Examples for secondary school students - page 157 of 237

Number of problems found: 4730

Isosceles trapezoid
Calculate the area of an isosceles trapezoid whose bases are at a ratio of 5:3. The arm is 6 cm long and 4 cm high.
Adam and Ben
When Ben reaches Adam's current age, Adam will be 23 years old. When Adam was Ben's current age, Ben was 2 years old. How old are Ben and Adam today?
Truncated cone 3
The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56 m and 42 m, and the height of the tang is found.
View angle
At a distance of 10 m from the river bank, they measured the base AB = 50 m parallel to the bank. Point C on the other bank of the river is visible from point A at an angle of 32°30' and from point B at an angle of 42°15'. Calculate the width of the river
Water channel
The cross-section of the water channel is a trapezoid. The bottom width is 19.7 m, the water surface width is 28.5 m, and the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flows
Decagon area
Find the area of a regular decagon if its side is 10 cm in size.
Three reds
What is the probability that all three of the seven cards will be red if three cards are drawn?
Inner angles
The inner angles of the triangle are 30°, 45°, and 105° and its longest side is 10 cm. Calculate the shortest side length, and write the result in cm up to two decimal places.
Regular n-gon
In a regular n-angle polygon, the internal angle is 144 degrees. Find the number n indicating the number of sides of this polygon.
Regular Matrix Rank
What is the rank of a second-order square matrix if we can say that this matrix is regular?
The determinant
The determinant of the unit matrix equals 7. Check how many rows the A matrix contains.
Savings interest
It was 1975, and Petr deposited the entire cash of 10,900.40 Euros in a savings account with 4% interest, credited monthly. He did not add anything to the book, and in exactly 15 years, he withdrew the entire amount in cash. How much did you choose?
Photocopier
A photocopier enlarges a picture in the ratio of 7:4. How many times will a picture of size 6 cm by 4 cm be enlarged to fit on a 30 cm by 20 cm page?
Pyramid surface
There is a regular quadrilateral pyramid with the base edge length a = 3 cm and with the length of the side edge h = 8 cm. Please calculate its surface area and volume.
Sequence 11
What is the nth term of this sequence 1, 1/2, 1/3, 1/4, 1/5 ...?
Arithmetic progression
In some arithmetic progression applies: 5a2 + 7a5 = 90 s3 = 12 Find the first member a =? and difference d =.
Calculate cylinder
A cylinder has a volume V = 120 cm³ and a height v = 4 cm. Calculate the radius and the lateral surface area S.
Diamond angles
The diagonals in diamond KLMN are 10 cm and 6 cm long. Determine the angle size that the longer diagonal makes with the side of the diamond.
Quadrilateral prism
The body diagonal of a regular quadrilateral prism forms an angle of 60° with the base. The edge of the base is 20 cm long. Calculate the volume of the body.
Cuboid edges in ratio
Cuboid edge lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm³.

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