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tamaranim1 [39]
3 years ago
9

Find the first term, a1, of an arithmetic sequence if a12 = 38 and a45 = 170.

Mathematics
1 answer:
snow_lady [41]3 years ago
8 0
Standard formula for arithmetic sequence:
an = a0 + d(n-1)

if we use the two terms given, setting a12 as starting term and a45 as the end term an.

170 = 38 + 33d 
170 - 38 = 33d
132 = 33d

132/33 = d
This is the common difference, use it to find the first term.

38 = a0 + (132/33)(12-1)
38 = a0 + (132/33)(11)
38 = a0 + 132/3
38 - 132/3 = a0
38 - 44 = a0
-6 = a0

The starting term is -6

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y =  \dfrac{2}{7} x - 3

When x = 4,

y =  \dfrac{2}{7} (4) - 3

y =  \dfrac{8}{7} - 3

y = -\dfrac{13}{7}

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Answer: (4 , -13/7)
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5 0
3 years ago
A 25-foot ladder is placed against a building. The bottom of the ladder is 7 feet from the building. If the top of the ladder sl
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Answer:

As per the statement:

A 25-foot ladder is placed against a building. The bottom of the ladder is 7 feet from the building.

⇒Length of the ladder against a building = 25 foot

and Length of the bottom of the ladder from the building= 7 feet.

You had Before the slip.

Let x be the height of the building where ladder hits the building

By Pythagoras theorem:

\text{Hypotenuse side}^2=\text{Perpendicular}^2+\text{Base}^2

Here, Perpendicular side = Height of the building = x ,  Base = Length of the bottom of the ladder from the building = 7 foot and Hypotenuse side = 25 foot

Substitute the value to solve for x;

25^2=x^2+7^2

625=x^2+49

or

x^2 = 625-49 = 576

x = \sqrt{576} = 24 foot.

⇒Height of the building = 24 foot

Now, if the ladder slips down 4 feet.

You had after slip

⇒Now, the height of the building becomes = 24-4 = 20 foot.

Let y be the distance from the building wall

then by Pythagoras theorem;

y^2+20^2 = 25^2

y^2+400 =625

y^2 = 625-400 = 225

y=\sqrt{225} = 15 foot.

We have to find how many feet will the bottom slide out.

Since, Originally the distance of the bottom from the building = 7 foot

And now, the distance is = 15 foot.

The bottom slide out will be = 15 - 7 =8 foot

Therefore, 8 feet will the bottom slide out

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3 years ago
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Answer:

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3 years ago
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Nataly_w [17]

Answer: Option C

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To solve this problem use the properties of the logarithms.

We know that the inverse function of y = log_2 (x) is y = 2 ^ x.

So when composing the function with its inverse function we have to:

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