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2 years ago

The center of circle q has coordinates (-2, 1). if circle q passes through r (6, 7), what is the length of its diameter?

Mathematics

1 answer:

Oksana_A [137]2 years ago

7 0

<h2>Diameter of a Circle</h2>

There are multiple strategies we can use to find the diameter of a circle. For this question, we must calculate the length of the radius first and multiply by 2 to find the diameter.

<h2>Solving the Question</h2>

We're given the centre and a point on the circumference: $(-2,1),(6,7)$ .

Find the distance between them using the distance equation:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Plug in the given points:

$d=\sqrt{(-2-x_1)^2+(1-y_1)^2}\\d=\sqrt{(-2-6)^2+(1-7)^2}\\d=\sqrt{(-8)^2+(-6)^2}\\d=\sqrt{64+36}\\d=\sqrt{100}\\d=10$

Therefore, the radius of the circle is 10 units.

Multiply the radius by 2 to find the length of the diameter:

10 × 2

= 20

Therefore, the length of the diameter is 20 units.

<h2>Answer</h2>

20 units

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Answer:

$\huge\boxed{(2,\ 3);\ (-1,\ 6)}$

Step-by-step explanation:

$f(x)=x^2-2x+3\to y=x^2-2x+3\\f(x)=-x+5\to y=-x+5\\\\\left\{\begin{array}{ccc}y=x^2-2x+3&(1)\\y=-x+5&(2)\end{array}\right$

substitute (1) to (2):

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$x^2-x+3=5$ subtract 5 from both sides

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$x^2-x-2=0\\\\x^2+x-2x-2=0\\\\x(x+1)-2(x+1)=0\\\\(x+1)(x-2)=0\iff x+1=0\ \vee\ x-2=0\\\\\boxed{x=-1\ \vee\ x=2}$

substitute the values of x to (2):

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3 years ago

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aleksklad [387]

Answer:

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Step-by-step explanation:

Let's assume total number of students registered is n

Last week n/4 people are absent

so people present are n - n/4 = <u>3n/4</u>

Today after return of Jen 1/5 n are absent

so people present are n - n/5 = 4n/5

which is also equal to last week present people + 1 (Jen)

= 3n/4 + 1

= (3n + 4) / 4

so (3n + 4) / 4 = 4n/5

=> 3n + 4 = 4n/5 * 4

=> (3n + 4) * 5 = 16n

=> 15n + 20 = 16n

=> 20 = n

=> n = 20

So total students registered for class is 20

today no of people absent = n/5 = 20/5 = 4

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