Find the mid point interval for all of the scores and multiply it by it’s respected frequency
10x9
13x29.5
21x49.5
34x69.5
17x89.5
Then add all of the equations together say the answer is x
Then you will go x/94
To get the mean
<span>parallel has same slope = 4
y = mx + b
b = y - mx
b = 3 - 4(-5)
b = 3 + 20
b = 23
equation
y = 4x + 23</span>
Plug
into the equation of the ellipsoid:
![x^2+7(x^2)^2+7z^2=49](https://tex.z-dn.net/?f=x%5E2%2B7%28x%5E2%29%5E2%2B7z%5E2%3D49)
Complete the square:
![7x^4+x^2=7\left(x^4+\dfrac{x^2}7+\dfrac1{14^2}-\dfrac1{14^2}\right)=7\left(x^2+\dfrac1{14}\right)^2+\dfrac1{28}](https://tex.z-dn.net/?f=7x%5E4%2Bx%5E2%3D7%5Cleft%28x%5E4%2B%5Cdfrac%7Bx%5E2%7D7%2B%5Cdfrac1%7B14%5E2%7D-%5Cdfrac1%7B14%5E2%7D%5Cright%29%3D7%5Cleft%28x%5E2%2B%5Cdfrac1%7B14%7D%5Cright%29%5E2%2B%5Cdfrac1%7B28%7D)
Then the intersection is such that
![7\left(x^2+\dfrac1{14}\right)^2+7z^2=\dfrac{1371}{28}](https://tex.z-dn.net/?f=7%5Cleft%28x%5E2%2B%5Cdfrac1%7B14%7D%5Cright%29%5E2%2B7z%5E2%3D%5Cdfrac%7B1371%7D%7B28%7D)
![\left(x^2+\dfrac1{14}\right)^2+z^2=\dfrac{1371}{196}](https://tex.z-dn.net/?f=%5Cleft%28x%5E2%2B%5Cdfrac1%7B14%7D%5Cright%29%5E2%2Bz%5E2%3D%5Cdfrac%7B1371%7D%7B196%7D)
which resembles the equation of a circle, and suggests a parameterization is polar-like coordinates. Let
![x(t)^2+\dfrac1{14}=\sqrt{\dfrac{1371}{196}}\cos t\implies x(t)=\pm\sqrt{\sqrt{\dfrac{1371}{196}}\cos t-\dfrac1{14}}](https://tex.z-dn.net/?f=x%28t%29%5E2%2B%5Cdfrac1%7B14%7D%3D%5Csqrt%7B%5Cdfrac%7B1371%7D%7B196%7D%7D%5Ccos%20t%5Cimplies%20x%28t%29%3D%5Cpm%5Csqrt%7B%5Csqrt%7B%5Cdfrac%7B1371%7D%7B196%7D%7D%5Ccos%20t-%5Cdfrac1%7B14%7D%7D)
![y(t)=x(t)^2=\sqrt{\dfrac{1371}{196}}\cos t-\dfrac1{14}](https://tex.z-dn.net/?f=y%28t%29%3Dx%28t%29%5E2%3D%5Csqrt%7B%5Cdfrac%7B1371%7D%7B196%7D%7D%5Ccos%20t-%5Cdfrac1%7B14%7D)
![z=\sqrt{\dfrac{1371}{196}}\sin t](https://tex.z-dn.net/?f=z%3D%5Csqrt%7B%5Cdfrac%7B1371%7D%7B196%7D%7D%5Csin%20t)
(Attached is a plot of the two surfaces and the intersection; red for the positive root
, blue for the negative)
1.
the angle should add up to 360
so
360-110-90=160
that is the answer
2.
the angle has to add up to 90
so
90-57=33
Answer:
f(-8) = -18
Step-by-step explanation:
given :
f(x) = 2(x – 3) + 4
to find f(-8), simply substitute x= -8 into the function:
f(x) = 2(x – 3) + 4
f(-8) = 2[(-8) – 3] + 4
= 2[-8 – 3] + 4
= 2[-11] + 4
= -22+4
= -18