With each<span> passing </span>day<span>, the </span>high tides occur<span> about an </span>hour later<span>. The moon rises about an </span>hour later each day<span>, too (actually, 54 minutes </span>later<span>). Since the moon pulls up the </span>tides<span>, these two delays are connected. As the earth rotates through </span>one day<span>, the moon moves in its orbit.</span>
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 the gymnast mass were doubled, her height (h) from the top of the board would be as follows,
с Stay the same
Explanation:
- The Mass of an object or body does not affect the acceleration due to gravity in any kind of way.
- Light weight objects accelerate more slowly than the heavy objects because when the forces other than the gravity also plays a major role.
- Mass increases of a body when an object has higher velocity or the speed.
- The greater the force of gravity, it would give a direct impact on the object's acceleration; thus considering only a force, the heavier the object is, it would accelerate faster. But an acceleration depends upon the two factors which are force and mass.
- Newton's second law of motion states that the acceleration of an object is dependent upon the two factors which are, the net force of an object and the mass of the object.
The distance covered is 25.9 m.
<h3>How deep is the cave?</h3>
We know that the speed of sound refers to the speed with which an sound moves in an object.
Given that;
speed of sound = 345m/s
Time taken = 0.15s
We know that;
v = 2d/t
v = speed of sound
d = distance
t = time taken
vt = 2d
d = vt/2
d = 345m/s * 0.15s/2
d = 25.9 m
Learn more about speed of sound:brainly.com/question/15137350
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