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4 years ago

Find an equation of the circle that has center (-1, 3) and passes through (1. 1)

Mathematics

2 answers:

pshichka [43]4 years ago

3 0

Answer:

(x + 1)² + (y - 3)² = 8

Step-by-step explanation:

radius (r): √(1 - (-1))² + (1 - 3)² = √8 = 2√2

Formula for circle with center (h,k): (x – h)² + (y – k)² = r²

(x + 1)² + (y - 3)² = 8

Dovator [93]4 years ago

3 0

Answer:

( x + 1)^2 + (y - 3)^2 = 8

Step-by-step explanation:

The equation of a circle with a center and a point

( x - a) ^2 + ( y - b) ^2 = r^2

( a , b) - center of the circle

( x, y) - any point on the circle

r^2 - radius of the circle

We are provided with a center and a point

( -1 , 3) - ( a, b) - center

a = -1

b = 3

( 1 , 1) - ( x, y) - point

x = 1

y = 1

Step1: substitute the center of the circle into the equation

( x - (-1)^2 + ( y - 3)^2 = r^2

(x + 1)^2 + (y - 3)^2 = r^2

Step 2: sub the point into the equation

( x + 1)^2 + (y - 3)^2 = r^2

x - 1

y - 1

( 1 + 1)^2 + ( 1 - 3)^2 = r^2

( 2)^2 + ( -2)^2 = r^2

4 + 4 = r^2

8 = r^2

Step 3 : sub the radius into the equation

( x + 1)^2 + ( y - 3)^2 = r^2

( x + 1)^2 + (y - 3 )^2 = 8

Therefore, the equation of the circle is

( x + 1)^2 + ( y - 3)^2 = 8

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Suppose that y varies inversely with x, and y=4 when x=7. What is an equation for the inverse variation

balu736 [363]

Answer:

xy = 28

Step-by-step explanation:

The formula for inverse variation is

xy =k

If y = 4 and x = 7

4*7 = k

28 = k

The equation is xy = 28

8 0

3 years ago

2. Find the value of x and y rounded to the nearest tenth.

SVETLANKA909090 [29]

Using relations in a right triangle, it is found that the values of x and y are given by: x = 24, y = 46.4, given by option a.

<h3>What are the relations in a right triangle?</h3>

The relations in a right triangle are given as follows:

The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.

The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.

The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

First, we start with the vertical line h that divides y, that is <u>opposite to an angle of 30º, with hypotenuse 34</u>, hence:

sin(30º) = h/34

0.5 = h/34

h = 17.

Then, h is opposite to an angle of 45º, while the hypotenuse is x, hence:

$\sin{45^\circ} = \frac{17}{x}$

$x = \frac{17}{\sin{45^\circ}}$

x = 24.

y is divided into two segments.

The first is the adjacent to the angle of 30º, while the hypotenuse is 34.

The second is adjacent to the angle of 45º, while the hypotenuse is 24.

Then:

$\cos{30^\circ} = \frac{y_1}{34}$

$y_1 = 34\cos{30^\circ} = 29.4$

$\cos{45^\circ} = \frac{y_2}{24}$

$y_2 = 24\cos{45^\circ} = 17$

Then, the value of y is given by:

$y = y_1 + y_2 = 29.4 + 17 = 46.4$ .

More can be learned about relations in a right triangle at brainly.com/question/26396675

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4 0

2 years ago

Tony allows his customers to create their own pizza. The customers choose exactly one type of crust, sauce, cheese, and meat for

Natalka [10]

In cases like these, you simply have to multiply the choices you have for each step.

In fact, you can choose between 4 different crusts. For each of these crusts you can choose 4 different sauces. This means that there are $4\cdot 4 = 16$ choices at this point. In fact, if we call the crust options 1,2,3,4 and the sauce options A,B,C,D, the 16 possible combinations are