Yes, they intersect at roughly (4.2,5.2).
Answer:
C. 40.2°
Step-by-step explanation:
Cosine rule (real handy to remember): c² = a² + b² - 2·a·b·cos(γ)
If you don't know this yet, look it up but in short: c, a and b are the lengths of the sides of the triangle, the angle opposite side a is called α, for b it is β and for c it is γ. That's the convention I've always used anyway, you can call them whatever of course. Anyhow:
c² = a² + b² - 2·a·b·cos(γ)
⇒ |AC|² = |AB|²+|BC|²-2·|AB|·|BC|·cos(∠B)
⇒ |AC|²-|AB|²-|BC|² = -2·|AB|·|BC|·cos(∠B)
⇒ ( |AC|²-|AB|²-|BC|² ) / ( -2·|AB|·|BC| ) = cos(∠B)
⇒ ∠B = arccos( ( |AC|²-|AB|²-|BC|² ) / ( -2·|AB|·|BC| ) )
= arccos( ( 11²-16²-16² ) / ( -2·16·16 ) )
= 40.21101958°
≈ 40.2°
Hello!
Recall that:
![\sqrt[z]{x^{y} }](https://tex.z-dn.net/?f=%5Csqrt%5Bz%5D%7Bx%5E%7By%7D%20%7D)
is equal to 
. Therefore:
![\sqrt[3]{x^{2} } = x^{\frac{2}{3} }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E%7B2%7D%20%7D%20%3D%20x%5E%7B%5Cfrac%7B2%7D%7B3%7D%20%7D)
There is also an exponent of '6' outside. According to exponential properties, when an exponent is within an exponent, you multiply them together. Therefore:
Surface area is 4piR^2
Volume is 4/3 piR^3
R is the radius (half the diameter). Just plug in the numbers
