Answer:
The circumference is 28.27in.
Answer:
x = 45/17
Step-by-step explanation:
We can move all x to 1 side and all the numbers to another. You can add 8.7 on both sides and get that 2.3x = 0.8x + 4.5. Next, we subtract by 0.8x on both sides to get that 1.7x = 4.5, where we can then divide by 17/10 on both sides to get that x is equal to 45/10 * 10/17, so that means that x = 45/17.
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)
The length of the rectangle would be 94m.
Answer:
1. n=
20
/13
2. n=10
3. n=35
4. n=9
That's all I could do, I got tired of typing lol
Step-by-step explanation:
1. 4/n=13/5 we cross multiply, (4)*(5)=13*n, 20=13n Flip the equation. 13n=20, divide 13 on both sides, 13n/13=20/13, n=
20
/13
2. 9/6= 15/n, we cross multiply 9*n=(15)*(6), 9n=90, Divide both sides by 9. 9n/9=90/9 n=10
3. 28/4=n/5 Cross-multiply, (28)*(5)=n*(4), 140=4n Flip the equation.4n=140 Divide both sides by 4. 4n/4=140/4 n=35
4. n/6=6/4 we cross multiply,n*(4)=(6)*(6), 4n=36, Divide both sides by 4 4n/4=36/4. n=9
