Let the lengths of the bottom of the box be x and y, and let the length of the squares being cu be z, then
V = xyz . . . (1)
2z + x = 16 => x = 16 - 2z . . . (2)
2z + y = 30 => y = 30 - 2z . . . (3)
Putting (2) and (3) into (1) gives:
V = (16 - 2z)(30 - 2z)z = z(480 - 32z - 60z + 4z^2) = z(480 - 92z + 4z^2) = 480z - 92z^2 + 4z^3
For maximum volume, dV/dz = 0
dV/dz = 480 - 184z + 12z^2 = 0
3z^2 - 46z + 120 = 0
z = 3 1/3 inches
Therefore, for maximum volume, a square of length 3 1/3 (3.33) inches should be cut out from each corner of the cardboard.
The maximum volume is 725 25/27 (725.9) cubic inches.
it's x ≤ 3 :))) I found it out after realizing what you were asking
A)37 because is a prime number just sear up prime numbers on google
Answer:
JK = 20
Step-by-step explanation:
Angle Bisector Theorem: an angle bisector of a triangle divide the opposite side into two segments that are proportional to the other two sides of the triangle
LK / JK = LM / JM
(45 - JK) / JK = 75 / 60 = 5 / 4
5 JK = 4 (45 - JK)
5 JK = 180 - 4 JK
9 JK = 180
JK = 20
To find a fraction of an amount you divide by the denominator and times by the numerator (divide by the bottom times by the top)
£1 divided by 10 is 10 pence
10 pence times 1 is 10 pence
£1 divided by 10 is 10 pence
10 pence times 3 is 30 pence
50 pence divided by 5 is 10 pence
10 pence times 1 is 10 pence
£1 divided by 2 is 50 pence
50 pence timed 1 is 50 pence