Answer:
x+10 =2
x = -8
Step-by-step explanation:
plus means add
x+10 =2
Subtract 10 from each side
x+10-10 =2-10
x = -8
Complete Question
The complete question is shown on the first and second uploaded image
Answer:
The derived ![h = \frac{b^{2} - 2a^{2} }{2a^{2}}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7Bb%5E%7B2%7D%20-%202a%5E%7B2%7D%20%20%7D%7B2a%5E%7B2%7D%7D)
Step-by-step explanation:
Step One : Consider the ellipse in equilibrium.
Looking at the ellipse in equilibrium i.e when the ellipse has settled down on the concave support (represented by a parabola ) as shown on the third uploaded image.
Step Two : Consider the ellipse equation.
Generally the equation of the ellipse is given as
![\frac{x^{2}}{a^{2}} + \frac{(y-h)^{2}}{b^{2}}\\](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E%7B2%7D%7D%7Ba%5E%7B2%7D%7D%20%2B%20%5Cfrac%7B%28y-h%29%5E%7B2%7D%7D%7Bb%5E%7B2%7D%7D%5C%5C)
Also the base on which it rest at equilibrium i.e the parabola is represented by ![y = x^{2} -1](https://tex.z-dn.net/?f=y%20%3D%20x%5E%7B2%7D%20-1)
Substituting the value of y in the ellipse equation we have
![\frac{x^{2}}{a^{2}}+ \frac{(x^{2}-1-h)^{2}}{b^{2}}=1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E%7B2%7D%7D%7Ba%5E%7B2%7D%7D%2B%20%5Cfrac%7B%28x%5E%7B2%7D-1-h%29%5E%7B2%7D%7D%7Bb%5E%7B2%7D%7D%3D1)
Let ![x^{2} = t](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%3D%20t)
So the equation becomes
![\frac{t}{a^{2}} + \frac{(t -1 -h)^{2}}{b^{2}} =1](https://tex.z-dn.net/?f=%5Cfrac%7Bt%7D%7Ba%5E%7B2%7D%7D%20%2B%20%5Cfrac%7B%28t%20-1%20-h%29%5E%7B2%7D%7D%7Bb%5E%7B2%7D%7D%20%3D1)
Rearranging, we get :
![a^{2} t^{2} + (b^{2}- 2a^{2}(h +1))t + a^{2}((h +1 )^{2} -b^{2} =0](https://tex.z-dn.net/?f=a%5E%7B2%7D%20t%5E%7B2%7D%20%2B%20%28b%5E%7B2%7D-%202a%5E%7B2%7D%28h%20%2B1%29%29t%20%2B%20a%5E%7B2%7D%28%28h%20%2B1%20%29%5E%7B2%7D%20-b%5E%7B2%7D%20%3D0)
This equation above is a quadratic equation or a bi-quadratic equation in x as t =
Step Three : Relate the equation an the graph on the third uploaded image
We can see that from the graph , if A and B are the two values of x for which the points is made , then A + B = 0 (because they are symmetric in nature)
From Vieta's Roots(Vieta's formula is a formula that shows the relationship between the coefficients of a polynomial and the sum of its roots )
![ax^{2} + bx + c =0](https://tex.z-dn.net/?f=ax%5E%7B2%7D%20%2B%20bx%20%2B%20c%20%3D0)
with A and B as roots
A+B = ![\frac{-b}{a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%7D%7Ba%7D)
But A + B = 0
So
= 0
or we can say that
![\frac{b^{2} - 2a^{2}(h +1 )}{a^{2}}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%5E%7B2%7D%20-%202a%5E%7B2%7D%28h%20%2B1%20%29%7D%7Ba%5E%7B2%7D%7D)
Rearranging we get
![h = \frac{b^{2}- 2a^{2}}{2a^{2}}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7Bb%5E%7B2%7D-%202a%5E%7B2%7D%7D%7B2a%5E%7B2%7D%7D)
Answer:
136
Step-by-step explanation:
7*5=35
35+35=70
1/2*6*4=12
12+12=24
6*7=42
70+42+24=136
sorry if it is wrong.
Answer:
The first graph in the top left hand corner
Step-by-step explanation:
30-5*4+2
30-20+2
30-22
8
THE ANSWER IS 8