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2 years ago

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Mathematics

1 answer:

MrRissso [65]2 years ago

7 0

Answer:

f(n)=-5-3n

Step-by-step explanation:

Given the recursive formula of a sequence

f(1)=−8

f(n)=f(n−1)−3

We are to determine an explicit formula for the sequence.

f(2)=f(2-1)-3

=f(1)-3

=-8-3

f(2)=-11

f(3)=f(3-1)-3

=f(2)-3

=-11-3

f(3)=-14

We write the first few terms of the sequence.

-8, -11, -14, ...

This is an arithmetic sequence where the:

First term, a= -8

Common difference, d=-11-(-8)=-11+8

d=-3

The nth term of an arithmetic sequence is determined using the formula:

T(n)=a+(n-1)d

Substituting the derived values, we have:

T(n)=-8-3(n-1)

=-8-3n+3

T(n)=-5-3n

Therefore, the explicit formula for f(n) can be written as:

f(n)=-5-3n

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A satellite is composed of 30 modular units, each of which is equipped with a set of sensors, some of which have been upgraded.

Marta_Voda [28]

Answer:

$\dfrac{1}{7}$

is the fraction of sensors upgraded per unit.

Step-by-step explanation:

We are given the following in the question:

Let x be the number of upgraded sensors in one unit and y be the number of non-upgraded sensors in one unit.

Number of modular units = 30

Since some part of unit is upgraded and some are non-upgraded, then, we can write the equation:

$x + y = 1$

Number of non-upgraded sensors =

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Thus, we can write the equation:

$y = \dfrac{30x}{5}\\\\y = 6x\\1-x = 6x\\\\x = \dfrac{1}{7}$

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3 0

2 years ago

QUESTION 11.1

lawyer [7]

The group paid $ 5250 at first city and $ 6250 at second city

<u>Solution:</u>

Let x = the charge in 1st city before taxes

Let y = the charge in 2nd city before taxes

The hotel charge before tax in the second city was $1000 higher than in the first

Then the charge at the second hotel before tax will be x + 1000

y = x + 1000 ----- eqn 1

The tax in the first city was 8.5% and the tax in the second city was 5.5%

The total hotel tax paid for the two cities was $790

<em><u>Therefore, a equation is framed as:</u></em>

8.5 % of x + 5.5 % of y = 790

$\frac{8.5}{100} \times x + \frac{5.5}{100} \times y = 790$

0.085x + 0.055y = 790 ------- eqn 2

<em><u>Let us solve eqn 1 and eqn 2</u></em>

<em><u>Substitute eqn 1 in eqn 2</u></em>

0.085x + 0.055(x + 1000) = 790

0.085x + 0.055x + 55 = 790

0.14x = 790 - 55

0.14x = 735

<em><u>Substitute x = 5250 in eqn 1</u></em>

y = 5250 + 1000

Thus the group paid $ 5250 at first city and $ 6250 at second city

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2 years ago

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Kruka [31]

Answer:

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Step-by-step explanation:

(see attached for reference)

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Answer:

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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago