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/sci/ - Science & Math

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4983719 No.4983719 [Reply] [Original]

Need help with two arithmetic series questions:

1) Determine the indicated sum for the arithmetic series given the following values. a=8, t16=68, s12=?

2) When an object is dropped from rest it falls about 5m in the first second, 15m in the 2nd second, 25m in the 3rd second, and so on. If a rock is dropped from a hot air balloon and takes 16 seconds to hit the ground, how high above the ground is the balloon?

>> No.4983746

For question one I don't understand what you mean by t.

For question 2, the equation is y = 10x - 5
So the answer is 155m.

>> No.4983760

2) the equation is y = 5 x^2
5*16^2=1280m

>> No.4983764

>>4983760
No.
15 = 5 * 4
15 = 20
Not true.

It increases by 10 each increment but starts with 5:
>>4983746
was correct.

>> No.4983770

>>4983764
1st second: 0-5 = 5m
2nd second: 5-20m = 15m
3rd second: 20-45m = 25m

>> No.4983767

the answer is 6.

>> No.4983776

>>4983760
How did you figure out the equation?

>> No.4983786

>>4983776
fit trendline in excel.

>> No.4983839
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4983839

I'm assuming that in question one t is supposed to be n. E.g the sum of a1 + a2 + ... + an.

Then d = 4. So to find a12 we do:
a12 = 8 + 4(11)
a12 = 8 + 44
a12 = 52

Then we find the sum:

S12 = 12(60)/2
S12 = 360

>> No.4983851

>>4983746
>>4983764

It was not correct, at all. It does some of the question then forgets to finish it. In the 16th second the rock falls 155m, but you have to integrate y=10x-5 between 0 and 16 to get the actual height. So that means y=5x^2, with a sum of 1280 metres, as has been said.

>> No.4983924
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4983924

>>4983851
How exactly do you integrate it?

>> No.4983940

>>4983924
>infantile cartoon

>> No.4983945

>>4983924
Nevermind, found a rather elegent way. You can just apply Gauss' formula to this problem as well. Notice that with the formula:
y = 10x - 5
The answer would be:
5 + 15 + 25 + 35 ... + 155
Then it's just a normal arithmetic series. Apply n(a1 + an)/2 and you get 1280.