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3 years ago

A circle is centered at the point (-3,2) and passes through the point (1,5). What is the radius of the circle?

Mathematics

1 answer:

Akimi4 [234]3 years ago

8 0

Answer:

Step-by-step explanation:

The radius is a distance on a circle from the center to a point on the circle.

We have both of these points describe here in this definition. Using the distance formula will give us the radius.

$\sqrt{(x \text{ difference })^2+(y \text{ difference})^2$

The difference between 1 and -3 is 1-(-3)=4.

The difference between 5 and 2 is 5-2=3.

$\sqrt{4^2+3^2}$

$\sqrt{16+9}$

$\sqrt{25}$

$5$

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The sum of the first 21 terms of the progression, - 18, - 15,-12.....is?

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3 years ago

Find the lowest common multiple of 8 12 18 by prime factories

Crank

Step-by-step explanation:

8=1,2,4,8.

12=1,2,3,4,6.

18=1,2,3,6,9.

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5 0

3 years ago

Rosalie is organizing a circus performance to raise money for a charity. She is trying to decide how much to charge for tickets.

Ray Of Light [21]

Answer:

she should charge $7.395 per ticket in order to make the most money.

Step-by-step explanation:

From the given information:

If Rosalie charges $5 then 1175 people will attend the circus performance

If Rosalie charges $7 then 935 people will attend the circus performance

Let x be the cost and y to be the number of people that will attend the performance . Then, we will have two points which are;

(5, 1175) and (7, 935)

The slope(m) of this points = $\dfrac{\Delta y}{\Delta x}$

= $\dfrac{y_2-y_1}{x_2-x_1}$

$=\dfrac{935-1175}{7-5}$

Slope (m) = $\dfrac{-240}{2}$

Slope (m) = -120

However; we can now have the linear equation:

$y-y_1 = m(x-x_1)$

$y-1175= -120(x-5)$

$y-1175= -120x+600$

$y= -120x+600+1175$

$y= -120x+1775$

The linear function is : y = -120x + 1775

Now; the total amount of money she can now earn is:

f(x) = xy

f(x) = x(-120x + 1775)

f(x) = -120x² + 1775x

The above expression is a quadratic equation; Using the quadratic formula; we have:

$=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$

where; a = -120 ; b = +1775 and c = 0

$=\dfrac{-(1775) \pm \sqrt{(1775)^2-4(-120)(0)}}{2(-120)}$

$=\dfrac{-(1775) + \sqrt{(1775)^2-4(-120)(0)}}{2(-120)} \ \ \ \ \ OR \ \ \ \ \dfrac{-(1775) -\sqrt{(1775)^2-4(-120)(0)}}{2(-120)}$

$=\dfrac{-(1775) + \sqrt{(1775)^2}}{(-240)} \ \ \ \ \ OR \ \ \ \ \dfrac{-(1775) -\sqrt{(1775)^2}}{(-240)}$

$=\dfrac{-(1775) + (1775)}{(-240)} \ \ \ \ \ OR \ \ \ \ \dfrac{-(1775) - (1775)}{(-240)}$

$=\dfrac{0}{(-240)} \ \ \ \ \ OR \ \ \ \ \dfrac{-3550}{(-240)}$

= 0 OR 14.79

Since; we are considering the value greater than zero

x = 14.79

maximum value of x = 14.79/2 = 7.395

Thus ; she should charge $7.395 per ticket in order to make the most money.

6 0

3 years ago