# The most difficult examples - page 5

- Pyramid

Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC. - Two triangles SSA

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14 - Isosceles trapezoid

Perimeter of the isosceles trapezoid is 48 cm. One side is two times greater than the second side. Determine the dimensions of the trapezoid. - Metal box

How much metal we need for the production of box with dimensions 5 dm, 30 cm and a height of 1 m? Add 12% of the waste and folds. - Reducing scale

I am sizing some landscaping and I measured everything for a 20 to 1 scale. I realized when I was done that it was at 30 to 1. How can I convert what I already have to 30 to 1. (Example, grass area is 22,871.6' at 20 to 1, how do you figure it out to be 30 - Diagonals of diamond

Find the area and circumference of the diamond ABCD with 15m and 11m diagonals. - Chord - TS

The radius of circle k measures 68 cm. Arc GH = 47 cm. What is TS? - Prism

Find the volume and surface area of prism with base of an equilateral triangle with side 7 dm long and the body height of 1.5 m. - The tram

The tram is moving with acceleration a = 0.3m/s2. How long it will pass the first meter of track? How long does it take 10 meters. What is its speed at the end of the 10 meters track? - Cone container

Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package. - 3d vector component

The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3? - Linear imaginary equation

Given that ? "this is z star" Find the value of the complex number z. - Geometric sequence 5

About members of geometric sequence we know: ? ? Calculate a_{1}(first member) and q (common ratio or q-coefficient) - Hexagon area

The center of the regular hexagon is 21 cm away from its side. Calculate the hexagon side and its area. - Evaluate expression

Evaluate expression using BODMAS rule: 1 1/4+1 1/5÷3/5-5/8 - Resultant force

Calculate mathematically and graphically the resultant of a three forces with a common centre if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25° - Ten fractions

Write ten fractions between 1/3 and 2/3 - 30-gon

At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area. - Math logic

There are 20 children in the group, each two children have a different name. Alena and John are among them. How many ways can we choose 8 children to be among the selected A) was John B) was John and Alena C) at least one was Alena, John D) maximum one w - Goniometric form

Determine goniometric form of a complex number ?.

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