Answer:
Step-by-step explanation:
![\sqrt[3]{\frac{27t^{9} }{729} }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B27t%5E%7B9%7D%20%7D%7B729%7D%20%7D)
27 is a perfect cube for 
and 729 is a perfect cube for 
![\sqrt[3]{\frac{3^{3} t^{9} }{9^{3} } }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B3%5E%7B3%7D%20t%5E%7B9%7D%20%7D%7B9%5E%7B3%7D%20%7D%20%7D)
now you can pull out the numbers from under the root, for t (divide the exponent by 3)
now simply to
Answer:
42.21 ft^2
Step-by-step explanation:
The formula: A=1
/2b √ c2﹣b2
c=hypotenuse
b=base
Answer:
-0.2
Step-by-step explanation:
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
-----------------------------------
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)
