Examples for secondary school students - page 14 of 213
Number of problems found: 4256
- Equation 81932
Write the general equation of a circle with point S(2;5) and point B(5;6) lying on this circle. - Inelastic/plastic 81907
Two inelastic/plastic balls move towards each other with equal velocities of 2 m/s. The weight of one ball is 3kg, the other 1kg. Determine the speed of the balls after the collision and the loss of kinetic energy. - Revolutions 81906
How much energy was supplied by the flywheel of the device if its number of revolutions decreased from 1200 to 720 revolutions per minute if it has a moment of inertia of 71.3 kg/m²? - Diagonals 81884
In an isosceles trapezoid, the basic lengths are 15 cm and 9 cm. The diagonals are 13 cm long. Calculate the perimeter and area of the trapezoid.
- Calculate 81860
The two terms of the geometric sequence are a2=12 and a5=three halves. a) calculate the tenth term of the sequence. b) calculate the sum of the first 8 terms of the sequence. v) how many first terms of the sequence need to be added so that the sum is equa - Difference 81849
Determine four numbers so that the first three form the successive three terms of an arithmetic sequence with difference d=-3 and the last three form the next terms of a geometric sequence with quotient q=one half. - Difference 81835
Determine the difference d in AP if a1=3 and a1+a2=12 - Department 81818
The department has 90 members. There are 4 more older adults in the section than younger adults. There are 10 more older pupils than all adults. How many older and younger teenagers and how many older pupils are there in the section? - Arithmetic 81811
In which arithmetic sequence is the sum of the first five terms with odd indices equal to 85 and the sum of the first five terms with even indices equal to 100?
- Arithmetic 81808
An increasing arithmetic sequence has an odd number of terms. The middle term is 302. If we remove the 4 largest terms from the sequence, the middle term will be 296. Determine the difference in the sequence. - Arithmetic 81798
Two arithmetic sequences have the same first term. The nth term of the first sequence is 15, and of the second sequence, 21. The sum of the first n terms of the first sequence is 63, and of the second sequence, 84. Write the sums of the first n terms of b - Descending 81797
The sum of the first two terms of the descending geometric sequence is five quarters, and the sum of the infinite geometric series formed from it is nine quarters. Write the first three terms of the geometric sequence. - Arithmetic 81795
In which arithmetic sequence is S5=S6=60? - Determine 81794
Determine the quotient of the geometric sequence with the first term a1=36 so that s2 is less than or equal to 252.
- Possibilities 81788
The ring consists of 4 beads. There are 5 different colors of beads in the package. How many possibilities are there to create one ring, and can the colors repeat? - Borrower 81777
You lent €400. The borrower paid you €440 back in 5 months. What was the yield on this loan? - Circumscribed 81759
In triangle ABC, we know a = 4 cm, b = 6 cm, γ = 60°. Calculate the area and radius of the inscribed and circumscribed circle. - Perpendicular 81758
Distribute the force of magnitude F = 100 N into two perpendicular components with magnitudes F1 and F2 so that the angle between forces F1 and F is 43°52'. - Calculate 81757
Calculate the size of the largest angle in triangle ABC if a = 7 cm, b = 8 cm, and c = 13 cm. Calculate the area of the triangle, the height per side a.
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