All categories

2 years ago

Angle CCC is inscribed in circle OOO.

Mathematics

1 answer:

DedPeter [7]2 years ago

3 0

Answer:

The radius of the circle = 5 units

Step-by-step explanation:

Since AB is a diameter of the circle, then CAB is a semi-circle with a total angle measure of 180 degrees.

Now to find the value of the radius of the. circle, we use an important circle geometry principle which states that angle at centre is twice the angle at circumference, this means that angle C is 90 degrees which makes CAB a right triangle with the diameter being the hypotenuse.

Now we can use Pythagoras’ theorem to get the value of the diameter.

Mathematically Pythagoras’ asserted that the square of the value of the hypotenuse equals the square of the value of the opposite added to the square of the value of the adjacent.

Let’s call the hypotenuse h

h^2 = 6^2 + 8^2

h^2 + 36 + 64

h^2 = 100

h = √100

h = 10

But the question asks us to calculate the value of the radius and that is half of the value of the diameter which is 10/2 = 5

You might be interested in

The price of a box of 15 cloud markers is $12.70. The price of a box of 42 cloud markers is $31.60. All prices are without tax,

stich3 [128]

Answer:

Here, The price of one box having N markers = Price of N markers + packaging charge

Let M be the price of one Marker and P' be the price of packaging of one box which is same for any size.

Since, The price of a box of 15 cloud markers is $12.70.

That is , 15 M + P' = 12.70 ---------(1)

Also, The price of a box of 42 cloud markers is $31.60,

That is, 42 M + P' = 31.60 ---------(2),

Equation (2) - Equation (1),

27 M = 18.90,

⇒ M = 0.7

By putting the value of P in equation (1),

We get,

10.5 + P' = 12.70 ⇒ P' = 2.2,

Thus, the price of one marker, M = 0.7

And, the price of packaging one box, P' = 2.2

Thus, the price of a box of 50 marker = 50 × M + P' = 50×0.7 + 2.2 = 35 + 2.2 = $ 37.2

And, the equation that shows the price(P) of a box of N markers,

P = 0.7 N + 2.2

3 0

2 years ago

Read 2 more answers

Explain how to find the greatest number of identical arrangements that can be made with 54 roses and 42 tulips with no flowers l

Basile [38]

Work out the Greatest Common Factor for both numbers

54 421×54 1×422×27 2×213×18 3×146×9 6×7

The common factors are: 1, 2, 3 and 6
The greatest common factor is 6
There are 6 identical arrangements that can be made

There will be 9 roses and 7 tulips in each arrangement

3 0

2 years ago

Read 2 more answers

Amy is biking to school from her father's house and Jeremy is biking to school from his aunt's house. Suppose Amy is moving at a

Mnenie [13.5K]

No, having the greater rate of change does not mean a function will necessarily reach an output with the smallest input. It also depends on the initial values of the functions. If Jeremy's aunt lives closer to school, Jeremy's rate of change is smaller, but he could still get to school before Amy.

9 0

2 years ago

Read 2 more answers

Sara borrowed $500 for four years at 3 percent interest, compounded annually. Use the formula to calculate the total amount she

Mama L [17]

A=500×(1+0.03)^(4)
A=562.75

8 0

2 years ago

Read 2 more answers

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 1 + sec

masha68 [24]

Using the washer method, the volume is given by the integral

$\displaystyle\pi\int_{-\pi/3}^{\pi/3}\bigg((3-1)^2-((1+\sec x)-1)^2\bigg)\,\mathrm dx=2\pi\int_0^{\pi/3}(4-\sec^2x)\,\mathrm dx$

where 3 - 1 = 2 is the distance from y = 3 to the axis of revolution, and similarly (1 + sec(x)) - 1 = sec(x) is the distance from y = 1 + sec(x) to the axis. The integrand is symmetric about x = 0, so the integral "folds" in on itself, and the integral from -π/3 to π/3 is twice the integral from 0 to π/3.

So the volume is

$\displaystyle2\pi\int_0^{\pi/3}(4-\sec^2x)\,\mathrm dx=2\pi(4x-\tan x)\bigg|_0^{\pi/3}=\boxed{\dfrac{8\pi^2}3-2\pi\sqrt3}$

4 0

2 years ago