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3 years ago

Give the equation of the circle centered at the origin and passing through the point (0,3)

Mathematics

1 answer:

rusak2 [61]3 years ago

5 0

Answer:

The equation would be x^2 + y^2 = 9

Step-by-step explanation:

In order to find this, start with the base form of the circle.

(x - h)^2 + (y - k)^2 = r^2

Now we input the center as (h, k).

(x - 0)^2 + (y - 0)^2 = r^2

x^2 + y^2 = r^2

Now we can input the radius of 3 in for r

x^2 + y^2 = 3^2

x^2 + y^2 = 9

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Help please:Suppose that x and y inversely, and x=10 when y=8 write the function that models the inverse variation

jarptica [38.1K]

SOLUTION

From the question, we are told that y varies inversely as x

This is mathematically written as

$\begin{gathered} y\propto\frac{1}{x} \\ \propto\text{ is a sign of proportionality } \end{gathered}$

Now, we will remove the proportionality sign and replace it with equal to sign =

If we do this, we will intoduce a constant k

$\begin{gathered} y\propto\frac{1}{x} \\ y=k\times\frac{1}{x} \\ y=\frac{k}{x} \end{gathered}$

So we have the formula

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We will substitute the values of x for 10 and y for 8 into the formula to get k, we have

$\begin{gathered} y=\frac{k}{x} \\ 8=\frac{k}{10} \\ k=8\times10 \\ k=80 \end{gathered}$

Now, we will substitute k for 80 back into the formula to get the inverse function, we have

$\begin{gathered} y=\frac{k}{x} \\ y=\frac{80}{x} \end{gathered}$

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