3 years ago

Simplify this problem

Mathematics

1 answer:

Ksju [112]3 years ago

3 0

Hope this helps u....!!

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A car travels at a rate of 45 miles per hour for 5 hours. Let y be the distance, in miles, the car travels for a given amount of

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Answer: A. 0<_ x <_ 5

Step-by-step explanation:

45 miles represents y and 5 hours amount of time represents x, you finding x-values. Your first will be 0, then <_, with x (domain:x-values), lastly 5 because 5 is an x-value and they want the domain of the function,

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5x+10

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What are m and b in the linear equation y= 5 + 1x

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If the 5th term of a geometric progression is 162 and the 8th term is 4374, find the (i) 1st three terms of the sequence; (ii) s

Alona [7]

Answer:

see explanation

Step-by-step explanation:

The nth term of a geometric progression is

$a_{n}$ = a₁ $r^{n-1}$

where a₁ is the first term and r the common ratio

Given a₅ = 162 and a₈ = 4374 , then

a₁ $r^{4}$ = 162 → (1)

a₁ $r^{7}$ = 4374 → (2)

Divide (2) by (1)

$\frac{a_{1}r^{7} }{a_{1}r^{4} }$ = $\frac{4374}{162}$

r³ = 27

r = $\sqrt[3]{27}$ = 3

Substitute r = 3 into (1) and solve for a₁

a₁ $(3)^{4}$ = 162

81a₁ = 162

a₁ = $\frac{162}{81}$ = 2

Then

a₂ = a₁ × 3 = 2 × 3 = 6

a₃ = a₂ × 3 = 6 × 3 = 18

The first 3 terms are 2, 6, 18

(ii)

The sum to n terms of a geometric progression is

$S_{n}$ = $\frac{a_{1}(r^{n}-1) }{r-1}$ , then

$S_{10}$ = $\frac{2(3^{10}-1) }{3-1}$

= $\frac{2(59049-1)}{2}$

= 59049 - 1

= 59048

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3 years ago