Find the quotient: 15x^4y^2 - 25x^2y^3 + 45xy / 5xy:

Mathematics

1 answer:

salantis [7]3 years ago

6 0

Answer:

3x^3y − 5xy^2 + 9

Step-by-step explanation:

When there is only one denominator term, the quotient can be found by dividing the numerator terms individually.

$\dfrac{15x^4y^2 - 25x^2y^3 + 45xy}{5xy}=\dfrac{15x^4y^2}{5xy}-\dfrac{25x^2y^3}{5xy}+\dfrac{45xy}{5xy}=3x^3y-5xy^2+9$

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There are a couple of things to keep in mind here:

an exponent tells the number of times the factor is repeated
equal numbers of identical factors cancel from numerator and denominator, for example x^3/x = (x·x·x)/x = x·x = x^2. (One factor of x cancels.)

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OK, lets start by drawing a basic graph (the first one) so we can visualize.

We already know that the y coordinate of the circle's center is $4$ .

We know that the circle is tangent to the $X$ axis at $(-2,0)$

That means the x coordinate of the center has to be $-2$ , as the tangent is a point on the edge of the circle that touches a line at exactly one point.

The radius is the distance from the center of the circle to its edge. We know the center's location now, it is $(-2, 4)$ and a point on the edge of the circle (the tangent point) which is $(-2,0)$ . so the distance between the points is 4 which is the radius (you can use the distance formula, but it's quite oblivious.)

We can imagine the circle should look like this (the second one):

Now we can piece together an equation

The equation of a circle is $(x-h)^2+(y-k)^2=r^2$ where $(h,k)$ is the center and $r$ is the radius. When we put the numbers in: we get $(x-(-2))^2+(y-(4))^2=4^2$ which can be simplified into $(x+2)^2+(y-4)^2=16$ which is the answer.