The vertical shifts in graphs are caused by a constant added to the output (y - axis).
<h3>What is vertical shift in a graph?</h3>
Vertical shifts are outside changes that affect the output (y- axis) values and shift the function up or down (vertical direction).
Horizontal shifts are inside changes that affect the input (x-) axis values and shift the function left or right
<h3>The cause of vertical shift in a graph</h3>
The vertical shift results from a constant added to the output (y - axis). The graph will move up if the constant added is positive OR it will move down if the constant is negative.
Thus, the vertical shifts in graphs are caused by a constant added to the output (y - axis).
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Answer:
>
Step-by-step explanation:
5 × 10^2 = 500
so 590 is greater than or > 5 × 10^2 or 500
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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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Answer:
180/147
Step-by-step explanation:
We need to find the additive inverse of the given numbers.
- For finding it we may simply out -1 as multiplication in front of the terms .
<u>SOLUTION</u><u> </u><u>1</u><u> </u><u>:</u><u>-</u>
→ 3/-7 - 11/21
→ -3/7 -11/21
→ 3×-3 - 11 /21
→ -9-11/21
→ -20/21
<u>SOLUTION</u><u> </u><u>2</u><u> </u><u>:</u><u>-</u><u> </u>
→ 9/5 ÷ 7/5
→ 9/5 × 5/7
→ 9/7
→ Product of nos . = -20/21 × -9/7
→ Ans = 180/147
Answer:
3.61 miles
Step-by-step explanation:
Given that:
Length of track = 5/6 of a mile
Number times Mary was able to run around the track = 4 1/3 times
Total miles ran by Mary :
(Equivalent mile of the track * number of times Mary ran around the track)
5/6 of a mile * 4 1/3 times
5/6 * 13/3
= 65 / 18
= 3.611111 miles
Hence, total Number of miles ran by Mary is 3.61 miles