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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
For, A to be greatest ,
⇒
⇒
⇒
Therefore, from equation (3), k = 5 - h²
⇒
Hence,
Width = 2h =√10 and
Height =
Answer:
So, the required width of rectangular piece of aluminium is 8 inches
Step-by-step explanation:
We are given:
Perimeter of rectangular piece of aluminium = 62 inches
Let width of rectangular piece of aluminium = w
and length of rectangular piece of aluminium = w+15
We need to find width i.e value of x
The formula for finding perimeter of rectangle is:
Now, Putting values in formula for finding Width w:
After solving we get the width of rectangular piece :w = 8
So, the required width of rectangular piece of aluminium is 8 inches