B.) Hibiscus Street
The key thing to remember is the slope of the lines. The equation for a line in slope intercept form is
y = ax + b
where
a = slope
b = y intercept
So the equation for Oak Street is y = 2/3x - 7. So it's slope is 2/3. And any street that has the same slope will be given a tree name. And any street that's perpendicular will be given a flower name. You can determine is a line is perpendicular if it has a slope that's the negative reciprocal. So a street that's perpendicular to Oak street will have a slope of -3/2.
Now you've just been given the equation to a new street that's y = -3/2x - 2. Since the slope is -3/2 and Oak street has a slope of 2/3, the new street is perpendicular to Oak street. And given the naming scheme, that means that the new street will have the name of a flower. So let's look at the available street names and pick a flower.
<span>
A.) Weeping Willow Street
* Nope a Weeping Willow is a tree. So this name won't work.
B.) Hibiscus Street
* Yes. A Hibiscus is a flower, so this name is suitable.
C.) Oak Street
* Nope. Not only is this a tree instead of a flower, but there's already an Oak street. So bad choice.
D.) Panther Street
* Nope, this is an animal, not a flower. Bad choice.
</span>
372819388338822814738288919147477483822 okay i guess
F(x)= 1/4x the slope goes 0.25 upwards
The formula for the average value of a function is
where b is the upper bound and a is the lower. For us, this formula will be filled in accordingly.
. We will integrate that now:
![\frac{1}{2}[ \frac{2x^3}{3}+3x]](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%5B%20%5Cfrac%7B2x%5E3%7D%7B3%7D%2B3x%5D%20%20)
from 0 to 2. Filling in our upper and lower bounds we have
![\frac{1}{2}[( \frac{2(2^3)}{3}+3(2))-0]](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%5B%28%20%5Cfrac%7B2%282%5E3%29%7D%7B3%7D%2B3%282%29%29-0%5D%20%20)
which simplifies to
and
which is 17/3 or 5.667
