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erma4kov [3.2K]
3 years ago
12

Identify the 12th term of the arithmetic sequence in which a7 = 40 and a18 = 106.

Mathematics
1 answer:
Lady_Fox [76]3 years ago
3 0

we are given

airthematic sequence

we can use nth term formula

a_n=a_1+(n-1)d

n is number of terms

an is nth term

d is common difference

a1 is first term

We are given

a7=40

we can use it

a_7=a_1+(7-1)d

40=a_1+6d

a_1+6d=40

a18 = 106

a_1_8=a_1+(18-1)d

a_1+17d=106

we can subtract both equations

a_1+17d-a_1-6d=106-40

11d=66

d=6

now, we can find a1

a_1+6d=40

we can plug d=6

a_1+6*6=40

a_1=4

12th term:

a_1_2=a_1+(12-1)d

now, we can plug values

a_1_2=4+(12-1)*6

a_1_2=4+66

a_1_2=70

so, 12th term is 70...........Answer

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The cost C (in dollars) to participate in a ski club is given by the literal equation C=85x+60, where X=C/85-12/17 is the number
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Given:

The cost C (in dollars) to participate in a ski club is given by,

\begin{gathered} C=85x+60 \\ (or) \\ x=\frac{C}{85}-\frac{12}{17} \end{gathered}

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To find:

The number of ski trips when a total cost of $315 and $485 is spent.

Explanation:

Substituting C = 315 in the given equation we get,

\begin{gathered} x=\frac{315}{85}-\frac{12}{17} \\ x=\frac{315-60}{85} \\ x=\frac{255}{85} \\ x=3\text{ ski trips} \end{gathered}

Substituting C = 485 in the given equation we get,

\begin{gathered} x=\frac{485}{85}-\frac{12}{17} \\ x=\frac{485-60}{85} \\ x=\frac{425}{85} \\ x=5\text{ ski trips} \end{gathered}

Thus,

If we spend a total cost of $315, we can take 3 ski trips.

If we spend a total cost of $485, we can take 5 ski trips.

Final answer:

• If we spend a total cost of $315, we can take 3 ski trips.

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• If we spend a total cost of $485, we can take 5 ski trips.

8 0
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Step 1: Convert \frac{5\pi }{12}, which is in radians into degrees. To convert it multiply by \frac{180}{\pi }

\frac{5\pi }{12} =\frac{180}{\pi }

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Step 2: 75 degrees isn't on the unit circle but 45 degrees and 30 degrees is. Since 45 + 30 = 75 you can use the cosine of 45 and 30 to find the exact value

cos45 = \frac{\sqrt{2} }{2}

cos30 =\frac{\sqrt{3} }{2}

Step 3: Add the cos45 and cos30 to get cos5pi/12

\frac{\sqrt{2} }{2} +\frac{\sqrt{3} }{2} = \frac{\sqrt{2}+\sqrt{3}}{2}

Hope this helped!

4 0
3 years ago
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