Dragan

Find, in simplest radical form, the shortest possible distance in centimetres that could be traced from A to B on the surface of this 6 cm x 10 cm x 24 cm block.

AB = 32 cm  

​Find the height, h, of the diagram if each circle has a radius of 12 cm.

h ≈ 65.569 cm 

An equilateral triangle has a side of length 12 inches. What is the area of the triangle, in square inches? Express your answer in simplest radical form.

a = 12 in

h = sqrt(3) * a/2 = 10.39230485

Δ Area = h * a/2 ≈ 62.354 in²  

Sammy has two similar boxes.  One box has side lengths that are 3 times larger than the other box.  If the larger box has a volume of 5400 inches cubed, what is the volume of the smaller box?

Let the larger box have these dimensions:  30 x 15 x 12 = 5400 in³

The volume of the smaller box is:  ( 30/3 )*( 15/3 )*( 12/3 ) = 200 in³  

The area of the triangle is   84.939 cm²  

Rectangle ABCD contains a point such that AX = 1, BX = 7 and CX = 8 Find DX.

BC = AD = sqrt (CX² - BX²) = 3.873

DX = sqrt (AX² + AD²) = 4

The length of DX is  4 units.  

ABCD is a isosceles trapezoid with AB=10, DB=8 and angle A=120 degrees what is the length of CD

( This question is not written correctly. Cannot be DB=8 It's either CB=8, or DA=8)

Angle FBC = 120° - 90° = 30°

FC = sin(∠FBC) * 8  = 4

CD = AB + 2 (FC) = 18 units  

AD = DC = 4 cm

MC = DC/2 = 2

∠ACD = 45°

AC = AD / sin(45°) = 5.656854249

∠BMC = tan^-1(BC/MC) = 63.435°

∠MOC = 180 - 45 - 63.435 = 71.565°

Let F be the foot of altitude from C to MO

CF = sin(∠BMC) * MC = 1.788854382

OC = CF / sin(∠MOC) = 1.885618645

OA = AC - OC = 3.771235604

The ratio of OC to OA = 1.885618645 / 3.771235604 = 0.5  or  1/2  

When 125 is added to a number, it becomes a perfect square. When 176 is added to that same number, it also becomes a perfect square. What is the number?

500 +125 = 625       sqrt(625) = 25

500 + 176 = 676      sqrt(676) = 26  

https://web2.0calc.com/questions/graph-question_4#r1