Examples for secondary school students - page 26 of 231

Number of problems found: 4612

Lever force distance
Calculate at what distance from the axis of rotation a force of 60N acts on one side of a double-return lever; if a force of 180N acts on the other side at a distance of 1 meter from the axis of rotation, the lever is in equilibrium.
Permutation element count
From how many elements can we make 5040 permutations without repetition?
Arithmetic sequence
Determine the sum of the first 12 terms of an AP (arithmetic sequence) if a4 is equal to 7 and a8 is equal to minus 1.
Theater seat rows
The theater has 20 rows of seats on the ground floor. There are 16 seats in the first row, and each subsequent row has two more seats than the previous one. Find the number of seats on the ground floor of the theater.
Parabola focus equation
Determine the equation of the parabola that has the point F = [3,2] as its focus and the line x+y+1=0 as its shift line.
Watch alarm price
The alarm clock, women's watch, and men's watch cost a total of 1370 CZK. How much does each item cost if a women's watch is six times more expensive than an alarm clock and a men's watch is 200 Sk more expensive than a women's watch?
Shirt price purchase
A customer was buying three shirts. First, he chose a white one, then a sports one, which was 32 Sk more expensive than a white one, and finally, a short-sleeved shirt, which was 27 Sk cheaper than a white shirt. How many crowns did the individual shirts
Triangle interior angles
Calculate the interior angles of the triangle. The angle alpha is 16° greater than beta, and the angle gamma is 17° less than alpha.
Right-angled - legs
The lengths of legs are a = 7.2 cm and b = 10.4 cm in the right-angled triangle ABC. Calculate: a) lengths of the sections of the hypotenuse b) height to the hypotenuse c
Grain flour grinding
We get 80 percent flour by grinding grain. How much grain do we need to grind to get 400 kg of flour?
Circus sector seats
In a circus, in one sector for spectators, the seats are arranged in such a way that in each higher row, there is one more seat than in the previous one. How many seats are there in a sector with 22 rows if there are 8 seats in the first row?
Triangle perimeter area
What are the sides of a right-angled triangle with a perimeter of 45 centimeters and a volume of 67.5 cm²?
Accelerated motion
The position of a mass point that moves along the x-axis is given by the relation x=10t²-5t. Express its velocity and acceleration.
Quadrilateral angle circle
The points ABC lie on the circle k(S, r) such that the angle at B is obtuse. How large must the angle at vertex B of quadrilateral SCBA be so that this angle is three times greater than the interior angle ASC of the same quadrilateral?
Circle equation points
Determine the equation of the circle that passes through the point M(-1,2) and N( 3,0) and whose center lies on the line p: x=-3+t, y=-1+t,
Meridian ground speed
The plane flies south at an average speed of 190 km/h, and the wind blows from west to east at a speed of 20 m/s. How fast and in what direction (relative to the meridian) will the plane move relative to the ground?
Play match
A hockey match played for three periods ended with a score of 2:3. How many possibilities are there on how the given thirds could have been completed?
Hypotenuse - construct problem
A line segment AA1 of length 6 cm is given. Construct all triangles ABC for which AA1 is the hypotenuse, side length BC is 5 cm, and angle gamma is 60°.
Office cable cross-section
In the office will be connected: computer 800 W, kettle 2.5 kW, lighting 650 W, oven 1.9 kW; electric stove 3.3 kW; air conditioning 6100 W. As the smallest cross-section of the cables, we have to bring them to this room. Recalculate for Copper and Alumin
Circle point equation
Determine the equation of the circle that is the set of all points of the plane that are twice as far from the point [3,7] as they are from the point [0,1].

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