Answer:
2.67 inches.
Step-by-step explanation:
Assuming that we represent the size of the squares with the letter y, such that after the squares are being cut from each corner, the rectangular length of the box that is formed can now be ( 23 - 2y), the width to be (13 - 2y) and the height be (x).
The formula for a rectangular box = L × B × W
= (23 -2y)(13-2y) (y)
= (299 - 46y - 26y + 4y²)y
= 299y - 72y² + 4y³
Now for the maximum volume:
dV/dy = 0
This implies that:
299y - 72y² + 4y³ = 299 - 144y + 12y² = 0
By using the quadratic formula; we have :
where;
a = 12; b = -144 and c = 299
Since the width is 13 inches., it can't be possible for the size of the square to be cut to be 9.33
Thus, the size of the square to be cut out from each corner to obtain the maximum volume is 2.67 inches.
(5, -1)(10, 2) are solutions to this equation
Set up an equation:
45 = 4x +5 Subtract 5 from both sides.
40 = 4x Divide by 10 on both sides
10 = x.
Sal is 10 years old.
Answer:
Almost Correct!
Step-by-step explanation:
The general form of the equation of a circle is: x2 + y2 + Dx + Ey + F = 0, where D, E, F are constants. No factor multiplies the terms x2 and y2.
Using Distributive Property:
Combine and get all the terms in left sides and set it equal to zero and solve for m.
(m-5) (m-1) = -3 //Basic step of distribution.
m(m-1) -5(m-1) = -3
m^2 - m - 5m + 5 = -3 //Combine like terms and add 3 on both sides.
m^2 - 6m + 8 = 0 //Factor
m^2 - 4m - 2m + 8 = 0
m(m-4) -2(m -4) = 0
(m-4)(m-2) = 0 //Solve for m.
Got two equations:
1)m - 4 = 0
m = 4
2) m - 2 = 0
m = 2
Solution: m = 4, 2
//Hope this helps