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Llana [10]
3 years ago
15

What is the sum of the seven terms of the geometric series 2- 8+32-...?

Mathematics
1 answer:
egoroff_w [7]3 years ago
6 0
The first term is 2 and the common ratio = -8/2 = -4

S7   = 2 * (-4)^7 - 1
                -------------    =      6554   answer
                  -4-1
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Joe can cut and split a cord of firewood in 3 fewer hours than Dwight can. When they work​ together, it takes them 2 hours. How
aalyn [17]

Answer:

Dwight will take 6 hours to finish the job alone and Joe will take 3 hours to finish the job alone.

Step-by-step explanation:

Let us assume the time taken by Dwight to split a cord of firewood  = K hrs

So, the per hour rate of Dwight  = (\frac{1}{K})

As, Joe uses 3 LESS hours then Dwight.

So, the time taken by Joe to split a cord of firewood  = (K- 3) hrs

So, the per hour rate of Joe  = (\frac{1}{K-3})

Now, when both of them wok together, it takes them 2 hours.

So, the per hour rate of BOTH of them  = (\frac{1}{2})

⇒ Per hour rate of ( Dwight  + Joe)  =(\frac{1}{2} )

\implies (\frac{1}{K}) +  (\frac{1}{K-3}) = (\frac{1}{2})

Now, solving for the value of K , we get:

(\frac{1}{K}) +  (\frac{1}{K-3}) = (\frac{1}{2})\\\implies  \frac{(K-3) + K}{K (K-3)}  = (\frac{1}{2})\\\implies 2(2K -3) = K^2 - 3K\\\implies k^2 - 3K -4K +6 = 0\\\implies K^2 - 7K  + 6=  0\\\implies K^2 - 6K - K  + 6=  0\\\implies K(K-6) -1(K - 6)=  0\\\implies (K-6)(K-1) = 0

Implies either K = 6 Or K = 1

But if K = 1, (K-3)  = 1- 3  = -2 hours would be A CONTRADICTION.

⇒ K  = 6 hours

Hence, Dwight will take 6 hours to finish the job alone and Joe will take (k-3) = (6-3) = 3 hours to finish the job alone.

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Which of the following is a reasonable estimate for the weight capacity of an elevator that can carry up to 15 people?
Bas_tet [7]

A is the most common

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I don’t understand lol
pogonyaev

Answer:

3*r = 3

Step-by-step explanation:

\dfrac{24}{r}=3\\\\24 = r*3\\\\\dfrac{24}{3}=r\\\\6 = r6 is a solution.

3*r=3\\\r =\dfrac{3}{3}\\\\r = 1\\

6 is not a solution.

7r = 42\\\\r =\dfrac{42}{7}\\\\r = 6

6 is a solution

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2 years ago
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Manuel rented a truck for one day. There was a base fee of $15.99, and there was an additional charge of 92 cents for each mile
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Answer:

8

Step-by-step explanation:

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3 years ago
Solving simple quadratic equations.
Umnica [9.8K]

Answer:

x=5

Step-by-step explanation:

the square root of 25 is 5 and 5*5=25 so the answer is 5

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