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3 years ago

Given △ABC, AB=15, BD=9, AD ⊥ BC , m∠C=30° Find: The perimeter of △ABC.

Mathematics

1 answer:

Ann [662]3 years ago

7 0

Answer:

48 + 12√3 units

Step-by-step explanation:

ALL LENGTHS MUST BE POSITIVE (I did this to avoid writing ± and showing that only + works)

1. Find AD (you'll find why later): 15² = 9² + AD² --> AD² = 144 --> AD = 12

2. 30-60-90: 12-DC-AC --> AC = 24, DC = 12√3 (side opposite of 90 is double side opposite of 30, side opposite of 60 is √3 times the opposite of 30)

P = AB + BD + DC + AC = 15 + 9 + 12√3 + 24 = 48 + 12√3 units

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A solid sphere is cut into 4 equal wedges the volume of each wedge is v=1/3r3 solve the volume for r

Dennis_Churaev [7]

Answer:

r = (3V/π)^1/3

Step-by-step explanation:

Given that :

Volume of a sphere = V = 4/3πr³

Dividing into 4

4/3 * 1/4 πr³ = 4/12πr³ = 1/3πr³

V = 1/3πr³

Cross multiply

3V = πr³

Divide both sides by π

3V/ π = πr³/ π

3V/ π = r³

Take the cube root of both sides

r = (3V/π)^1/3

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3 years ago

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Vinil7 [7]

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5 0

3 years ago

Explain how you could use the conversion table to convert 700 centimeters to meters.

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8 0

3 years ago

B = 4 and c = -5, evaluate b 2 - c 2

NISA [10]

Hey!

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Steps To Solve:

~Substitute

(4)2 - (-5)2

~Multiply

8 - (-10)

~Subtract

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Answer:

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4 0

3 years ago

Read 2 more answers

The following data are the distances between 20 retail stores and a large distribution center. The distances are in miles.

Free_Kalibri [48]

Answer:

1191.4 ; 34.5

Step-by-step explanation:

Given the data:

29; 37; 38; 40; 58; 67; 68; 69; 76; 86; 87; 95; 96; 96; 99; 106; 112; 127; 145; 150

The sample variance and standard deviation can be obtained thus :

Σ(X - m)² / (n - 1)

Where, m = mean of the sample

n = sample size

The standard deviation equals, sqrt(variance )

Using a calculator:

The variance, σ² ;

Mean = Σx / n = 1681 / 20 = 84.05

(x -m)^2

[(29-84.05)^2 + (37-84.05)^2 + (38-84.05)^2 + (40-84.05)^2 + (58-84.05)^2 + (67-84.05)^2 + (68-84.05)^2 + (69-84.05)^2 + (76-84.05)^2 + (86-84.05)^2 + (87-84.05)^2 + (95-84.05)^2 + (96-84.05)^2 + (96-84.05)^2 + (99-84.05)^2 + (106-84.05)^2 + (112-84.05)^2 + (127-84.05)^2 + (145-84.05)^2 + (150-84.05)^2] / 19

22636.95 / 19

= 1191.4184 = 1191.42

Standard deviation = sqrt( Variance)

Standard deviation = sqrt(1191.4184)

Standard deviation = 34.516929 = 34.52

4 0

3 years ago