Answer:
Step-by-step explanation:
The formula to find the angle between 2 vectors is
which is the dot product of u*v over the (magnitude of u times the magnitude of v). We also know that θ = 
. Filling in that formula requires us to find the dot product of u and v, which is
u·v = (2×(-6)) + (a×8) so
u·v = -12 + 8a. Then we need the magnitudes of both u and v:
and
Putting all of together looks like this:
. Cross multiply to get
which is tricky to simplify. You really need to know the rules for multiplying radicals to do this correctly. The simplification is
and we need to solve for a. Begin by squaring both sides to get rid of the square root to get:
100(8 + 2a²) = 256a² - 768a +576 and simplify some more by distributing through the parenthesis to get
800 + 200a² = 256a² -768a + 576. Combine like terms to come up with
0 = 56a² - 768a - 224 and we need to factor that. Assuming since you're this far in math (pre-calc or maybe late algebra 2) you know how to factor, when you do, you get values for a of - .285714... and 14.
Therefore, the value for a is 14. I checked it...it works
So to find the volume/ area of the cylinder, it is A =
, so the radius is half of the diameter which is 16, so the radii is 8. h is height, so multiply those together and youll get C: 2010.62
Answer:
Step-by-step explanation:
Answer:
x = 3.8
y = 15.2
Step-by-step explanation:
y = 4x
y = 19 - x,
if y = y then,
4x = 19 - x
5x = 19
x = 19/5 = 3.8 now inputting the answer to x into one of the unchanged equations above (y = 4x),
y = 4x = 4*3.8 = 15.2
Double check:
y = 19 - x = 19 - 3.8 = 15.2
