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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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Mark and Don are planning to sell each other their marble collections at a garage sale. If Don has 1 more than 3 times the numbe

Volgvan

Answer: Mark has 28 marbles while Don has 85 marbles.

Step-by-step explanation:

Let x represent the number of marbles that Mark has.

Let y represent the number of marbles that Don has.

If Don has 1 more than 3 times the number of marbles Mark has, it means that

y = 3x + 1

The total number of marbles is 113. It means that

x + y = 113- - - - - - - - - - - - 1

Substituting y = 3x + 1 into equation 1, it becomes

x + 3x + 1 = 113

4x + 1 = 113

4x = 113 - 1 = 112

x = 112/4

x = 28

y = 3x + 1 = 3 × 28 + 1

y = 85

4 0

3 years ago

Plz help me I need your help plz help me plz plz plz help me plz help me plz

Fynjy0 [20]

answer is 250 which is D Because 250 of 24%=60, so subtract 60 from 250 it will give you 190

7 0

3 years ago

Read 2 more answers

Forces of 9 lbs and 13 lbs act at a 38º angle to each other. Find the magnitude of the resultant force and the angle that the re

fiasKO [112]

Answer: $R=20.84\ lb\quad 22.57^{\circ},15.43^{\circ}$

Step-by-step explanation:

Given

Two forces of 9 and 13 lbs acts $38^{\circ}$ angle to each other

The resultant of the two forces is given by

$\Rightarrow R=\sqrt{a^2+b^2+2ab\cos \theta}$

Insert the values

$\Rightarrow R=\sqrt{9^2+13^2+2(9)(13)\cos 38^{\circ}}\\\Rightarrow R=\sqrt{81+169+184.394}\\\Rightarrow R=\sqrt{434.394}\\\Rightarrow R=20.84\ lb$

Resultant makes an angle of

$\Rightarrow \alpha=\tan^{-1}\left( \dfrac{b\sin \theta}{a+b\cos \theta}\right)\\\\\text{Considering 9 lb force along the x-axis}\\\\\Rightarrow \alpha =\tan^{-1}\left( \dfrac{13\sin 38^{\circ}}{9+13\cos 38^{\circ}}\right)\\\\\Rightarrow \alpha =\tan^{-1}(\dfrac{8}{19.244})\\\\\Rightarrow \alpha=22.57^{\circ}$