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 = 
Answer: it is 1/6
You can solve by saying, 1 out of 6 in each tray is red, so my fraction should be 1/6.
It doesn't matter the amount of trays because the pattern is always the same.
But if you want to check it out you can do it in this way.
You know there is 1 red color per tray, if there are 20 then you'd have 20 of them, in each tray there are 6 colors so the total is 120.
Now you solve it if there are 20 red colors out of 120 them the answer is 20/120, thus you get 1/6
Step-by-step explanation:
You multiply 80 by 0.15 to get 12. Twelve is the amount taken off from the original for the 15% off sale.
So, to get the sale price, subtract 12 dollars from 80.
The answer is $68.
Altogether there are 22 pencils
the probability of picking 1 blue pencil is 8/22
i hope this helps and is right :)
