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katrin [286]
2 years ago
10

Sydney placed 10 guppies in a fish tank she recorded the number of guppies in the tank

Mathematics
1 answer:
pav-90 [236]2 years ago
7 0

Answer:

g(n) = 10 * 3^{n}

Step-by-step explanation:

Given

See attachment for table

Required

Determine the explicit formula for the table

First, we need to check if the guppies increases at arithmetic progression or geometry progression.

For arithmetic progression:

We calculate the common difference (d)

d = g(n) - g(n-1)

Take n as 1

d = g(1) - g(1-1)

d = g(1) - g(0)

From the table:

g(1) = 30\ \&\ g(0) = 10

d = 30 - 10

d = 20

Take n as 2

d = g(2) - g(1)

From the table:

g(1) = 30\ \&\ g(2) = 90

d = 90 - 30

d = 60

The two differences are not equal. So, this

For geometry progression:

We calculate the common ratio (r)

r = \frac{g(n)}{g(n-1)}

Take n as 1

r = \frac{g(1)}{g(1-1)}

r = \frac{g(1)}{g(0)}

From the table:

g(1) = 30\ \&\ g(0) = 10

r = \frac{30}{10}

r = 3

Take n as 2

r = \frac{g(2)}{g(1)}

From the table:

g(1) = 30\ \&\ g(2) = 90

r = \frac{90}{30}

r = 3

The two ratios are equal.

So, the next step is to calculate the explicit formula using n term of a geometric progression.

Because the progression starts from 0, we make use of the following formula

g(n) = g(0) * r^{n}

Substitute values for g(0) and r

g(n) = 10 * 3^{n}

Hence:

The explicit formula is: g(n) = 10 * 3^{n}

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In triangle ABC, side AC and the perpendicular bisector of BC meet in point D, and BD bisects ∠ABC。 If AD = 9 and DC = 7, 145–√5  is the area of a triangle.

I supposed here that [ABD] is the perimeter of ▲ ABD.

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Thus first root  cos2α=12  cannot be chosen and we have to stick with the second root  cos2α=49. This gives  cosα=23  and  sinα=5√3.

The area of a triangle ABD=12h∗AD  where h  is the distance from  B  to  AC.

h=BCsinC=14cosαsinα

Area of  triangle ABD=145–√5

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Incomplete question please read below for the proper question.

In triangle ABC, side AC and the perpendicular bisector of BC meet in point D, and BD bisects ∠ABC。 If AD = 9 and DC = 7, what is the area of triangle ABD?

Learn more about the Area of the triangle at

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