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.
The answers are: 4.5 g and 56.25 g respectively.
Since the first type of measurement in this question is weight or mass, I'll suppose that the percentage concentration is % mass/mass. For that type of concentration measurement, just multiply the percentage by the total mass to get the mass of the wanted material.
So 150 g * 3% = 150 g * 0.03 = 4.5g
For the 8% solution with the same amount of dry substance, use the ratio of percentages, multiplied by the mass of the first solution to get the wanted amount of new solution:
3/8 * 150 g = 56.35 g
ME but i have a math test sadly
Option B) 37.12 is the right answer
Step-by-step explanation:
It is given that the qudrilateral is a rectangle which means that opposite sides wil be equal and all interior angles will be 90 degrees
So
PS = 17
PQ = SR = 33
The diagonal PR will form a right-angles triangle with PR being the hypotenuse
So,
Base = SR = 33
Perpendicular = PS = 17
Hypotenuse = PR = ?
The Pythagoras theorem will be used to find the length of PR
So,
Taking square root on both sides
Rounding off to nearest 100th
PR = 37.12
Hence,
Option B) 37.12 is the right answer
Keywords: Triangle, Pythagoras theorem
Learn more about triangles at:
#LearnwithBrainly
A- 3 o clock
b- 11
c- 7
d- 4
e- 10
f- 1
