Answer:
The diameter is 13.88 feet.
Step-by-step explanation:
1. The formula for calculate the volume of a sphere is:
Where 
is the radius.
2. The diameter is:
3. So, you must solve for the radius in the first equation:
![r=\sqrt[3]{\frac{4V}{3\pi}}](https://tex.z-dn.net/?f=r%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B4V%7D%7B3%5Cpi%7D%7D)
![r=\sqrt[3]{\frac{4(790.272ft^{3} )}{3\pi}}\\r=6.94ft](https://tex.z-dn.net/?f=r%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B4%28790.272ft%5E%7B3%7D%20%29%7D%7B3%5Cpi%7D%7D%5C%5Cr%3D6.94ft)
4. Then, the diameter is:
The rate of change is -29/5x^2
(6+2*3)/(9-7)^2
(6+6)/(2)^2
12/4
3
Final answer: 3
Remember to simplify within parentheses first and then divide the two values in the end.
Part A
Answer: The common ratio is -2
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Explanation:
To get the common ratio r, we divide any term by the previous one
One example:
r = common ratio
r = (second term)/(first term)
r = (-2)/(1)
r = -2
Another example:
r = common ratio
r = (third term)/(second term)
r = (4)/(-2)
r = -2
and we get the same common ratio every time
Side Note: each term is multiplied by -2 to get the next term
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Part B
Answer:
The rule for the sequence is
a(n) = (-2)^(n-1)
where n starts at n = 1
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Explanation:
Recall that any geometric sequence has the nth term
a(n) = a*(r)^(n-1)
where the 'a' on the right side is the first term and r is the common ratio
The first term given to use is a = 1 and the common ratio found in part A above was r = -2
So,
a(n) = a*(r)^(n-1)
a(n) = 1*(-2)^(n-1)
a(n) = (-2)^(n-1)
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Part C
Answer: The next three terms are 16, -32, 64
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Explanation:
We can simply multiply each previous term by -2 to get the next term. Do this three times to generate the next three terms
-8*(-2) = 16
16*(-2) = -32
-32*(-2) = 64
showing that the next three terms are 16, -32, and 64
An alternative is to use the formula found in part B
Plug in n = 5 to find the fifth term
a(n) = (-2)^(n-1)
a(5) = (-2)^(5-1)
a(5) = (-2)^(4)
a(5) = 16 .... which matches with what we got earlier
Then plug in n = 6
a(n) = (-2)^(n-1)
a(6) = (-2)^(6-1)
a(6) = (-2)^(5)
a(6) = -32 .... which matches with what we got earlier
Then plug in n = 7
a(n) = (-2)^(n-1)
a(7) = (-2)^(7-1)
a(7) = (-2)^(6)
a(7) = 64 .... which matches with what we got earlier
while the second method takes a bit more work, its handy for when you want to find terms beyond the given sequence (eg: the 28th term)
Since the unit rate is $1.93 per yard, you need to multiply the number of yards by 1.93. So 1.93 x 3 = 5.79. Next, you convert 5% to a decimal, which is 0.05. Now, multiply 5.79 by 0.05, which is about 0.29. Finally, add 0.29 to 5.79, giving you the answer of 6.08. Alice payed $6.08; D.
