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stiv31 [10]
2 years ago
13

The sum of three numbers in g.p. is 21 and the sum of their squares is 189. find the numbers.

Mathematics
1 answer:
sashaice [31]2 years ago
3 0
Let the three gp be a, ar and ar^2
a + ar + ar^2 = 21 => a(1 + r + r^2) = 21 . . . (1)
a^2 + a^2r^2 + a^2r^4 = 189 => a^2(1 + r^2 + r^4) = 189 . . . (2)
squaring (1) gives
a^2(1 + r + r^2)^2 = 441 . . . (3)
(3) ÷ (2) => (1 + r + r^2)^2 / (1 + r^2 + r^4) = 441/189 = 7/3
3(1 + r + r^2)^2 = 7(1 + r^2 + r^4)
3(r^4 + 2r^3 + 3r^2 + 2r + 1) = 7(1 + r^2 + r^4)
3r^4 + 6r^3 + 9r^2 + 6r + 3 = 7 + 7r^2 + 7r^4
4r^4 - 6r^3 - 2r^2 - 6r + 4 = 0
r = 1/2 or r = 2
From (1), a = 21/(1 + r + r^2)
When r = 2:
a = 21/(1 + 2 + 4) = 21/7 = 3
Therefore, the numbers are 3, 6 and 12.
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3 years ago
A boat can travel 105 miles on 15 gallons of gasoline. How much gasoline will it need to go 140 miles?
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3 years ago
Read 2 more answers
Suppose Cotangent (theta) = StartFraction 5 Over 12 EndFraction, where Pi less-than theta less-than StartFraction 3 pi Over 2 En
Agata [3.3K]

Answer:

Sin theta = 12/13

Step-by-step explanation:

From the question;

Cot theta = 5/12

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Cot theta = 1/ tan theta

Hence, tan theta = 12/5

Mathematically

tan theta= opposite/adjacent

to get hypotenuse, we will use Pythagoras’ theorem which states that the square of the hypotenuse equals sum of the squares of the two other sides

let hypotenuse be h

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5 0
2 years ago
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Archy [21]

Answer:

62.5 mph

Step-by-step explanation:

Given that :

Peter :

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Emily :

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For Emily to cover 125 miles in (11:30 - 9:30) = 2 hours

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Speed = 125 miles / 2 hours

Speed = 62.5 miles per hour

7 0
2 years ago
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