Answer:
7√2
Step-by-step explanation:
Knowing that the angle is 45° (or π/4 radians) and the opposite leg has a length of 7, you can find the length of b with:
7 / b = sin(π / 4)
7 / (sin(π / 4)) = b
b = 7 / (1 / √2)
b =7√2
A simpler way to get the answer is to note that a right triangle with one 45° angle must be an isoceles right triangle, so both legs are the same length. Using the Pythagorean Theorem:
a² + 7² = b²
Since we know a = 7,
7² + 7² = b²
b = √(2 * 49)
b = 7√2
Answer:
When proving identities, the answer is in the explanation.
Step-by-step explanation:

I have two terms in this denominator here.
I also know that
by Pythagorean Identity.
So I don't know how comfortable you are with multiplying this denominator's conjugate on top and bottom here but that is exactly what I would do here. There will be other problems will you have to do this.

Big note here: When multiplying conjugates all you have to do is multiply fist and last. You do not need to do the whole foil. That is when you are multiplying something like
, the result is just
.
Let's do that here with our problem in the denominator.





In that last step, I apply the Pythagorean Identity I mentioned way above.
Now You have a factor of cos(y) on top and bottom, so you can cancel them out. What we are really saying is that cos(y)/cos(y)=1.

This is the desired result.
We are done.
1 L, or 1000 mL, of the drink contains 360 mL juice. If there is a total of 1600 mL, we have 360/1600=9/40 (or .225) as the concentration of juice.
Answer:
0.62
Step-by-step explanation:
Height = Volume / πr²
Answer:B
Step-by-step explanation:
y=13xy=\dfrac{1}{3}xy=31xy, equals, start fraction, 1, divided by, 3, end fraction, x