Answer: 0.22hz
Step-by-step explanation:
Hi to answer this question we have to analyze the information given:
- <em>Period (T) = 4.5 Seconds
</em>
So, to calculate the frequency of the pendulum we have to apply the formula;
Frequency (f)= 1 / period
Replacing with the value given:
f = 1/ 4.5 sec = 0.22 hz
Feel free to ask for more if needed or if you did not understand something.
The amount paid by Heron for the video game is $46.64.
Step-by-step explanation:
Here, the marked price of the video game = $55
The discount percentage on the video game = 20%
Calculating 20% of the $55, we get:

So, the discount offered on the video game = $11
Selling Price = Marked Price - Discount
=$55 - $11 = $44
Now, the tax percentage on the video game = 6%
Calculating 6% of the $44, we get:

So, the tax on the video game = $2.64
New Selling Price = Selling Price + Tax
=$44 + $2.64 = $46.64
So, the amount paid by Heron for the video game is $46.64.
Answer: Choice C

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Explanation:
The graph is shown below. The base of the 3D solid is the blue region. It spans from x = 0 to x = 1. It's also above the x axis, and below the curve 
Think of the blue region as the floor of this weirdly shaped 3D room.
We're told that the cross sections are perpendicular to the x axis and each cross section is a square. The side length of each square is
where 0 < x < 1
Let's compute the area of each general cross section.

We'll be integrating infinitely many of these infinitely thin square slabs to find the volume of the 3D shape. Think of it like stacking concrete blocks together, except the blocks are side by side (instead of on top of each other). Or you can think of it like a row of square books of varying sizes. The books are very very thin.
This is what we want to compute

Apply a u-substitution
u = -2x
du/dx = -2
du = -2dx
dx = du/(-2)
dx = -0.5du
Also, don't forget to change the limits of integration
- If x = 0, then u = -2x = -2(0) = 0
- If x = 1, then u = -2x = -2(1) = -2
This means,

I used the rule that
which says swapping the limits of integration will have us swap the sign out front.
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Furthermore,
![\displaystyle 0.5\int_{-2}^{0}e^{u}du = \frac{1}{2}\left[e^u+C\right]_{-2}^{0}\\\\\\= \frac{1}{2}\left[(e^0+C)-(e^{-2}+C)\right]\\\\\\= \frac{1}{2}\left[1 - \frac{1}{e^2}\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%200.5%5Cint_%7B-2%7D%5E%7B0%7De%5E%7Bu%7Ddu%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Cleft%5Be%5Eu%2BC%5Cright%5D_%7B-2%7D%5E%7B0%7D%5C%5C%5C%5C%5C%5C%3D%20%5Cfrac%7B1%7D%7B2%7D%5Cleft%5B%28e%5E0%2BC%29-%28e%5E%7B-2%7D%2BC%29%5Cright%5D%5C%5C%5C%5C%5C%5C%3D%20%5Cfrac%7B1%7D%7B2%7D%5Cleft%5B1%20-%20%5Cfrac%7B1%7D%7Be%5E2%7D%5Cright%5D)
In short,
![\displaystyle \int_{0}^{1}e^{-2x}dx = \frac{1}{2}\left[1 - \frac{1}{e^2}\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_%7B0%7D%5E%7B1%7De%5E%7B-2x%7Ddx%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Cleft%5B1%20-%20%5Cfrac%7B1%7D%7Be%5E2%7D%5Cright%5D)
This points us to choice C as the final answer.
C as you know what you’re going through to your point of what time you’re leaving the school you
Answer:
6/24
Step-by-step explanation: