Answer and Step-by-step explanation:
<u>Picture this:</u>
There is a base number, and when this number gets multiplied by itself 3 times, we say the number got cubed.
To find the cubic root, we find the number that had to multiply itself 3 times that got the bigger number.
<u>Example:</u>
Let's say we are given the number 27.
If we take the cube root of 27, we get 3.
![\sqrt[3]{27}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B27%7D)
= 3
This is because 3 times itself 3 times is 27.
3 × 3 × 3 = 27
9 × 3 = 27
27 = 27
<u>Another Example:</u>
We are given the number 970299.
If we put this into a calculator and press the button to do this: ![\sqrt[3]{x}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%7D)
, then, in some calculators, it would look like this: ![\sqrt[3]{972099}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B972099%7D)
We we click to solve, we get that base number, or the cubed root, to be 99.
That means 99 was multiplied by itself 3 times to get 972099.
<em><u>#teamtrees #PAW (Plant And Water)</u></em>
Answer:
10%
Step-by-step explanation:
1 is ten percent of 10, and 11-10 = 1. Thus the percent increase in her running time is 10 %
Answer:
x 1 2 5 7
y 5 10 25 35
Step-by-step explanation:
The y values are all just the x values times 5
Answer:
Step-by-step explanation:
The measures of the angles are 2x, 5x, and 5x.
2x+5x+5x = 180°
12x = 180°
x = 15°
2x = 30°
5x = 75°
The ratio of the angles are 30:75:75
Part A)
f(x) = 5^x
f(0) = 5^0
f(0) = 1
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f(x) = 5^x
f(1) = 5^1
f(1) = 5
----------
f(x) = 5^x
f(2) = 5^2
f(2) = 5*5
f(2) = 25
----------
f(x) = 5^x
f(3) = 5^3
f(3) = 5*5*5
f(3) = 125
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Rate of change for section A = (f(1) - f(0))/(1 - 0)
Rate of change for section A = (5 - 1)/(1 - 0)
Rate of change for section A = 4/1
Rate of change for section A = 4
Rate of change for section B = (f(3) - f(2))/(3 - 2)
Rate of change for section B = (125 - 25)/(3 - 2)
Rate of change for section B = 100/1
Rate of change for section B = 100
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Part B)
From part A) above, we found,
Rate of change for section A = 4
Rate of change for section B = 100
Which means that section B's rate of change is 25 times greater (since 100/4 = 25, or 25*4 = 100)
Answer for part B: 25
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Extra: Explain why one rate of change is greater than the other.
The rate of change for section B is larger because the exponential function is growing faster as x increases. This is shown visually by the sharper and steeper incline as the function curve goes upward. The function starts off with relatively slower growth but it accelerates in speed.
