<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>
Answer: An object's motion can be changed by unbalanced forces. Balanced forces do not change the motion of an object.
The motion of an object acted on by a force depends partly on the strength of the push or pull. The stronger the push or pull, the faster the object will move. For example, the father in the picture below is pushing his daughter in a swing. When he uses more force to push, the swing moves higher.
Explanation:
it has a rocky core so the gravity from that compacts the gases extremly tight
Setting up an integral of
rotation is used as a method of of calculating the volume of a 3D object formed
by a rotated area of a 2D space. Finding the volume is similar to finding the
area, but there is one additional component of rotating the area around a line
of symmetry.
<span>First the solid of revolution
should be defined. The general function
is y=f(x), on an interval [a,b].</span>
Then the curve is rotated
about a given axis to get the surface of the solid of revolution. That is the
integral of the function.
<span>It all depends of the
function f(x), which must be known in order to calculate the integral.</span>
Answer:
Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. What this means is that pushing on an object causes that object to push back against you, the exact same amount, but in the opposite direction.
Explanation: