Answer:
sin(2A) = (2√2 + √3) / 6
Step-by-step explanation:
2A = (A+B) + (A−B)
sin(2A) = sin((A+B) + (A−B))
Angle sum formula:
sin(2A) = sin(A+B) cos(A−B) + sin(A−B) cos(A+B)
sin(2A) = 1/2 cos(A−B) + 1/3 cos(A+B)
Pythagorean identity:
sin(2A) = 1/2 √[1 − sin²(A−B)] + 1/3 √[1 − sin²(A+B)]
sin(2A) = 1/2 √(1 − 1/9) + 1/3 √(1 − 1/4)
sin(2A) = 1/2 √(8/9) + 1/3 √(3/4)
sin(2A) = 1/3 √2 + 1/6 √3
sin(2A) = (2√2 + √3) / 6
B (don’t mind this I need 20 characters
Answer:
x-1 = 0 or x-7 =0
x=1 or x=7
Step-by-step explanation:
(x-1) (x-7) =0
Using the zero product property
x-1 = 0 or x-7 =0
x-1+1 =0 +1 or x-7+7 =0+7
x=1 or x=7
Answer:
Add and subtract the second term to the expression and factor by grouping.
2
x
3
(
3
x
−
1
)
(
x
−
1
)
Step-by-step explanation:
now, that's the equation or polynomial in factored form, hmmm we also know that it has a y-intercept of -11, namely, when x = 0 y = -11, well let's plug in a factor to it, that will reflect those values, namely say hmmm factor "a", so
![(x+4)(x+2)(x-1)=y\qquad \stackrel{\textit{adding "a" factor for vertical shift}}{a(x+4)(x+2)(x-1)}=y \\\\\\ \stackrel{\textit{we know that when x = 0, y = -11}}{a(0+4)(0+2)(0-1)=-11}\implies -8a=-11\implies a=\cfrac{-11}{-8}\implies a = \cfrac{11}{8} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\mathbb{FOIL}}{\cfrac{11}{8}(x^2+6x+8)}(x-1)=y\implies \cfrac{11}{8}(x^3+6x^2+8x-x^2-6x-8)=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{11}{8}(x^3+5x^2+2x-8)=y~\hfill](https://tex.z-dn.net/?f=%28x%2B4%29%28x%2B2%29%28x-1%29%3Dy%5Cqquad%20%5Cstackrel%7B%5Ctextit%7Badding%20%22a%22%20factor%20for%20vertical%20shift%7D%7D%7Ba%28x%2B4%29%28x%2B2%29%28x-1%29%7D%3Dy%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bwe%20know%20that%20when%20x%20%3D%200%2C%20y%20%3D%20-11%7D%7D%7Ba%280%2B4%29%280%2B2%29%280-1%29%3D-11%7D%5Cimplies%20-8a%3D-11%5Cimplies%20a%3D%5Ccfrac%7B-11%7D%7B-8%7D%5Cimplies%20a%20%3D%20%5Ccfrac%7B11%7D%7B8%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Cmathbb%7BFOIL%7D%7D%7B%5Ccfrac%7B11%7D%7B8%7D%28x%5E2%2B6x%2B8%29%7D%28x-1%29%3Dy%5Cimplies%20%5Ccfrac%7B11%7D%7B8%7D%28x%5E3%2B6x%5E2%2B8x-x%5E2-6x-8%29%3Dy%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20~%5Chfill%20%5Ccfrac%7B11%7D%7B8%7D%28x%5E3%2B5x%5E2%2B2x-8%29%3Dy~%5Chfill)
