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Galina-37 [17]
3 years ago
7

For each sequence, find the first 4 terms and the 10th term. A) n+5 B)2n-1

Mathematics
1 answer:
snow_tiger [21]3 years ago
5 0

Answer:

see explanation

Step-by-step explanation:

(a)

To find the first 4 terms substitute n = 1, 2, 3, 4 into the n th term formula.

a₁ = 1 + 5 = 6

a₂ = 2 + 5 = 7

a₃ = 3 + 5 = 8

a₄ = 4 + 5 = 9

For the 10 th term substitute n = 10, that is

a₁₀ = 10 + 5 = 15

The first 4 terms are 6, 7, 8, 9 and the 10 th term is 15

(b)

Substitute n = 1, 2, 3, 4 and 10 into the n th term formula

a₁ = 2(1) - 1 = 2 - 1 = 1

a₂ = 2(2) - 1 = 4 - 1 = 3

a₃ = 2(3) - 1 = 6 - 1 = 5

a₄ = 2(4) - 1 = 8 - 1 = 7

a₁₀ = 2(10) - 1 = 20 - 1 = 19

The first 4 terms are 1, 3, 5, 7 and the 10 th term is 19

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Answer:

The graph in the attached figure

see the explanation

Step-by-step explanation:

Let

x----> the time in hours

y ----> liters of water remaining in the fish pond

we have

y=-60x+480

This is the equation of a line in slope intercept form

y=mx+b

where

m is the slope or unit rate

b is the y-intercept or initial value

In this problem we have

The slope or unit rate is equal to

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The y-intercept or initial value is

b=480\ liters

The graph in the attached figure

Remember that

The y-intercept is the value of y when the value of x is equal to zero

The y-intercept is the point (0,480)

That means----> The initial amount of liters of water in the fish pond was 480 liters before drainage began (for x=0 hours).

The x-intercept is the value of x when the value of y is equal to zero

The x-intercept is the point (8,0)

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3 years ago
Mr. Mole left his burrow and started digging his way down. AAA represents Mr. Mole's altitude relative to the ground (in meters)
julia-pushkina [17]

Answer:

  • <u><em>Mr. Mole's burrow lie 7 meters below the ground.</em></u>

Explanation:

The information given can be summarized as:

  • Mr Mole's altitude relative to the ground, in meters: A = - 2.3t - 7
  • Time, since Mr. Mole started digging, in minutes: t

<u>Interpetration of the terms in the model A = -2.3t - 7</u>

The equation A = -2.3t - 7 is a linear function, which consists of two terms:

  • The term -2.3t indicates that the altitude of Mr Mole decreases by 2.3 meters every minute. This is, -2.3 is the slope of the line in the graph that represents the altitude.

  • The constant term - 7 is the altitude at t = 0, because at t = 0 A = -2.3(0) - 7 = 0 - 7 = 0. This is, -7 is the intercept with the vertical axis in the graph that represents the altitude.

Thus, altitude at which <em>Mr. Mole's burrow lie</em> is the initial value given by the function, this is the altitude at t = 0, or the vertical intercept of the line; which, as just said is - 7. The negative sign tells that the value is below the ground (ground level is 0 meters). Then, <em>Mr. Mole's burrow lie 7 meters below the ground.</em>

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