Dragan

Points M, N, P and are the midpoints of sides TU, US, ST and of triangle STU, respectively, and UZ is an altitude of the triangle. If angleTSU=71, angle STU=39, and angle TUS=70, then what is angle NZM+angle NPM in degrees? If you see this, please answer when you can.

Angle  NZM = 70°

Angle  NPM = 70°  

Bravo, guys!  You've just proved that " all roads lead to Rome"   

urw!

AP = 3      BP = 4     CP = 6     DP = 2

CD =  CP + DP = 8     ( Long side of a rectangle )

BP - AP = 1             ( Short side of a rectangle )

Diagonal of this rectangle is the diameter of the circle.

Diameter     D = sqrt [(CD²) + ( 1² )]  = 8.062257748 units   

Angle  RAC = 32°  

A sphere of radius 1 and a sphere of radius 2 are inscribed in a right circular cone, as shown below. Find the volume of the cone.

Volume of the cone is:   V = 59.574 u³   

Triangle ABC is an equilateral triangle and O is the center of its inscribed circle. If the area of the circle is  4*pi cm², what is the area, in square centimeters, of triangle ABC? Express your answer in simplest radical form.

The area of  Δ ABC ≈ 20.785 cm²    
 

The shortest distance from A to B that can be traced on the surface is the sum of longest diagonal of the block's surface (26cm) and the thickness of the block ( 6cm)

The length of diagonal  D = sqrt ( 24² + 10² ) = 26 cm

The shortest distance from A to B that can be traced is:      26 + 6 = 32 cm    

is 0 greater than or equal to negative 12

See..., -12 and 0 are dark holes; but -12 is much deeper and darker.  

A solid metal sphere rests in a rectangular tray. The radius of the metal ball is 2cm. The width and the length of the base of the tray are 7cm and 12cm respectively. The depth of water in the tray is 2cm.
(a)Find the volume of the water in the tray
(b)If the height of the tray is 55cm, find the volume of water needed to be poured into the tray so that the metal sphere is just submerged.

Archimedes' principle

Sphere volume   V = 4/3 * pi * r³  = 33.51 cm³

a)     7cm * 12cm * 2cm = 168cm³             168cm³ - (33.51cm³/2) = 151.245cm³

b)     ( 2 *168cm³) - 33.51cm³ = 302.49 cm³   

( It's been corrected )