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Scorpion4ik [409]
3 years ago
10

Point p is the center of two concentric circle pq =2.5 and ps= 5 RS is tangent to the smaller circle and a chord of the larger c

ircle what is length of RS to the nearest tenth

Mathematics
2 answers:
lukranit [14]3 years ago
7 0

The answer is 8.7

..............................

konstantin123 [22]3 years ago
5 0

Here Q and S are the points on smaller and larger circles respectively and P is the center of both circles.

Given that, radius of smaller circle, PQ= 2.5

and radius of larger circle, PS= 5

RS is a chord of the larger circle and tangent to the smaller circle at point Q.

That's why, ∠PQS will be 90° and the ΔPQS is a right angle triangle.

For ΔPQS, we will use Pythagorean Theorem, according to this theorem here:

(PS)² = (PQ)² + (QS)²

⇒ (5)² = (2.5)² + (QS)² [By plugging PS= 5 and PQ= 2.5]

⇒ 25 = 6.25 + (QS)²

⇒ 18.75 = (QS)² [Subtracting 6.25 from both sides]

⇒ QS = √18.75

⇒ QS = 4.3301

Here Q is the midpoint of the cord RS, so RQ= QS

That means, RS = 2× QS

= 2× 4.3301

= 8.6602

= 8.7 [Rounding to the nearest tenth]

So, the length of RS to the nearest tenth is 8.7

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25. Michael is studying population changes in two
g100num [7]

Answer: Average rates of change for Bird A is 0.045 and for Bird B is 3.816.

Step-by-step explanation: Through its graph, a function can be analyzed and be identified its attributes. Average Rate of Change is the ratio of change in the function values to the change of x-value, i.e., it is the slope of the function in a specific interval of x. With the Average it is possible to compare two function.

<u>Average Rate of Change</u>

<em><u>Bird A</u></em>:

For the interval [0,18]:

x₁ = 0 f(0) = 8.3

x₂ = 18 f(18) = 9.1

Average = \frac{f(18) - f(0)}{x_{2} - x_{1} }

Average = \frac{9.1 - 8.3}{18 - 0}

Average = 0.045

<em><u>Bird B</u></em>: y = 3.6(1.06)x

For the interval [0,18]:

x₁ = 0 y = 3.6(1.06)0 = 0

x₂ = 18 y = 3.6(1.06)18 = 68.7

Average = \frac{f(18) - f(0)}{x_{2} - x_{1} }

Average = \frac{68.7 - 0}{18 - 0}

Average = 3.816

The Average Rate for Change for Bird A is 0.045 and for Bird B is 3.816. This means that the population of Bird B increase in rate faster than the population of Bird A.

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3 years ago
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