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lisabon 2012 [21]
3 years ago
7

1. The sum of first n terms of an arithmetic sequence is 3n²+4n

Mathematics
1 answer:
valentina_108 [34]3 years ago
5 0

Answer:

<h3>           a.  a₁=7,     b.  a_n=7n+1,    c.  a₂₀=141</h3>

Step-by-step explanation:

a.

 a_1=S_1=3\cdot1^2+4\cdot1=3+4=7

b.

   a_1+a_2=S_2\\\\a_1+a_1+d=3\cdot2^2+4\cdot2\\\\7+7+d=3\cdot4+8\\\\14+d=12+8\\\\d=6\\\\\\a_n=a_1+d(n-1)\\\\a_n=7+6(n-1)\\\\a_n=7+6n-6\\\\\underline{a_n=7n+1}

c.

 a_{20}=7\cdot20+1=141

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The floor of the cage measures 11 yardyard wide by 66 feetfeet long. One bag of shavings covers 55 square feetfeet. How many bag
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Answer:

3 3/5 bags

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We have to find the surface area of the floor of the cage first.

The cage measures 1 yard wide by 6 feet long.

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To find the number of bags we need to cover the floor, we divide the surface area of the floor by the number of bags per square feet.

The number of bags needed for the floor of the cage is therefore :

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3 years ago
You are choosing a song for your dance recital. Song A has 11 beats in 10 seconds. Song B has 7 beats in 6 seconds. Which song h
Pachacha [2.7K]
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3 years ago
How do I solve this question?
Montano1993 [528]

Answer:

p = \frac{3}{2} , q = 9

Step-by-step explanation:

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2 years ago
Find the solution of the given initial value problem:<br><br> y''- y = 0, y(0) = 2, y'(0) = -1/2
igor_vitrenko [27]

Answer:  The required solution of the given IVP is

y(x)=\dfrac{3}{4}e^x+\dfrac{5}{4}e^{-x}.

Step-by-step explanation:  We are given to find the solution of the following initial value problem :

y^{\prime\prime}-y=0,~~~y(0)=2,~~y^\prime(0)=-\dfrac{1}{2}.

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Then, we have

y^\prime=me^{mx},~~~~~y^{\prime\prime}=m^2e^{mx}.

Substituting these values in the given differential equation, we have

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So, the general solution of the given equation is

y(x)=Ae^x+Be^{-x}, where A and B are constants.

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y^\prime(x)=Ae^x-Be^{-x}.

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y(0)=2\\\\\Rightarrow A+B=2~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

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y^\prime(0)=-\dfrac{1}{2}\\\\\\\Rightarrow A-B=-\dfrac{1}{2}~~~~~~~~~~~~~~~~~~~~~~~~(ii)

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Thus, the required solution of the given IVP is

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