<span>40.7 miles.
For this problem, we want to know the length of the chord created by the line and the circle. So let's first create the equations needed.
The slope intercept equation for a line is:
y = ax + b
the value for a will be the the difference in y divided by the difference in x. We're going from y=61 to y=0 for a chance of -61 and from x=0 to x=62 for a change of 62. So the value of a is
-61/62, giving us the formula
y = -(61/62)x + b
Substituting x = 0, we can calculate b
61 = -(61/62)0 + b
61 = b
So the equation for the line is:
y = -(61/62)x + 61
Now for the equation for the circle. Since the circle is centered at the origin, the equation is:
x^2 + y^2 = 48^2
Now we to calculate the intersections.
y = -(61/62)x + 61
x^2 + y^2 = 48^2
x^2 + (-(61/62)x + 61)^2 = 48^2
x^2 + (3721/3844)x^2 - (3721/31)x + 3721 = 2304
(7565/3844)x^2 - (3721/31)x + 3721 = 2304
(7565/3844)x^2 - (3721/31)x + 1417 = 0
1.968002081x^2 - 120.0322581x + 1417 = 0
And we have a rather ugly quadratic equation which we can solve using the quadratic formula, giving the solutions x = 16.00512574 and x = 44.98681081
Now we need to calculate the y values for those 2 x values.
y = -(61/62)x + 61
y = -(61/62)16.00512574 + 61
y = 45.25302145
y = -(61/62)x + 61
y = -(61/62)44.98681081 + 61
y = 16.73878292
So the 2 endpoints are
(16.00512574, 45.25302145) and (44.98681081, 16.73878292)
The distance between those points can be calculated using the Pythagorean theorem.
sqrt((16.00512574 - 44.98681081)^2 + (45.25302145 - 16.73878292)^2)
= sqrt(-28.98168506^2 + 28.51423853^2)
=
sqrt(839.938069 + 813.0617988)
=
sqrt(1652.999868)
= 40.65710107
And finally, we have the solution of 40.7 miles.</span>
The answer is 54.675 J
<span>The kinetic energy (Ke) of an object is the product of half of its mass (m) and the square of its velocity (v²):
</span>Ke = 1/2 m * v²
We have:
Ke = ?
m = 15 kg
v = 2.7 m/s
_____
Ke = 1/2 * 15 kg * (2.7 m/s)² = 1/2 * 15 kg * 7.29 m²/s² = 54.675 kg * m²/s²
Ke = 54.675 J
Answer:
1. He feels worse off.
2. His awareness of the grim situation.
Explanation:
Elie Weisel's memoir "Night" is about the persecution of the jews by the Germans during the worst genocide in world history. The events leading up to the Holocaust and the resulting after-effects through his personal experience provides one of the most prominent witness accounts of the crime.
When Weisel states that <em>"lying down wasn't an option</em>", he reveals how congested space was in the cabin. The <u>"lucky ones" were able to breathe in the fresh air from the window, while the rest have to be satisfied with wherever they are.
</u> This reveals his realization of the grim situation inside the over-packed cabin, where there is hardly any space to move.
And when he said that they <em>"never ate enough to satisfy our hunger"</em>, he presents the realization and understanding of the grim situation in the train's cabin where eating is not a luxury, but a necessity to stay alive. And for that, they know they have to <em>"economize, to save for tomorrow"</em> rather than just stay full once.
The answer is C because its shiny
In a string of length L, the wavelength of the n-th harmonic of the standing wave produced in the string is given by:
The length of the string in this problem is L=3.5 m, therefore the wavelength of the 1st harmonic of the standing wave is:
The wavelength of the 2nd harmonic is:
The wavelength of the 4th harmonic is:
It is not possible to find any integer n such that , therefore the correct options are A, B and D.