Answer:
The time it would take to inflate the balloon to approximately two-thirds of its maximum volume is approximately 46.90 minutes
Step-by-step explanation:
The given parameters are;
The diameter of the balloon = 55 feet
The rate of increase of the radius of the balloon when inflated = 1.5 feet per minute
We have;
dr/dt = 1.5 feet per minute = 1.5 ft/min
V = 4/3·π·r³
The maximum volume of the balloon = 4/3 × 3.14 × 55³ = 696556.67 ft³
When the volume is two-thirds the maximum volume, we have;
2/3 × 696556.67 ft³ = 464371.11 ft³
The value of the radius, r₂ at that point is found as follows;
4/3·π·r₂³ = 464371.11 ft³
r₂³ = 464371.11 ft³ × 3/4 = 348278.33 ft³
348278.333333
r₂ = ∛(348278.33 ft³) ≈ 70.36 ft
The time for the radius to increase to the above length = Length/(Rate of increase of length of the radius)
The time for the radius to increase to the above length ≈ 70.369 ft/(1.5 ft/min) ≈ 46.90 minutes
The time it would take to inflate the balloon to approximately two-thirds of its maximum volume ≈ 46.90 minutes.
Answer:
Step-by-step explanation:
Firstly, note that -2i really is just z = 0 + (-2)i, so we see that Re(z) = 0 and Im(z) = -2.
When we're going from Cartesian to polar coordinates, we need to be aware of a few things! With Cartesian coordinates, we are dealing explicitly with x = blah and y = blah. With polar coordinates, we are looking at the same plane but with angle and magnitude in consideration.
Graphing z = -2i on the Argand diagram will look like a segment of the y axis. So we ask ourselves "What angle does this make with the positive x axis? One answer you could ask yourself is -90°! But at the same time, it's 270°! Why do you think this is the case?
What about the magnitude? How far is "-2i" stretched from the typical "i". And the answer is -2! Well... really it gets stretched by a factor of 2 but in the negative direction!
Putting all of this together gives us:
z = |mag|*(cos(angle) + isin(angle))
= 2*cos(270°) + isin(270°)).
To verify, let's consider what cos(270°) and sin(270°) are.
If you graph cos(x) and look at 270°, you get 0.
If you graph sin(x) and look at 270°, you get -1.
So 2*(cos(270°) + isin(270°)) = 2(0 + -1*i) = -2i as expected.
Answer:
$11.20
Step-by-step explanation:
The regular price of the T-Shirt is $14 dollars. The discount is 20% off.
20 percent of 14:
14 * 0.2 = 2.80
You would save $2.80.
14 - 2.80 = 11.20
The discount price should be $11.20.
Hope this helps.
Answer:
C
Step-by-step explanation:
