Y is inversely proportional to a^3

Mathematics

1 answer:

Ludmilka [50]2 years ago

6 0

Answer:

y = 0.64/x^3

Step-by-step explanation:

If y is inversely proportional to a^3, we can write the equation:

y * a^3 = k

Using a = 2 and y = 10, we have:

10 * 2^3 = k

k = 80

If a is directly proportional to x, we can write the equation:

a = c * x

Using x = 4 and a = 20, we have:

20 = c * 4

c = 5

Now, using the value of a = 5*x in the equation y * a^3 = 80, we have:

y * (5x)^3 = 80

y * 125x3 = 80

y = 80/(125x3) = 0.64/x^3

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Solve for x. 83 = 35^x Express the answer to the hundredths place (i.e., two digits after the decimal point). x =

devlian [24]

Answer:

x = 1.24

Step-by-step explanation:

In order to get that x down from its current position of exponential, you need to take either the log or the natural log of both sides. The power rule tells us that we can then pull the exponent down in front. So let's take the natural log of both sides:

$ln(83)=ln(35)^x$

We can bring the x down in front to give us:

ln(83) = x ln(35)

The right side of this is "stuck" together by multiplication, so we can undo that multilication by division of the ln(35). That leaves us with just x on the right:

$\frac{ln(83)}{ln(35)}=x$