jugoslav

Two of the altitudes of an acute triangle divide the sides into segments of lengths 5,3,2 and x units, as shown. What is the value of x?

x = 18

The total of green marbles is 4 + 5/6(70 - 4)

You are absolutely right, Phill! I don't know what happened but I didn't see this: "PQRS is a parallelogram of perimeter  26". My focus was on a triangle STR, and I assumed that that triangle was 3-4-5

wrong answer!!! and the first answer is incorrect too!!!

Where was my head?!?

Bob had 160 and Jay had 240 at first. Each boy spent an equal amount of money. Then the ratio of the amount of money bob had left to the amount of money Jay had left was 3:5. How much money did each boy spend?

(160 - x) / (240 - x) = 3 / 5

x = 40

A 288-degree circular sector with a radius of 18 is rolled to form a cone. Find the height of the cone.

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Shortcut:

The radius of a sector:      R = 18

The radius of a cone:      r = R * (288 / 360) = 14.4

Cone slant height:          L = 18

Cone height:                  h = sqrt(18² - 14.4²) = 10.8

Excellent work, Phill !!!

https://web2.0calc.com/questions/abcdefgh-is-a-regular-octagon-of-side-12cm

 I'm laughing at my own error.

Instead of   ∠DCG = ∠CBG = arctan(2 / 1)    should be  ∠DCG = ∠CBG = arctan(1 / 0.5)