Answer:
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola
y=5−x^2. What are the dimensions of such a rectangle with the greatest possible area?
Width =
Height =
Width =√10 and Height 
Step-by-step explanation:
Let the coordinates of the vertices of the rectangle which lie on the given parabola y = 5 - x² ........ (1)
are (h,k) and (-h,k).
Hence, the area of the rectangle will be (h + h) × k
Therefore, A = h²k ..... (2).
Now, from equation (1) we can write k = 5 - h² ....... (3)
So, from equation (2), we can write
![A =h^{2} [5-h^{2} ]=5h^{2} -h^{4}](https://tex.z-dn.net/?f=A%20%3Dh%5E%7B2%7D%20%5B5-h%5E%7B2%7D%20%5D%3D5h%5E%7B2%7D%20-h%5E%7B4%7D)
For, A to be greatest ,
⇒ ![h[10-4h^{2} ]=0](https://tex.z-dn.net/?f=h%5B10-4h%5E%7B2%7D%20%5D%3D0)
⇒ 
⇒ 
Therefore, from equation (3), k = 5 - h²
⇒ 
Hence,
Width = 2h =√10 and
Height = 
The top-left graph goes with the bottom-right equation, y=90(1/4)^x
The bottom-left graph goes with the top-right equation, y = 120(3/4)^x
The top-right graph goes with the bottom-left equation, y = 120(1/4)^x
The bottom-right graph goes with the top-left equation, y = 90(3/4)^x
y=90(1/4)^x has a larger percent decrease than y = 90(3/4)^x
cause if you multiply a number by 1/4, that's smaller than multiplying number by 3/4. so y=90(1/4)^x decreases really fast
same with the y = 120(3/4)^x ones
Answer:
division
Step-by-step explanation:
2x/2=8/2=x=4
x=4
Just by simply adding the two quantities you can get the net change. $67.12 +(addition sign because we want the net change) $2.56= $69.68. The last number is the net change!
Divide 327 by 12 to get 27.25. Howard pays 27 dollars and 25 cents for each card.
