The dimensions of the square base after cutting the corners will be (40-2x). The depth of the box will be x, so its volume is given by
V = x(40-2x)²
You can differentiate this to get
V' = 12x² -320x -1600
Setting this to zero and factoring gives
(3x-20)(x-20) = 0
The appropriate choice of solutions is
x = 20/3 = 6 2/3
The
dimensions of the box of maximum volume are
26 2/3 in square by 6 2/3 in deepThe
maximum volume is
(80/3 in)²(20/3 in) =
4740 20/27 in³
Answer:
45 degrees
Step-by-step explanation:
Since we have a right triangle, we use the appropriate trigonometric ratio
The angle marked P faces QR and that makes it the opposite side
PR faces the right angle and that makes it the hypotenuse
The trigonometric ratio that links the opposite and the hypotenuse is the sine
It is the ratio of the opposite to the hypotenuse
Thus;
sin P = √26/2 √13
Sin P = √2/2
P = arc sin √2/2
P = 45 degrees
Answer:
Yes
Step-by-step explanation:
As long as the slopes of these two lines are not the same, they will intersect.
Given two points on a line, we can find the slope by taking the difference in the y coordinates and dividing it by the difference in the x coordinates.
Slope of 1st line: 
Slope of 2nd line: 
The slopes are not equal, therefore the lines intersect.
Answer:
$1200
Step-by-step explanation:
180 divided by 9 is 20, so they earned $20 per car washed. They want to wash 60 cars, and if they wash 60 cars they would earn $1200. (60 x 20)