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Sever21 [200]
4 years ago
14

The sequence -14, -9, -4, 1, ..., 41 has 12 terms. evaluate the related series.

Mathematics
1 answer:
sesenic [268]4 years ago
6 0
The answer is 162.

sequence is arithmetic; d = 5

sum = (n/2)(a1+an)

an = a1 +d(n-1)

a12 = -14 + 5(11)

a12 = -14 + 55 ----> a12 = 41

sum: (12/2)(-14 + 41)
 = 6(27)
= 162
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Let's solve the next equation:

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1 year ago
In a triathlon, Jenny swam for 1 hour, biked for 1.75 hours, and ran for 1 hour. Her average biking speed was 2 times her averag
expeople1 [14]

Answer:

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Step-by-step explanation:

Some values you know (given or calculated) and some things you do not know.

             RATE         TIME         DISTANCE

BIKE          2*8r         1.75

RUN           8r

SWIM           r            1

Total                                     55

Give a variable to unknown running speed and fill in everything.

             RATE         TIME         DISTANCE

BIKE          16r         1.75           28r        

RUN           8r            t            8rt

SWIM           r            1             r

Total                                     55

Notice some trouble? WHY? I missed seeing the "ran for one hour". the variable t is KNOWN! This will be corrected here:

             RATE         TIME         DISTANCE

BIKE          16r         1.75           28r        

RUN           8r            1            8r

SWIM           r            1             r

Total                                     55

Calculations used to fill out the graph:

Then her running speed was 8r,

and her biking speed was 2*(8r) = 16r.

Swimming for 1    hour, Jenny covered the distance of 1*r = r kilometers.

Biking   for 1.75 hour, Jenny covered the distance of 1.75*16r = 28r kilometers.

Running  for 1    hour, Jenny covered the distance of 1*2r = 8r kilometers.

Everything is filled and looks good. There is a sum of distances in just the one single variable, r.

Solve for r, and this is the swimming speed.

28r + 8r + r = 55

4 0
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