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3 years ago

If XY=18, YZ=14, and XZ=20, find the radius of each circle.

Mathematics

1 answer:

Pachacha [2.7K]3 years ago

8 0

Let`s assume that points M, N and P are the touching points of those 3 circles:Then:Y M + M Z = 14,Z N + N X = 20X P + P Y = 18And also: M Z = ZN, Y M = P Y and N X = X P.Now we have a system of 3 equations ( Y M, M Z and X P are the radii of each circle ):Y M + M Z = 14M Z + X P = 20X P + Y M = 18 Y M - M Z = - 14+X P + Y M = 18 X P - M Z = 4Y M - M Z = - 14+M Z + X P = 20 X P - Y M = 6 /* ( - 1 )X P - M Z = 4 X P + Y M = - 6 X P - M Z = 4 Y M - M Z = - 2 Y M + M Z = 14 2 Y M = 12 => Y M = 6M Z - 6 = 2 => M Z = 8X P + 6 = 18
X P = 12
Radii of the circles are: 12, 8 and 6.

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3 years ago

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Mazyrski [523]

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4.013

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3 years ago

Cathy lives in a state where speeders are fined $15 for each mile per hour over the speed limit. Cathy was given a ticket for $1

Simora [160]

Answer:

Cathy was driving at a speed of 67 miles per hour.

Step-by-step explanation:

Fined $15 for each mile per hour over the speed limit. Cathy was given a ticket for $105.

We solve this using a rule of three.

1 mile - $15

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Applying cross multiplication:

15x = 105

x = 105/5 = 7.

Cathy was 7 miles above the speed limit.

How fast was Cathy driving?

7 miles above the speed limit of 60 miles per hour, so 60 + 7 = 67 miles per hour.

Cathy was driving at a speed of 67 miles per hour.

3 0

3 years ago

Select the correct word to describe the function. the equation y = startfraction 5 x cubed over 8 endfraction represents functio

balandron [24]

The functions and their descriptions are:

Polynomial: $y = \frac{5x^3}{8}$ and $y = 5x^3 + 8$
Logarithm: $y = 6 + 0.25\ln(x)$
Exponential $y = \frac{18}{1 + 6e^{-0.25x}}$

<h3>How to describe the functions?</h3>

The functions are given as:

$y = \frac{5x^3}{8}$

$y = 6 + 0.25\ln(x)$

$y = \frac{18}{1 + 6e^{-0.25x}}$

$y = 5x^3 + 8$

The functions would be described based on the type of function they represent.

Functions that use the "ln" keyword are logarithmic functions, while functions that use the "e" keyword are exponential functions.