Answer:
For this case, the parent function is given by:
f (x) = x ^ 2
We apply the following transformations:
Horizontal translations:
Suppose that h> 0
To graph y = f (x + h), move the graph of h units to the left.
We have then for h = 5:
y = (x + 5) ^ 2
Vertical translations :
Suppose that k> 0
To graph y = f (x) -k, move the graph of k units down.
We then have for k = 9:
g (x) = (x + 5) ^ 2 - 9
Answer:
The graph of g (x) is the graph of f (x) 5 units to the left and 9 units to down
<h2>
Please mark me as brainlyist</h2>
Answer:
Radius=2.09 cm
Height,h=14.57 cm
Step-by-step explanation:
We are given that
Volume of cylinderical shaped can=200 cubic cm.
Cost of sides of can=0.02 cents per square cm
Cost of top and bottom of the can =0.07 cents per square cm
Curved surface area of cylinder=![2\pi rh](https://tex.z-dn.net/?f=2%5Cpi%20rh)
Area of circular base=Area of circular top=![\pi r^2](https://tex.z-dn.net/?f=%5Cpi%20r%5E2)
Total cost,C(r)=![0.02\times 2\pi rh+2\pi r^2\times 0.07](https://tex.z-dn.net/?f=0.02%5Ctimes%202%5Cpi%20rh%2B2%5Cpi%20r%5E2%5Ctimes%200.07)
Volume of cylinder,![V=\pi r^2 h](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E2%20h)
![200=\pi r^2 h](https://tex.z-dn.net/?f=200%3D%5Cpi%20r%5E2%20h)
![h=\frac{200}{\pi r^2}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B200%7D%7B%5Cpi%20r%5E2%7D)
Substitute the value of h
![C(r)=0.02\times 2\pi r\times \frac{200}{\pi r^2}+2\pi r^2\times 0.07](https://tex.z-dn.net/?f=C%28r%29%3D0.02%5Ctimes%202%5Cpi%20r%5Ctimes%20%5Cfrac%7B200%7D%7B%5Cpi%20r%5E2%7D%2B2%5Cpi%20r%5E2%5Ctimes%200.07)
![C(r)=\frac{8}{r}+0.14\pi r^2](https://tex.z-dn.net/?f=C%28r%29%3D%5Cfrac%7B8%7D%7Br%7D%2B0.14%5Cpi%20r%5E2)
Differentiate w.r.t r
![C'(r)=-\frac{8}{r^2}+0.28\pi r](https://tex.z-dn.net/?f=C%27%28r%29%3D-%5Cfrac%7B8%7D%7Br%5E2%7D%2B0.28%5Cpi%20r)
![C'(r)=0](https://tex.z-dn.net/?f=C%27%28r%29%3D0)
![-\frac{8}{r^2}+0.28\pi r=0](https://tex.z-dn.net/?f=-%5Cfrac%7B8%7D%7Br%5E2%7D%2B0.28%5Cpi%20r%3D0)
![0.28\pi r=\frac{8}{r^2}](https://tex.z-dn.net/?f=0.28%5Cpi%20r%3D%5Cfrac%7B8%7D%7Br%5E2%7D)
![r^3=\frac{8}{0.28\pi}=9.095](https://tex.z-dn.net/?f=r%5E3%3D%5Cfrac%7B8%7D%7B0.28%5Cpi%7D%3D9.095)
![r=(9.095)^{\frac{1}{3}}=2.09](https://tex.z-dn.net/?f=r%3D%289.095%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D2.09)
Again, differentiate w.r.t r
![C''(r)=\frac{16}{r^3}+0.28\pi](https://tex.z-dn.net/?f=C%27%27%28r%29%3D%5Cfrac%7B16%7D%7Br%5E3%7D%2B0.28%5Cpi)
Substitute the value of r
![C''(2.09)=\frac{16}{(2.09)^3}+0.28\pi=2.63>0](https://tex.z-dn.net/?f=C%27%27%282.09%29%3D%5Cfrac%7B16%7D%7B%282.09%29%5E3%7D%2B0.28%5Cpi%3D2.63%3E0)
Therefore,the product cost is minimum at r=2.09
h=![\frac{200}{\pi (2.09)^2}=14.57](https://tex.z-dn.net/?f=%5Cfrac%7B200%7D%7B%5Cpi%20%282.09%29%5E2%7D%3D14.57)
Radius of can,r=2.09 cm
Height of cone,h=14.57 cm
Product of powers property tells us that when you multiply powers with the same base you just have to add the exponents.
Answer:
it’s 15x+30y-220
Step-by-step explanation:
Because you distribute and then you add the like terms
Answer:
so b=-9 while c=12.
Step-by-step explanation:
If you have x-intercepts 1 and -4, then that means f(1)=0 and f(-4)=0.
You are given ![f(x)=-3x^2+bx+c](https://tex.z-dn.net/?f=f%28x%29%3D-3x%5E2%2Bbx%2Bc)
So you have the system of equations to solve:
![f(1)=-3(1)^2+b(1)+c=0](https://tex.z-dn.net/?f=f%281%29%3D-3%281%29%5E2%2Bb%281%29%2Bc%3D0)
![f(-4)=-3(-4)^2+b(-4)+c=0](https://tex.z-dn.net/?f=f%28-4%29%3D-3%28-4%29%5E2%2Bb%28-4%29%2Bc%3D0)
Evaluating the exponents:
![-3(1)+b+c=0](https://tex.z-dn.net/?f=-3%281%29%2Bb%2Bc%3D0)
![-3(16)-4b+c=0](https://tex.z-dn.net/?f=-3%2816%29-4b%2Bc%3D0)
Doing a little bit of multiplying:
![-3+b+c=0](https://tex.z-dn.net/?f=-3%2Bb%2Bc%3D0)
![-48-4b+c=0](https://tex.z-dn.net/?f=-48-4b%2Bc%3D0)
Let's add 3 on both sides of equation 1 and 48 on both sides of equation 2:
![b+c=3](https://tex.z-dn.net/?f=b%2Bc%3D3)
![-4b+c=48](https://tex.z-dn.net/?f=-4b%2Bc%3D48)
Subtracting the equations will eliminate c.
Let's do that:
![5b+0c=-45](https://tex.z-dn.net/?f=5b%2B0c%3D-45)
![5b=-45](https://tex.z-dn.net/?f=5b%3D-45)
Divide both sides by 5:
![b=\frac{-45}{5}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B-45%7D%7B5%7D)
Simplify:
![b=-9](https://tex.z-dn.net/?f=b%3D-9)
If b=-9 and b+c=3 then -9+c=3 implies c=9+3=12.
so b=-9 while c=12.