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3 years ago

Points N and R both lie on circle O. Line segment RQ is tangent to the circle at point R.

Mathematics

2 answers:

Anton [14]3 years ago

5 0

Answer: 15.0

explanation: i dont know im just good at maths

4vir4ik [10]3 years ago

4 0

Answer:

15.0

Step-by-step explanation:

Let's start by looking at triangle ORQ. Since RQ is tangent to the circle, we know that angle ∠ORQ is 90°. Then, since OR is equivalent to the radius of 5, RQ is 5√3, and side OQ is clearly larger than RQ, we can identify this as a 90-60-30 degree triangle. This makes side OQ have a length of 10, and angle ∠QOR, opposite of the second largest side, has the second largest angle of 60°, leaving ∠OQR with an angle of 30°.

The formula for the chord length is 2r*sin(c/2), with c being the angle between the two points on the circle (in this case, ∠QOR=∠NOR).. Our radius is 5, so the length of chord NR is 2*5*sin(60/2)=5, making our answer 5(ON)+5(OR)+5(RN)

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Given points A (1, 2/3), B (x, -4/5), and C (-1/2, 4) determine the value of x such that all three points are collinear

AlladinOne [14]

Answer:

$x=\frac{83}{50}$

Step-by-step explanation:

we know that

If the three points are collinear

then

$m_A_B=m_A_C$

we have

A (1, 2/3), B (x, -4/5), and C (-1/2, 4)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

step 1

Find the slope AB

we have

$A(1,\frac{2}{3}),B(x,-\frac{4}{5})$

substitute in the formula

$m_A_B=\frac{-\frac{4}{5}-\frac{2}{3}}{x-1}$

$m_A_B=\frac{\frac{-12-10}{15}}{x-1}$

$m_A_B=-\frac{22}{15(x-1)}$

step 2

Find the slope AC

we have

$A(1,\frac{2}{3}),C(-\frac{1}{2},4)$

substitute in the formula

$m_A_C=\frac{4-\frac{2}{3}}{-\frac{1}{2}-1}$

$m_A_C=\frac{\frac{10}{3}}{-\frac{3}{2}}$

$m_A_C=-\frac{20}{9}$

step 3

Equate the slopes

$m_A_B=m_A_C$

$-\frac{22}{15(x-1)}=-\frac{20}{9}$

solve for x

$15(x-1)20=22(9)$

$300x-300=198$

$300x=198+300$

$300x=498$

$x=\frac{498}{300}$

simplify

$x=\frac{83}{50}$

8 0

3 years ago

Help please thanks .

serious [3.7K]

Answer:

Step-by-step explanation:

3 0

3 years ago

Need help will reward

sweet [91]

Submit anwser it’s correct can i get brainliest

5 0

2 years ago

In the diagram below PQR are point on the circle with centre o and diameter 14cm <PRQ=35° Find the length of the minor arc PQ

Gekata [30.6K]

Answer:

Step-by-step explanation:

I'll draw a quick sketch. It's hard to "see" this kinda of problem w/o a drawing , so start there. just draw as much as you can from what the problem tells you.

diameter = 14 cm

radius = 7 cm

pi = 3.142

PRQ = 35 °

to find Y use law of sines

sin(70) / Y = sin(55) / 7

sin(70) / sin(55) / 7 = Y ( I'll use my calculator for all the non standard angles )

sin(70) * 7 / sin(55) = Y ( and invert and multiply the fraction in the denom )

8.03007 = Y

x = 70 °

if you have questions, and you should, just put them in the comments , I'll see them later :)

5 0

2 years ago

A circular piece of glass has a radius of 0.8 meters. The glass sells for $4.60 per square meter. What is the total cost of the

Mama L [17]

Here given that r= 0.8

Area of circular glass = area of circle = pi r^2

= 3.14 ( 0.8)^2 = 2.009 square meter

cost of one square meter = 4.60

cost of 2.009 square meter = 4.60 * 2.009 = 9.244

Answer $ 9.244 .

5 0

3 years ago

Read 2 more answers