Answer:
the length of the opposite side (x), is 27.2
Step-by-step explanation:
For the given right triangle problem;
the opposite side of the given angle, opp. = 22
the hypothenuse side, hypo. = x
given angle of the triangle, θ = 54⁰
The length of the opposite side (x), is calculated as follows;
![sin \ \theta = \frac{opp.}{hypo.} \\\\sin (54) = \frac{22}{x} \\\\x = \frac{22}{sin(54)} \\\\x = 27.2](https://tex.z-dn.net/?f=sin%20%5C%20%5Ctheta%20%3D%20%5Cfrac%7Bopp.%7D%7Bhypo.%7D%20%5C%5C%5C%5Csin%20%2854%29%20%3D%20%5Cfrac%7B22%7D%7Bx%7D%20%5C%5C%5C%5Cx%20%3D%20%5Cfrac%7B22%7D%7Bsin%2854%29%7D%20%5C%5C%5C%5Cx%20%3D%2027.2)
Therefore, the length of the opposite side (x), is 27.2
Answer:
4.5 % alloy
Step-by-step explanation:
Let x = amt of 30% alloy
The resulting total is to be 25 oz, therefore:
(25-x) = amt of 5% alloy:
A typical mixture equation:
.30x + .05(25-x) = .20(25)
.30x + 1.25 - .05x = 5 .30x - .05x = 5 - 1.25
.25x = 3.75
x = 3.75%2F.25
x = 15 oz of 30% alloy required
then
25-15 = 10 oz of 5% alloy:
Check solution
.30(15) + .05(10) = .20(25)
4.5 + .5 = 5
![f(x)=\frac{1}{x^2-9}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7Bx%5E2-9%7D)
The denominator can't be equal to 0.
![x^2-9 \not= 0 \\ x^2 \not= 9 \\ x \not= -3 \ \land \ x \not= 3](https://tex.z-dn.net/?f=x%5E2-9%20%5Cnot%3D%200%20%5C%5C%0Ax%5E2%20%5Cnot%3D%209%20%5C%5C%0Ax%20%5Cnot%3D%20-3%20%5C%20%5Cland%20%5C%20x%20%5Cnot%3D%203)
The domain is all numbers except -3 and 3.
13h and 5min. Hope this helps:)