Answer:
96
Step-by-step explanation:
The loan duration is for 8 years, a total of 12·8 = 96 monthly payments. The 96th payment is the balloon payment.
Centripetal acceleration is given by:
g=v^2/r
where:
v=velocity
r=rate
But
V=200 m/s, g=9.8 m/s^2
plugging the values in the formula we obtain:
9.8=200^2/r
r=200^2/9.8
r=4081.63 m
Step-by-step explanation:
With reference to the regular hexagon, from the image above we can see that it is formed by six triangles whose sides are two circle's radii and the hexagon's side. The angle of each of these triangles' vertex that is in the circle center is equal to 360∘6=60∘ and so must be the two other angles formed with the triangle's base to each one of the radii: so these triangles are equilateral.
The apothem divides equally each one of the equilateral triangles in two right triangles whose sides are circle's radius, apothem and half of the hexagon's side. Since the apothem forms a right angle with the hexagon's side and since the hexagon's side forms 60∘ with a circle's radius with an endpoint in common with the hexagon's side, we can determine the side in this fashion:
tan60∘=opposed cathetusadjacent cathetus => √3=Apothemside2 => side=(2√3)Apothem
As already mentioned the area of the regular hexagon is formed by the area of 6 equilateral triangles (for each of these triangle's the base is a hexagon's side and the apothem functions as height) or:
Shexagon=6⋅S△=6(base)(height)2=3(2√3)Apothem⋅Apothem=(6√3)(Apothem)2
=> Shexagon=6×62√3=216
D
An easier way of doing it mentally is 3 x 25 which is 75 and then 1 x 25 which is 25
Answer:
Step-by-step explanation:
Here's the formula for the volume of a right circular cylinder:

Here's what we are given and what we need to find:
Given that d = 10 cm, h = 20 cm, dd/dt = 1 cm/sec
Need to find dh/dt when V is constant
Since our formula has a radius in it and not a diameter but the info given is a diameter, we can use the substitution that
so

Now we can rewrite the formula in terms of diameter:
which simplifies down to

Now we will take the derivative of this equation with respect to time using the product rule. That derivative is
![\frac{dV}{dt}=\frac{\pi }{4}[d^2*\frac{dh}{dt}+2d\frac{dd}{dt}*h]](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B%5Cpi%20%7D%7B4%7D%5Bd%5E2%2A%5Cfrac%7Bdh%7D%7Bdt%7D%2B2d%5Cfrac%7Bdd%7D%7Bdt%7D%2Ah%5D)
Now we can fill in our values. Keep in mind that if the volume is constant, there is no change in the volume, so dV/dt = 0.
and

Multiply both sides by pi/4 to get
and solve for dh/dt:

Interpreted within the context of our problem, this means that the volume will be constant at those given values of diameter and height when the liquid in the cylinder is dropping at a rate of 4 cm/sec.