Any tangent line to
![y=x^2-x](https://tex.z-dn.net/?f=y%3Dx%5E2-x)
at a point
![(a,b)=(a,a^2-a)](https://tex.z-dn.net/?f=%28a%2Cb%29%3D%28a%2Ca%5E2-a%29)
will have slope
![y'(a)=2x-1\bigg_{x=a}=2a-1](https://tex.z-dn.net/?f=y%27%28a%29%3D2x-1%5Cbigg_%7Bx%3Da%7D%3D2a-1)
. Such a line has equation
![y-(a^2-a)=(2a-1)(x-a)\implies y=(2a-1)x-a^2](https://tex.z-dn.net/?f=y-%28a%5E2-a%29%3D%282a-1%29%28x-a%29%5Cimplies%20y%3D%282a-1%29x-a%5E2)
For this (these) line(s) to pass through (2, -3), you must have
![-3=(2a-1)\times2-a^2\implies a^2-4a-1=0\implies a=2\pm\sqrt5](https://tex.z-dn.net/?f=-3%3D%282a-1%29%5Ctimes2-a%5E2%5Cimplies%20a%5E2-4a-1%3D0%5Cimplies%20a%3D2%5Cpm%5Csqrt5)
So the two lines in questions are
![y=(2a-1)x-a^2](https://tex.z-dn.net/?f=y%3D%282a-1%29x-a%5E2)
for these values of
![a](https://tex.z-dn.net/?f=a)
.
To show there is no tangent line that passes through (2, 7), you have to show there is no solution for
![a](https://tex.z-dn.net/?f=a)
in
![7=(2a-1)\times2-a^2](https://tex.z-dn.net/?f=7%3D%282a-1%29%5Ctimes2-a%5E2)
You have
![a^2-4a+9=0](https://tex.z-dn.net/?f=a%5E2-4a%2B9%3D0)
but this has no real solutions, so no such tangent line exists.
You need to split the shape into simpler shapes so you would get a rectangular prism and a triangular prism finding the volume is pretty straightforward the formula is
Volume of a triangular prism = area of base triangle × height
The formula for finding the volume of a rectangular prism is the following: Volume = Length * Height * Width, or V = L * H * W.
After solving for this you would just have to add the 2 shapes volume together tie get the volume of the composite figure
Finding the surface area is also pretty simple since it would only require you to know the formulas
S = 2(lw + lh + wh) to find the surface area of a rectangle or prism
A=12bh is used to find the area of the top and bases triangular faces, where A = area, b = base, and h = height.
And by adding the two surface areas of the shapes you can get the surface area of the composite figure but remember to subtract the top face of the rectangular prism and the bottom face of the triangular prism
Hope this helps <3
Answer:
x=22.8 inches
I think T__T
Step-by-step explanation:
YES... SOMETHING I KNOW!
Use Pythagorean theroy
say 42.7=a
48.4=b
x=c
the formula is: a^2+c^2=b^2
so: 42.7^2+x^2=48.4^2
if we simplify:=1823.29+x^2=2342.56
then:519.27=x^2
It says, round to the nearest TENTH
x=22.787497
so then x would be
22.80
The formula for exponential growth is y = amount(1+r)^x
Where amount would be the starting value, r would be the percentage and x would be the length of time.
The listed formula that meets that is D. y = 35(1.35)^x