How much tax would you pay on items that cost $13.25 if the tax rate is 7%?

Mathematics

1 answer:

yKpoI14uk [10]2 years ago

7 0

7% of 13.25 is 0.9275

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Whats the radius for the circle? x^2+2x+y^2+4y-6=0

MAXImum [283]

Answer:

r = $\sqrt{11}$

Step-by-step explanation:

So we need to complete the square for both parts of the equation

First though we can add the 6 to the other side so we have x² + 2x + y² + 4y = 6

So first we can complete the square for x² + 2x

To do so we need to use $(\frac{b}{2} )^{2}$ to figure out the number we need to add to both sides

In this case our b is 2, so substituting this in we get $(\frac{2}{2} )^{2} =(1)^{2} =1$

Here we add 1 to both sides and now we have x² + 2x + 1 + y² + 4y = 6 + 1

Now we can follow the same steps to complete the square for y² + 4y

Here our b is 4, so substituting this in we get $(\frac{4}{2} )^{2}=(2)^{2} =4$

Now we add 4 to both sides and now we have x² + 2x + 1 + y² + 4y + 4 = 6 + 1 + 4

Now condensing everything we have (x + 1)² + (y + 2)² = 11

The formula for a circle is (x - h)² + (y - k)² = r²

In our equation we have r² = 11

To find the radius we need to take the square root of both sides $\sqrt{r^{2}} =\sqrt{11}$ to get r = $\sqrt{11}$

5 0

2 years ago

Given a soda can with a volume of 15 and a diameter of 2, what is the volume of a cone that fits perfectly inside the soda can?

Naddika [18.5K]

Check the picture below.

so, a cone, that fits inside the cylinder, will have the same height "h" and radius "r". Thus

$\bf \textit{volume of a cylinder}\\\\
V=\pi r^2 h\qquad \boxed{\pi r^2 h}=15
\\\\\\
\textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}\implies V=\cfrac{\boxed{15}}{3}$