Answer:
x=20
Step-by-step explanation:
Square both sides
4+x/6=4
4+x=4*6
x=24-4
x=20
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:
P = $2448.89
P ~= $2,449
He need to deposit $2,449
Step-by-step explanation:
Given:
Interest rate r= 7% = 0.07
Number of years n = 3 years
Future value that should be meet A = $3000
We need to calculate the initial investment (Principal P). Using the compound interest formula:
A = P(1+r)^n
P = A/(1+r)^n
Substituting the values of A, r, n, we have;
P = 3000/(1+0.07)^3
P = $2448.89
P ~= $2,449
Answer:
2x^2 + 7x + 3 is the area of the rectangular piece of wood.
Step-by-step explanation:
Here,
Length ( l ) = x + 3
Breadth ( b ) = 2x + 1
Formula : -
Ar ( rectangle ) = lb
lb
= ( x + 3 ) ( 2x + 1 )
= x ( 2x + 1 ) + 3 ( 2x + 1 )
= 2x^2 + x + 6x + 3
= 2x^2 + 7x + 3
Answer:
$496,800
Step-by-step explanation:
Present cost = $480,000
%increase = 3.5%
Present price of the house = 480,000 + 3.5% of 480,000
= 480,000 + 0.035 * 480,000
= 480,000 + 16,800
= $496,800
Present price of the house = $496,800
