Step-by-step explanation:
You have found a function r(V(t)). We can see that this function is a one variable function. The variable is time.
So in this specific function we can call r(v(t)), r(t).
So:
![r(t) = \sqrt[3]{ \frac{3 \times (10 + 20t)}{4\pi} }](https://tex.z-dn.net/?f=r%28t%29%20%3D%20%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7B3%20%5Ctimes%20%2810%20%2B%2020t%29%7D%7B4%5Cpi%7D%20%7D%20)
If α is the moment that the radius is 10 inches and since the function above gives radius in inches we have to solve the equation:
Which is the same as:
![\sqrt[3]{ \frac{3 \times (10 + 20 \alpha )}{4\pi} } = 10 \\ \frac{3 \times (10 + 20 \alpha )}{4\pi} = 1000 \\ (10 + 20 \alpha ) = \frac{4000\pi}{3} \\ 20 \alpha = \frac{(4000\pi - 30)}{3} \\ \alpha = \frac{(4000\pi - 30)}{60}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7B3%20%5Ctimes%20%2810%20%2B%2020%20%5Calpha%20%29%7D%7B4%5Cpi%7D%20%7D%20%20%3D%2010%20%5C%5C%20%20%5Cfrac%7B3%20%5Ctimes%20%2810%20%2B%2020%20%5Calpha%20%29%7D%7B4%5Cpi%7D%20%20%3D%201000%20%5C%5C%20%2810%20%2B%2020%20%5Calpha%20%29%20%3D%20%20%5Cfrac%7B4000%5Cpi%7D%7B3%7D%20%20%5C%5C%2020%20%5Calpha%20%20%3D%20%20%5Cfrac%7B%284000%5Cpi%20-%2030%29%7D%7B3%7D%20%5C%5C%20%20%5Calpha%20%20%3D%20%20%5Cfrac%7B%284000%5Cpi%20-%2030%29%7D%7B60%7D%20)
Using translation concepts, it is found that the equation that represents the graph of g(x) is:
![g(x) = \sqrt[3]{x + 2}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx%20%2B%202%7D)
.
<h3>What is a translation?</h3>
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, we have that g(x) is a shift left of 2 units of f(x), hence:
More can be learned about translation concepts at brainly.com/question/4521517
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Exponential function is characterized by an exponential increase or decrease of the value from one data point to the next by some constant. When you graph an exponential function, it would start by having a very steep slope. As time goes on, the slope decreases until it levels off. The general from of this equation is: y = A×b^x, where A is the initial data point at the start of an event, like an experiment. The term 'b' is the constant of exponential change. This is raised to the power of x, which represents the independent variable, usually time.
So, the hint for you to find is the term 500 right before the term with an exponent. For example, the function would be: y = 500(1.8)^x.
The answer is 21.2 ft²
To do this we need to calculate the volume of the cylinder shaped drum.The volume (V) of the cylinder with height h and radius r is:V = π r² h
We have:π = 3.14r = 1.5 fth = 3 ft
Therefore:V = π r² hV = 3.14 * (1.5 ft)² * 3 ftV = 21.2 ft²
here you go
Answer:
Multiply the top equation by 3
Step-by-step explanation:
