Let us say that x is the cut that we will make on the
sides to make a box, therefore the new dimensions are:
l = 15 – 2x
w = 8 – 2x
It is 2x since we cut on two sides.
We know that volume is:
V = l w x
V = (15 – 2x) (8 – 2x) x
V = 120x – 30x^2 – 16x^2 + 4x^3
V = 120x – 46x^2 + 4x^3
Taking the 1st derivative:
dV/dx = 120 – 92x + 12x^2
Set dV/dx = 0 to get maxima:
120 – 92x + 12x^2 = 0
Divide by 12:
x^2 – (92/12)x + 10 = 0
(x – (92/24))^2 = -10 + (92/24)^2
x - 92/24 = ±2.17
x = 1.66, 6
We cannot have x = 6 because that will make our w
negative, so:
x = 1.66 inches
So the largest volume is:
V = 120x – 46x^2 + 4x^3
V = 120(1.66) – 46(1.66)^2 + 4(1.66)^3
V = 90.74 cubic inches
If its just a number 2,300 is an answer
Acceleration means speeding up, slowing down, or changing direction. The graph doesn't show anything about direction, so we just have to examine it for speeding up or slowing down ... any change of speed.
The y-axis of this graph IS speed. So the height of a point on the line is speed. If the line is going up or down, then speed is changing.
Sections a, c, and d are all going up or down. Section b is the only one where speed is not changing. So we can't be sure about b, because we don't know if the track may be curving ... the graph can't tell us that. But a, c, and d are DEFINITELY showing acceleration.
Answer:
The car must be moving away from the person.
Explanation:
From Doppler's Effect, we know that when a sound source moves towards a stationary observer, the apparent frequency of that sound increases. While the apparent frequency decreases if the source moves away from the stationary observer.
The audible range of frequencies for a human ear is 20 Hz to 20000 Hz. Therefore, in order for the sound of a loud speaker to be audible for the person, the frequency must decrease below 20000 Hz.
<u>Due to this reason, the car must be moving away from the person.</u>
Answer:
A. 231.77 J
B. 5330.71 J
C. 46 donuts
Explanation:
A. To lift the barbell once, she will have to extend it the full length of her arm. The work done will then be:
W = F * d
Where the force is the weight of the barbell.
F = m * g
Hence, the work done in lifting the barbell is:
W = m * g * d
W = 43 * 9.8 * 0.55
W = 231.77 J
B. If she does 23 repetitions, the total energy she expend will be equal to the Potential energy when the barbell is lifted multiplied by 23:
E = 23 * m * g * d
E = 23 * 231.77
E = 5330.71 J
C. 1 Joule = 4.184 calories
5330.71 Joules = 5330.71 * 4.184 = 22303.69
If 1 donut contains 490 calories, the number of donuts she will need will be:
N = 22303.69/490 = 45.5 donuts or 46 donuts
