Examples for secondary school students - page 12
- Playing cards
How many possible ways are to shuffle 7 playing cards?
- Right triangle
Calculate the missing side b and interior angles, perimeter and area of a right triangle if a=10 cm and hypotenuse c = 16 cm.
- Two forces
Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
- Truncated cone
Calculate the height of the rotating truncated cone with volume V = 1057 cm3 and a base radii r1 = 8.1 cm and r2 = 9.7 cm.
- Perimeter and legs
Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm2.
- MO - triangles
On the AB and AC sides of the triangle ABC lies successive points E and F, on segment EF lie point D. The EF and BC lines are parallel and is true this ratio FD:DE = AE:EB = 2:1. The area of ABC triangle is 27 hectares and line segments EF, AD, and DB se
- Wire D
Wire length 1 m is bent so that it forms a semicircle circuit (including the diameter). Determine the radius of the semicircle.
- House roof
The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m2 is needed to cover roof if roof pitch is 57° and we calculate 11% of waste, connections and overlapping of area roof?
The lenght, width and height of a right prism are 6, 17 and 10 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?
- Airplane navigation
An airplane leaves an airport and flies due west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?
Calculate the length of the belt on pulleys with diameters of 105 mm and 393 mm at shaft distance 697 mm.
At the table sit 8 people, 4 on one side and 4 on the other side. Among them are 3 pairs. Every pair wants to sit opposite each other. How many ways can they sit?
- Hexagonal pyramid
Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm.
- Triangle in circle
Vertices of the triangle ABC lies on a circle with radius 3 so that it is divided into three parts in the ratio 4:4:4. Calculate the circumference of the triangle ABC.
- Sphere in cone
A sphere of radius 3 cm desribe cone with minimum volume. Determine cone dimensions.
From statistics of sales goods, item A buy 51% of people and item B buys 59% of people. What is the probability that from 10 people buy 2 item A and 8 item B?
If you know that cos(γ) = sin (806°), what is the angle γ?
The boys from scout group traveled 5 days distance 115 km. Every day walked 1.5 km less than the previous day. How many kilometers scouts walked in the first day?
Cardboard box shaped quadrangular prism with a rhombic base. Rhombus has a side 5 cm and one diagonal 8 cm long and height of the box is 12 cm. The box will open at the top. How many cm2 of cardboard we need to cover overlap and joints that are 5% of ar
- Cardboard box
We want to make a cardboard box shaped quadrangular prism with rhombic base. Rhombus has a side of 5 cm and 8 cm one diagonal long. The height of the box to be 12 cm. The box will be open at the top. How many square centimeters cardboard we need, if we cal