Answer:
7/25
Step-by-step explanation:
Let
so we have 
As
, we'll have ![\cos[2\arcsin(\frac{3}{5})]=\bigr[\cos(\arcsin(\frac{3}{5}))\bigr]^2-\bigr[(\sin(\arcsin(\frac{3}{5}))\bigr]^2](https://tex.z-dn.net/?f=%5Ccos%5B2%5Carcsin%28%5Cfrac%7B3%7D%7B5%7D%29%5D%3D%5Cbigr%5B%5Ccos%28%5Carcsin%28%5Cfrac%7B3%7D%7B5%7D%29%29%5Cbigr%5D%5E2-%5Cbigr%5B%28%5Csin%28%5Carcsin%28%5Cfrac%7B3%7D%7B5%7D%29%29%5Cbigr%5D%5E2)
To determine
, construct a right triangle with an opposite side of 3 and a hypotenuse of 5. This is because since
, then
. If you recognize the Pythagorean Triple 3-4-5, you can figure out that the adjacent side is 4, and thus,
. This means that
.
Hence, ![\cos[2\arcsin(\frac{3}{5})]=(\frac{4}{5})^2-(\frac{3}{5})^2=\frac{16}{25}-\frac{9}{25}=\frac{7}{25}](https://tex.z-dn.net/?f=%5Ccos%5B2%5Carcsin%28%5Cfrac%7B3%7D%7B5%7D%29%5D%3D%28%5Cfrac%7B4%7D%7B5%7D%29%5E2-%28%5Cfrac%7B3%7D%7B5%7D%29%5E2%3D%5Cfrac%7B16%7D%7B25%7D-%5Cfrac%7B9%7D%7B25%7D%3D%5Cfrac%7B7%7D%7B25%7D)
Answer:
≈ 52m^2
Step-by-step explanation:
1)the face of a semicircle: (
*r^2)/2
2)the face of a rectangle: 6*5
3)the face of a triangle: (3*5)/2
1) d=6m r=3m (3.14*3^2)/2=28.26/2=14.13
2) 6*5=30
3) (3*5)/2=15/2=7,5
Full surface: 14.13+30+7.5=51.63
answer: 51.63m^2 ≈ 52m^2
Answer:
87.5(the first one)
Step-by-step explanation:
first simplify 4 to the 5th power(20) and multiply by 4 to the -7th(-35) and you will get -700 divide that by 4 to the -2nd(-8) and you will get 87.5
Answer:
x = 3 ± 
or
x = 3 +
, x = 3 - 
Step-by-step explanation:
given f(x) = 2(x - 3)^2 - 8, find when f(x) = 40
So, we plug in 40 for f(x) in the 1st equation and solve for x. (Aim to got x on its own)
40 = 2 (x - 3)^2 - 8
+ 8 + 8
-----------------------------
48 = 2 (x - 3)^2
/2 /2
-----------------------------
24 = (x - 3)^2
square root both sides
--------------------
= x - 3
x = 3 ± 