Ok so im not good with words and math, but i am going to try my best to explain it. first you will take 45/60 which is the 45 miles per hour. next you will put it equal to 40/x. x is how many minutes. they are set equal to each other because they are the same ratio. (i honestly dont know why you cross multiply, but you just do). you then multiply 40*60 and 45*x. this gives you 2400=45x. you then divide both sides by 45 and get 53 1/3 minutes. or 53 minutes and 20 seconds
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A quick and easy way to do this particular question is to think all of these numbers are close to 1/2 except 2/31. So, the lowest is 2/31.
H O P E T H I S H E L P S!
Answers:
x = -8/5 or x = 8/5
Sum of the first ten terms where all terms are positive = 4092
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Explanation:
r = common ratio
- first term = 4
- second term = (first term)*(common ratio) = 4r
- third term = (second term)*(common ratio) = (4r)*r = 4r^2
The first three terms are: 4, 4r, 4r^2
We're given that the sequence is: 4, 5x, 16
Therefore, we have these two equations
Solve the second equation for r and you should find that r = -2 or r = 2 are the only possible solutions. If r = -2, then 5x = 4r solves to x = -8/5. If r = 2, then 5x = 4r solves to x = 8/5.
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To find the sum of the first n terms, we use this geometric series formula
Sn = a*(1 - r^n)/(1 - r)
We have
- a = 4 = first term
- r = 2, since we want all the terms to be positive
- n = 10 = number of terms to sum up
So,
Sn = a*(1 - r^n)/(1 - r)
S10 = 4*(1 - 2^10)/(1 - 2)
S10 = 4*(1 - 1024)/(-1)
S10 = 4*(-1023)/(-1)
S10 = 4092
