civonamzuk

You got this wrong:   8/12 = BD/DC

Should be:  6/12 = BD/DC        (But there's nothing you can do with this.)

The correct way is          6/12 = BD / (8 - BD)        correct!!!

AD => x          BD => 17 - x

8² - x² = 16² - (17 - x)²

x = 97/34                 AD = 97/34

CD = sqrt(8² - x²)       CD = (15√287) / 34

[ACD] = 1/2(AD * CD) 

[ACD] = (1455√287) / 2312 = 10.66144601

A circle has a radius of 25. A circular sector, with an angle of 120 degrees at the center, is cut from the circle, and then rolled to form a cone. Find the volume of the cone.

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Circle radius = 25               Sector angle = 120º

Cone slant height   sh = 25

The length of 120º arc = 16²/₃ pi

Cone radius              r = 8¹/₃

Cone height            h = sqrt[25² - (8¹/₃)²]

Cone volume = [pi(8¹/₃)² * h] / 3

Cone volume = 1714.075208

This one's very hard to solve.

We know that triangle ABC must be an isosceles triangle (AC = BC)!!!

Who did give you 2 ++ for the wrong answer? Read the question again.

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Angle Z = 90º             XY = 10            YZ = √51            XZ = 7  (correct)

XY =>  hypotenuse            YZ => opposite              XZ => adjacent

tan(X) = opposite / adjacent

tan(X) = √51 / 7

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btw...   7 / 10 = sin(Y)

Triangle ABC has the height AD and angle A = 90º. If CD = 4, and BD = 5, find this ratio [ACD]/[ABD].

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AD = x

√(4²+x²) * √(5²+x²) = 9x

AD = 2√5

[ACD] / [ABD] = 4/5

If the ratio of children to adults is 3:53:5 and there are 120120 children at an amateur surfing competition, how many adults are in attendance?

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3/5 = 120/adults

adults = 200

Answer #2 is correct!!!

Sorry to say, but you made a couple of mistakes:

1/      Triangles MOQ and NOR are not similar!!!

2/      QO and RO are not equal!!! 

QN and RM are the medians of triangle PQR.

The ratio of QO to NO is 2:1

OR = sqrt[(QN/3)² + (PR/2)²]

Neither of the above answers is correct!!!

The correct answer is as follows:

PM = [sqrt(2 * 13² + 2 * 18² - 14²)] / 2 

PM ≈ 14.053 

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Sides: a = 13   b = 18   c = 14

Area: T = 90.421
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 45.859° = 45°51'32″ = 0.8 rad
Angle ∠ B = β = 83.533° = 83°31'57″ = 1.458 rad
Angle ∠ C = γ = 50.609° = 50°36'31″ = 0.883 rad

Height: ha = 13.911
Height: hb = 10.047
Height: hc = 12.917

Median: ma = 14.756
Median: mb = 10.075
Median: mc = 14.053

Hey, what's going on here? Someone doesn't like correct answers; that must be you, Melody.

Would you give me a reasonable explanation for blocking my answer?

Hey, what's going on here? Someone doesn't like correct answers; that must be you, Melody.

Would you give me a reasonable explanation for blocking my answer?

PM = [sqrt(2 * 13² + 2 * 18² - 14²)] / 2 

PM ≈ 14.053

A cube has edges of length 1 cm and has a dot marked in the center of the top face. The cube is sitting on a flat table. The cube is rolled, without lifting or slipping, in one direction so that at least two of its vertices are always touching the table. The cube is rolled until the dot is again on the top face. The length, in centimeters, of the path followed by the dot is c(pi), where c is a constant. What is c?

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c = φ     (Golden ratio  φ ≈ 1.618033989)

c = (1 + √5) / 2

Angle AEC = arctan(6/13) = 24.77514057º

Your numbers are wrong!!! 

EG must be smaller than AD!!!

w = - 4¹/₃

x = - 11¹/₃

y = 13²/₃

z = 19²/₃

xz + yz = 45⁸/₉