Find the volume of the sphere. Round to the nearest tenth. - 14 in.
1 answer:
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Answer:
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Explanation:
Point-slope form is
where m is the slope and is the point the line goes through.
We're given the slope of m = 5/6, and we want the line going through (-8,0) which is the x-intercept -8. The x-intercept always occurs when y = 0.
So,
We can replace the y-0 with y; however, I'm going to keep that 0 so that the equation better matches the point-slope form.
Answer:
Step-by-step explanation:
Because we have to rewrite this equation in the format , we have to divide, or factor to find basic terms,
Expanding the value of k(x), we have . We see that each term can be divisible by 4, so we can factor out 4 to get
Now, we have two different terms getting multiplied. We can separate the two to get
Because we are multiplying 4 by the other term, this is represented by
Now, we can just set f(x) and g(x) to these functions:
Now, just to make sure, we can plug a value into k(x) and the same value into f(g(x)). Plugging in 1, we have (2(1)+4)2 as 2(2+4), which is 2(6) = 12.
Plugging 1 into f(g(x)), we can evaluate g(1) first, to get 1 + 2 = 3. Now, f(3) = 4(3)= 12, which is the same for k(x).
Answers:
a) See the table below
b) The equation is
c) $40,024.02
d) See the graph below
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Explanations:
a)
Start with part (b) where I detail how to get the equation.
Once the equation is found, plug in x = 0 to get
Repeat for x = 1
Repeat for x = 2, x = 3, x = 4 and x = 20 to get the table shown below.
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b)
The template for any exponential equation is
a = starting amount = 32000
b = growth factor
The annual interest rate is 4.5%
We compound quarterly, so the quarterly rate is (4.5%)/4 = 1.125% which converts to the decimal form 0.01125; adding one to this leads to the growth factor of b = 1.01125
We go from to
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c)
Plug in x = 20 to represent 20 quarters have elapsed (aka 20/4 = 5 years)
The investment would be worth $40,024.02 after five years, aka twenty quarters.
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d)
See below for the graph. I'm using GeoGebra to make the graph. Another option is Desmos. It's preferable to use technology than to graph by hand. If you wanted to graph by hand, then you'd plot each of the points found in the table. Then draw a curve through all those points.
