1
cosx = - 1/2
x = 2pi/3, 4pi/3
To do this problem you need to find angle adc which is a part of angle BDA. angle BDA is 90 degrees so the 2 parts must add up to 90 degrees so you set up the problem like this
-2x + 144 - 3x +51 =90
then you combine like terms
-5x +195 = 90
then you subtract 195 from 90
-5x = -105
then you divide -5 by -5 and -105 by -5 and get
x=21
then you plug x in and get your angle measure
-3(21) +51
then you get the angle measure as 114 degrees.
