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sesenic [268]
3 years ago
11

In the diagram below,AB is the diameter of the circle with centre P.Point C lies on the y-axis.Given the coordinates of A and B

are (-6,3) and (2,-3) respectively ,calculate
a)the coordinates of P





b)radius of the circle





c)the coordinates of C





d)the area of the circle in term of
\pi
​

Mathematics
1 answer:
Step2247 [10]3 years ago
4 0

Answer:

<em>The coordinates of P are (-2,0)</em>

<em>The radius of the circle is 5.</em>

Step-by-step explanation:

<u>Analytic geometry</u>

The diagram shows a circle with center P, and two points A(-6,3) and B(2,-3) that form the diameter of the circle.

a)

The center of the circle lies at the midpoint of A and B. The midpoint (xm,ym) can be calculated by:

\displaystyle x_m=\frac{x_1+x_2}{2}

\displaystyle y_m=\frac{y_1+y_2}{2}

Substituting x1=-6, x2=2, y1=3, y2=-3:

\displaystyle x_m=\frac{-6+2}{2}=\frac{-4}{2}=-2

\displaystyle y_m=\frac{3-3}{2}=0

Thus, the coordinates of P are (-2,0)

b) The radius of the circle is the distance from the center to any point in its circumference. We can use the distance from P to A or B indistinctly.

Given two points A(x1,y1) and P(x2,y2), the distance between them is:

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

Substituting x1=-6, x2=-2, y1=3, y2=0:

r=\sqrt{(-2+6)^2+(0-3)^2}

r=\sqrt{4^2+(-3)^2}

r=\sqrt{16+9}=\sqrt{25}=5

The radius of the circle is 5.

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Two dice are rolled. Determine the probability of the following: rolling a 6 or doubles
gtnhenbr [62]

Answer as an exact fraction = 5/18

Answer as an approximate decimal = 0.2778

Answer as an approximate percentage = 27.78%

============================================================

Explanation:

x = result of the first die

y = result of the second die

(x,y) paired together shows the results of both dice at the same time.

Something like (x,y) = (4,2) means we got 4 on the first die and 2 on the second die.

--------

Let's list the ways of rolling a 6

  • (1,5)
  • (2,4)
  • (3,3)
  • (4,2)
  • (5,1)

There are 5 ways to roll a 6. Each pair listed has the property x+y = 6.

--------

List all the ways of getting doubles

  • (1,1)
  • (2,2)
  • (3,3)
  • (4,4)
  • (5,5)
  • (6,6)

There are 6 ways to roll doubles. Each pair mentioned has x = y.

--------

We have 5+6 = 11 items listed above. However, there are only 10 unique pairs though because (3,3) was listed twice. So we could say 5+6-1 = 11-1 = 10.

This is out of 6*6 = 36 different ways to roll the two dice. The probability is therefore 10/36 = 5/18.

Using a calculator, 5/18 = 0.2778 = 27.78%

7 0
3 years ago
Evaluate expressions-What should go in the blank spot
gladu [14]

Answer:

10

Step-by-step explanation:

0.08 {x}^{3}

0.08( {5)}^{2}

0.08 \times 125

10

<h3>Hope it is helpful...</h3>
4 0
3 years ago
i am using my big brothers acount. i need help johnny got 10 apples and he had 10 dollars now he dosent have money. did he spend
Oxana [17]

Answer:

Yes. He spent 10 dollars.

Step-by-step explanation:

If he bought 10 apples, and he had 10 dollars, he would have no money left because each apple was 1 dollar.

hope this helps!

4 0
3 years ago
Solve for x. Write both solution, separated by a comma. 4x^2-x-3=0.
Step2247 [10]

Answer:

x = -3/4, 1

Step-by-step explanation:

Factor left side of the equation.

(4x + 3)(x - 1) = 0

Set factors equal to 0.

4x + 3 = 0

4x = -3

x = -3/4

x - 1 = 0

x = 1

6 0
3 years ago
Read 2 more answers
The vertex of this parabola is at (-2, -3). When the x-value is -1, the
valina [46]

Answer:

-2

Step-by-step explanation:

Start with the vertex form of the equation of a parabola:  y - k = a(x - h)^2

Here h = -2, k = -3, x = -1, y = -5.  Find a:

-5 - [-3] = a(-1 - [-2])^2, or

-5 + 3 = a(1)^2, or

-2 = a

The unknown coefficient is -2.

7 0
3 years ago
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