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Rom4ik [11]
2 years ago
6

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

Mathematics
1 answer:
Pachacha [2.7K]2 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 0
2 years ago
Given a 30-60-90 triangle with a long<br> leg of 9 in, determine the length of the<br> hypotenuse.
aniked [119]

Answer:

10.38 in

Step-by-step explanation:

Long side would be opposite to 60°.

Since, side opposite to 60° is root 3 upon 2 times of hypotenuse.

9 =  \frac{ \sqrt{3} }{2} \times hypotenuse \\  \\ hypotenuse =  \frac{9 \times 2}{ \sqrt{3} }  \\  =  \frac{18}{ \sqrt{3} }  =  \frac{18 \sqrt{3} }{3}  = 6 \sqrt{3}  = 6 \times 1.73 \\   \:  \:  \: \red{ \bold{hypotenuse = 10.38 \: in}}

8 0
3 years ago
A carpenter must pick up a wooden beam from the Home Depot. The wooden beam is 12 feet long. The bed of his truck is 5.5 ft by 8
rosijanka [135]

Answer:

Beam stick out = 2.09 ft

Step-by-step explanation:

Given:

Length of wooden beam = 12 ft

Side of bed =  5.5 ft by 8 ft by 2 ft

Find:

Length of wooden beam needed.

Computation:

Length\ of \ diagonal = \sqrt{a^2+ b^+ c^} \\\\\\ Length\ of\ diagonal =  \sqrt{5.5^2+ 8^2+ 2^2}\\\\ Length\ of\ diagonal =  \sqrt{30.25+64+4}\\\\Length\ of\ diagonal =  \sqrt{98.25}\\\\Length\ of\ diagonal =  \sqrt{30.25+64+4}\\\\Length\ of\ diagonal = 9.91

Length of wooden beam needed = 9.91 ft

Beam stick out = 12 ft - 9.91 ft

Beam stick out = 2.09 ft

4 0
3 years ago
-1/5 divided by 20
Kryger [21]

Answer:

-0.01

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
What expression is equivalent to 12x⁴ over 4x¹⁶
alexgriva [62]

Answer:

\frac{3}{x^1^2}

Step-by-step explanation:

\frac{12x^4}{4x^1^6}=3x^4/x^16

bring "x^4" to the bottom to subtract it with x^16

3/x^16*x^-4

3/x^12

hope this helps!

7 0
3 years ago
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