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2 years ago

If a ∝ b and a = 18 when b = 3, then find a when b = 5.

Mathematics

1 answer:

Elden [556K]2 years ago

4 0

"a ∝ b" means "a is proportional to b", which in turn means there is some constant k such that

a = kb

We're given that a = 18 and b = 3, so that

18 = 3k ⇒ k = 6

Then when b = 5, we would have

a = 6 × 5 = 30

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6 hours

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6 hours

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3 years ago

If f(x) = 4(3x - 5), find f-1(x)

deff fn [24]

Answer:

$f^{-1}(x) = \frac{1}{12}(x+20)$

Step-by-step explanation:

Given: f(x) = 4(3x - 5)

Is required to find f⁻¹(x)

f(x) = y = 4(3x - 5)

∴ y = 4 * 3x - 4 * 5

∴ y = 12x - 20 ⇒ add 20 to both sides

∴ y + 20 = 12x ⇒ divide both sides by 12

∴ $\frac{1}{12} (y+20) = x$

Replace the places of x and y.

∴ $y=\frac{1}{12} (x+20)$

∴ $f^{-1}(x) = \frac{1}{12}(x+20)$

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