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4 years ago

Given the Arithmetic sequence A1,A2,A3,A4 45, 51, 57, 63 What is the value of A34?

Mathematics

1 answer:

Natasha_Volkova [10]4 years ago

8 0

Answer:

Value of A(34) = 219

Step-by-step explanation:

A1, A2,A3,A4,45,51,57,63 are in Arithmetic sequence

Common difference in this Arithmetic sequence = 63 - 57 = 06

so, A4 = 45 - 6 = 39

A3 = 39 - 6 = 33

A2 = 33 - 6 = 27

A1 = 27 - 6 = 21

First term of Arithmetic sequence = 21

Common difference = 06

Using general term of Arithmetic sequence,

A(n) = First term + (n - 1) common difference

A(34) = 21 + (34 - 1) 6

A(34) = 21 + 33 × 6

A(34) = 21 + 198

A(34) = 219

Value of A(34) = 219

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What is the prime factorization of 210

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Answer:

= 2*3 * 5 * 7

Step-by-step explanation:

210 = 21* 10

= 3*7 * 5*2

= 2*3 * 5 * 7

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3 years ago

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anzhelika [568]

Well we know that... $a^{-1}=\frac{1}{a^{1} }\\$ .

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3 years ago

mafiozo [28]

Answer:

$x$ = 12

Step-by-step explanation:

The shape ABCDEF is an irregular polygon.

The sum of the interior angles of any regular or irregular polygon = (n - 2) x 180 (where n is the number of sides of the polygon).

Therefore, the sum of the interior angles of shape ABCDEF = (6 - 2) x 180 = 720°

So to find the value of $x$ , we need to add together all the interior angles and equal it to 720, then solve for $x$ .

Before we do that, we need to determine angle F.

From inspection, we can see that angle F and 52° are a linear pair. We know that a linear pair of angles add up to 180°, so F + 52 = 180 ⇒ F = 180 - 52 = 128°

Therefore:

A + B + C + D + E + F = 720

(10 $x$ - 5) + 108 + (8 $x$ - 3) + (14 $x$ - 25) + 133 + 128 = 720

Collect like terms:

10 $x$ + 8 $x$ + 14 $x$ - 5 + 108 - 3 - 25 + 133 + 128 = 720

Combine like terms:

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3 years ago

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Tatiana [17]

Answer:

$\frac{4}{3(e^2+1)}$

Step-by-step explanation:

We want to evaluate:

$\int\limits^1_{-1} {\frac{x^2+1}{e^2+1} } \, dx$

This is the same as:

$\frac{2}{e^2+1} \int\limits^1_{0} {x^2+1} \, dx$

We integrate to obtain:

$\frac{2}{e^2+1} (\frac{x^3}{3}+x)|_0^1$

We evaluate to obtain:

$\frac{2}{e^2+1} (\frac{1^3}{3}+1)=\frac{4}{3(e^2+1)}$

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3 years ago

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ololo11 [35]

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