SA = 2 pi r^2 + 2 pi r h
SA = 2 * pi * 25 + 2 pi * 5 * 13
SA = 565.2 in ^3
this is using 3.14 for pi
It was 210 cm.
The function she used is h(t) = 210 + 33t. This is a linear function, since it is of the form f(x) = mx+b. In a linear function, we have the slope, m, which tells us how much the height increases per year, and the y-intercept, b, which tells us how tall it was when we began measuring. Our m value would be 33 and our b would be 210, so the original height was 210.
Answer:

General Formulas and Concepts:
<u>Calculus</u>
Integration
Integration Rule [Reverse Power Rule]: 
Integration Rule [Fundamental Theorem of Calculus 1]: 
Integration Property [Multiplied Constant]: 
Integration Property [Addition/Subtraction]: ![\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint%20%7B%5Bf%28x%29%20%5Cpm%20g%28x%29%5D%7D%20%5C%2C%20dx%20%3D%20%5Cint%20%7Bf%28x%29%7D%20%5C%2C%20dx%20%5Cpm%20%5Cint%20%7Bg%28x%29%7D%20%5C%2C%20dx)
Area of a Region Formula: ![\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20A%20%3D%20%5Cint%5Climits%5Eb_a%20%7B%5Bf%28x%29%20-%20g%28x%29%5D%7D%20%5C%2C%20dx)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify.</em>
y = 2x + 3
<em>x</em>-interval [3, 4]
<em>x</em>-axis
<em>See attachment for graph.</em>
<u>Step 2: Find Area</u>
- Substitute in variables [Area of a Region Formula]:

- [Integral] Rewrite [Integration Property - Addition/Subtraction]:

- [Integrals] Rewrite [Integration Property - Multiplied Constant]:

- [Integrals] Integrate [Integration Rule - Reverse Power Rule]:

- [Integrals] Integrate [Integration Rule - FTC 1]:

- Simplify:

∴ the area bounded by the region y = 2x + 3, x-axis, and the coordinates x = 3 and x = 4 is equal to 10.
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Learn more about integration: brainly.com/question/26401241
Learn more about calculus: brainly.com/question/20197752
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Hello!
The answer is:
Luke did a work of 308N.m or 308 Joules.
<h2>
Why?</h2>
When a force is applied on a object making it to move covering a distance we call it "work". The movement caused by the force, will follow the same direction that the force.
We can calculate the work done by using the following equation:

Where,
Work is the transferred energy.
Force, is the force applied to the object.
Distance, is the distance covered due to the applied force.
α, is the angle at the work is done.
We are given the following information to calculate the work done:

So, substituting the given information into the equation to calculate work, we have:

Hence, we have that Luke did a work of 308N.m or 308 Jouls.
Have a nice day!
X= 75/2
Y=0
That is the answer to your question I used Photomath to help me