Answer:
C
Step-by-step explanation:
For any of the functions described above, the only way any of those could be functions is that there has to be a difference value for each x, unless it is the same x-value. If the x is mentioned twice, that is fine, as long as the y point is also the same. If it is different, it is not a function.
Answer:
x=11, y=10
Step-by-step explanation:
x= 6+ (1/2)y
x+y=21
substitute the first equation into the second equation:
(6+ (1/2y)) + y =21
to get:
y=10
then to find x:
x+ 10 = 21
x=11
Answer: 32 feet
Step-by-step explanation:
well if each side is 8ft you would then add up all the sides, and it would equal 32ft
Answer:
Option C.
The distance from the point to the circle is 6 units
Step-by-step explanation:
we know that
The distance between the circle and the point will be the difference of the distance of the point from the center of circle and the radius of the circle
step 1
Find the center and radius of the circle
we have
![x^{2} +y^{2}-8y=0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2By%5E%7B2%7D-8y%3D0)
Convert to radius center form
Complete the square
![x^{2} +(y^{2}-8y+16)=0+16](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%28y%5E%7B2%7D-8y%2B16%29%3D0%2B16)
Rewrite as perfect squares
![x^{2} +(y-4)^{2}=16](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%28y-4%29%5E%7B2%7D%3D16)
so
The center is the point (0,4)
The radius is
![r^{2}=16\\r=4\ units](https://tex.z-dn.net/?f=r%5E%7B2%7D%3D16%5C%5Cr%3D4%5C%20units)
step 2
Find the distance of the point from the center of circle
the formula to calculate the distance between two points is equal to
![d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28y2-y1%29%5E%7B2%7D%2B%28x2-x1%29%5E%7B2%7D%7D)
we have
(6,-4) and (0,4)
substitute the values
![d=\sqrt{(4+4)^{2}+(0-6)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%284%2B4%29%5E%7B2%7D%2B%280-6%29%5E%7B2%7D%7D)
![d=\sqrt{(8)^{2}+(-6)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%288%29%5E%7B2%7D%2B%28-6%29%5E%7B2%7D%7D)
![d=\sqrt{100}\ units](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B100%7D%5C%20units)
![d=10\ units](https://tex.z-dn.net/?f=d%3D10%5C%20units)
step 3
Find the difference of the distance of the point from the center of circle and the radius of the circle
![10\ units-4\ units=6\ units](https://tex.z-dn.net/?f=10%5C%20units-4%5C%20units%3D6%5C%20units)
therefore
The distance from the point to the circle is 6 units
see the attached figure to better understand the problem
Given the rate of water flow is given by:
r(t)=85e^(-0.04t)
thus the amount of water flow in the first hour when t=1, will be:
r(1)=85e^(-0.04*1)
=81.667
thus the amount of water that flowed out will be:
85-81.667
=3.333 liters