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3 years ago

If y varies inversely as X and Y equals 5 when x equals 3 find X when Y is 15

Mathematics

1 answer:

omeli [17]3 years ago

5 0

Answer:

x = 1

Step-by-step explanation:

Given that y varies inversely as x then the equation relating them is

y = $\frac{k}{x}$ ← k is the constant of variation

To find k use the condition y = 5 when x = 3

k = yx = 5 × 3 = 15, thus

y = $\frac{15}{x}$ ← equation of variation

When y = 15 then

15 = $\frac{15}{x}$ ( multiply both sides by x )

15x = 15 ( divide both sides by 15 )

x = 1

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Solve the inequality for x 3^(6x+18)<27^(3x)

Lera25 [3.4K]

Answer:

$\displaystyle x > 6$

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Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle 3^{6x + 18} < 27^{3x}$

Step 2: Solve for x

Rewrite: $\displaystyle 3^{6x + 18} < 3^{3(3x)}$
Set: $\displaystyle 6x + 18 < 3(3x)$
Factor: $\displaystyle 3(2x + 6) < 3(3x)$
[Division Property of Equality] Divide 3 on both sides: $\displaystyle 2x + 6 < 3x$
[Subtraction Property of Equality] Subtract 3x on both sides: $\displaystyle -x + 6 < 0$
[Subtraction Property of Equality] Subtract 6 on both sides: $\displaystyle -x < -6$
[Division Property of Equality] Divide -1 on both sides: $\displaystyle x > 6$

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3 years ago

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For f(x) = 4x+ 1 and g(x) = x2 - 5, find (f+ g)(x).

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Answer:

x^2+4x-4

Step-by-step explanation:

4x+1+x^2-5

x^2+4x-4

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Step-by-step explanation:

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Product of two natural numbers p and q is 590 and their hcf is 59. how many set of values of p and q is possible

djverab [1.8K]

$\text{Let the product of two natural numbers p and q is 590, and their HCF is 59}\\
\\
\text{we know that the product of LCM and HCF of any two numbers is equal}\\
\text{to the product of the numbers. that is}\\
\\
\text{HCF}\times \text{ LCM}=p\times q\\
\\
\Rightarrow 59 \times \text{LCM}=590\\
\\
\Rightarrow \text{LCM}=\frac{590}{59}\\
\\
\Rightarrow \text{LCM}=10\\
\\
\text{for any two natural numbers, their Least Common Multiple (LCM) is always}$

$\text{greater than their HCF.}\\
\\
\text{but here we can see that }LCM$

Hence there is no such natural numbers exist.

7 0

3 years ago

PLEASE ANSWER AS QUICK AS POSSIBLE

Lady_Fox [76]

Answer:

(a) h^-1(x) = (x+6)/6

Step-by-step explanation:

The inverse relation can be found by solving for y: x = h(y).

<h3>Solution</h3>

x = h(y) . . . . . the inverse relation

x = 6y -6 . . . . . use the function definition

x +6 = 6y . . . . add 6

(x +6)/6 = y . . . . divide by 6

The inverse function is ...

$\boxed{h^{-1}(x)=\dfrac{x+6}{6}}$

4 0

2 years ago

If y varies inversely as X and Y equals 5 when x equals 3 find X when Y is 15​

If y varies inversely as X and Y equals 5 when x equals 3 find X when Y is 15