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3 years ago

Point B is a point of tangency. Find the radius r of OC.

Mathematics

1 answer:

Bumek [7]3 years ago

6 0

Answer:

r = 16 units

Step-by-step explanation:

From the figure attached,

AB is the tangent drawn from a point A to the circle C.

BC = r [Radius of the circle]

Length of AC = (18 + r)

AB = 30

By the property of a tangent drawn to a circle,

"Radius of a circle and tangent are perpendicular to each other"

AB ⊥ BC

By applying Pythagoras theorem in ΔABC,

AB² + BC² = AC²

(30)² + r² = (r + 18)²

900 + r² = r² + 36r + 324

36r = 900 - 324

r = $\frac{576}{36}$

r = 16 units

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Daniel [21]

5/6 - 1/5 = 19/30 = 0.633

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3 years ago

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Suppose 2' is a normally distributed random variable with ft = 10.3 and 0 = 3.8. For the following probability,draw an appropria

TiliK225 [7]

GIVEN

The following values are given:

$\begin{gathered} \mu=10.3 \\ \sigma=3.8 \end{gathered}$

SOLUTION

The z-score for the x values 9 and 14 can be calculated using the formula:

$z=\frac{x-\mu}{\sigma}$

For x = 9:

$\begin{gathered} z=\frac{9-10.3}{3.8} \\ z=-0.34 \end{gathered}$

For x = 14:

$\begin{gathered} z=\frac{14-10.3}{3.8} \\ z=0.97 \end{gathered}$

The probability can be calculated as follows:

$P(9\le x\le14)=Pr(-0.34The region that represents the solution is shown below:Therefore, the probability is given to be:[tex]P(9\le x\le14)=0.4671$

The probability is 0.4671.

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1 year ago

If the diagonal of a square is 11.3 meters, approximately what is the perimeter of the square?

Stells [14]

Answer:

Step-by-step explanation:

The diagonal of a square has a length of x sqrt(2), where x is the side length. This means the perimeter of the square is 4 (11.3/sqrt(2)), which means the perimeter is approx. 4*8, which is 32

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3 years ago

Use the pythagorean theorem to prove that this point lies on the unit circle. Find csc(0) where 0=-120.

exis [7]

By applying Pythagorean theorem, we have proven that the point (-1/2, -√3/2) lies on the unit circle.

<h3>How to prove this point lies on the unit circle?</h3>

In Trigonometry, an angle with a magnitude of -120° is found in the third quarter and as such, both x and y would be negative. Also, we would calculate the reference angle for θ in third quarter as follows:

Reference angle = 180 - θ

Reference angle = 180 - 120

Reference angle = 60°.

For the coordinates, we have:

sin(-120) = -sin(60) = -1/2.

cos(-120) = -cos(60) = -√3/2.

By applying Pythagorean theorem, we have:

z² = x² + y²

z = √((-1/2)² + (-√3/2)²)

z = √(1/4 + 3/4)

z = √1

z = 1.

Read more on unit circle here: brainly.com/question/9797740

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Sedaia [141]

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Step-by-step explanation:

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3 years ago