Examples for secondary school students - page 90 of 232
Number of problems found: 4622
- Shopping malls
The chain of department stores plans to invest up to 24,000 euros in television advertising. Ads will place all commercials on a television station where the broadcast of a 30-second spot costs EUR 1,000 and is watched by 14,000 potential customers. Durin - Function 3
Function f(x)=a(x-r)(x-s) the graph of the function has an x-intercept at (-4, 0) and (2, 0) and passes through the point (-2,-8). Find constant a, r, s. - Variation element increase
If the number of elements increases by two, the number of variations of the second class of these elements created by 38 increases. What is the original number of elements? - Circle line probability
A rectangular grid consists of two mutually perpendicular systems of parallel lines with a distance of 2. We throw a circle with a diameter of 1 on this plane. Calculate the probability that this circle: a) overlaps one of the straight lines; b) do any of - Menelaus theorem proof
Show (using Meneal's theorem) that the center of gravity divides the line in a 1:2 ratio. - Real and imaginary parts
Let z1=x1+y1i and z2=x2+y2i Find: a = Im (z1z2) b = Re (z1/z2) - Metal sheets
How much metal sheet is needed to produce eight 4 m long and 12 cm in diameter gutters? During production, joints are calculated at 3% of total consumption. - Which
Which of the following numbers is the most accurate area of a regular decagon with side s = 2 cm? (A) 9.51 cm² (B) 20 cm² (C) 30.78 cm² (D) 31.84 cm² (E) 32.90 cm2 - Pentadecagon
Calculate the area of a regular 15-side polygon inscribed in a circle with a radius r = 4. Express the result to two decimal places. - Dodecagon
Calculate the size of the smaller angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees. - Rectangle area function
A rectangle with sides of lengths a, b (cm) has a circumference of 100 cm. The dependence of its area P (in cm2) on the number a can be expressed by the quadratic function P = sa + ta². Find the coefficients s, t. - Table side calculation
The area of the work surface of the rectangular table is 70 dm2, and its perimeter is 34 dm. Determine (in dm) the length of the shorter side of this table. - Lookout tower
How high is the lookout tower? If each step was 3 cm lower, 60 more were on the lookout tower. If it were 3 cm higher again, it would be 40 less than it is now. - Coffe cups
We have 4 cups with four different patterns. How many possible combinations can we create from 4 cups? - 1 page
One page is torn from the book. The sum of the page numbers of all the remaining pages is 15,000. What numbers did the pages have on the page that was torn from the book? - An observer An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower?
- Coordinates
Determine the coordinates of the vertices and the area of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0, and the diagonal on the line 3x + 2y + 3 = 0 - Tournament
How many matches will be played in a football tournament in which there are two groups of 5 teams if one match is played in groups with each other and the group winners play a match for the tournament's overall winner? - Wagons
We have six wagons: two white, two blue, and two red. We assemble trains from them; wagons of the same color are exactly the same, so if we change only two white wagons on a train, it's still the same train because I don't know any difference. How many di - The tower
The observer sees the tower's base 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands?
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