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
Answer: If you think of the relationship between two quantities, you can think of this relationship in terms of an input/output machine. If there is only one output for every input, you have a function. If not, you have a relation. You can conclude that this set of ordered pairs does not represent a function
Step-by-step explanation:
Hope this helps :) good luck!!
I think that is proportional
We know that:
time=distance/speed
if the tortoise speed is x m/min, then since 0.5 m/hr=1/120 m/min
18/x=23+18/(x+1/120)
solving for x we get:
x=0.08 m/min
speed of hare is:
(0.08+1/120)=0.088 m/min
