Examples for secondary school students - page 97 of 230
Number of problems found: 4593
- Vector perpendicular
Find the vector a = (2, y, z) so that a⊥ b and a ⊥ c where b = (-1, 4, 2) and c = (3, -3, -1) - Average speed
A car traveled from city A to city B at a speed of 40 km/h, then from B to C at 60 km/h, and finally from C to D at 50 km/h. Calculate the car's average speed over the entire route from A to D if the distance from A to B is 20% of the total distance and f - Table and chairs
Four people should sit at a table in front of a row of 7 chairs. What is the probability that there will be no empty chairs between them if people randomly choose their place? - Tiles
The tile is square and has a side of 15 cm. What dimensions can a rectangle composed of 90 tiles have so that no tile remains? - Trapezoid: 18703
In the ABCD trapezoid: | AD | = | CD | = | BC | a | AB | = | AC |. Determine the size of the delta angle. - Speedometer 18693
The Macháček family went on a 3-day trip to Třeboň. They didn't want to get too tired but wanted to see a lot. Therefore, they drove at a walking pace, and at the end of the 3rd day, they measured 90 km on the speedometer. On the second day, they traveled - Pavel 3
Pavel has deposits in two accounts. One in a current account with an annual interest of 2% and the other in a savings account with an annual interest of 4%. Both deposits earned him CZK 1,000 per year. If Pavel transferred the deposit from one account to - Successively 18673
Vašek likes to go to the forest to pick mushrooms. He collected them successively for 3 days. Day 1 found seven less than Day 3. On the second day, he collected eight more than on the third day. He collected a total of 79 mushrooms. How much did he collec - The tourist
The tourist wanted to walk the route 16 km at a specific time. He, therefore, came out at the necessary constant speed. However, after a 4 km walk, he fell unplanned into the lake, where he almost drowned. It took him 20 minutes to get to the shore and re - Trapezoid 18313 Find the points A1 B1 symmetric along the y-axis to the points A [-4,0] and B [-1,4]. Calculate the perimeter of the trapezoid AB B1 A1.
- Sine theorem 2
From the sine theorem, find the ratio of the sides of a triangle whose angles are 30°, 60°, and 90°. - Vector equation
Let's v = (1, 2, 1), u = (0, -1, 3) and w = (1, 0, 7). Solve the vector equation c1 v + c2 u + c3 w = 0 for variables c1, c2, c3 and decide whether v, u, and w are linear dependent or independent - Angle of the body diagonals
Using the vector dot product calculate the angle of the body diagonals of the cube. - Cuboid and ratio
A cuboid has a volume of 810 cm³. The lengths of edges from the same vertex are in a ratio of 2:3:5. Find the dimensions of a cuboid. - Probability 18073
Determine the probability that three balls, ten red, and ten blue balls, will be drawn from 3 balls of the same color. - Porcelain 18063
Four cups and one porcelain saucer cost € 140. Two cups and five saucers cost € 160. How much is a cup? - Five-gon
Calculate the side a, the circumference, and the area of the regular 5-angle if Rop = 6cm. - Fall sum or same
Find the probability that if you roll two dice, the sum of 10 will fall, or the same number will fall on both dice. - Equations 18023
Solve a system of equations with four unknowns: 2a + 2b-c + d = 4 4a + 3b-c + 2d = 6 8a + 5b-3c + 4d = 12 3a + 3b-2c + 2d = 6 - Annulus
Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n.
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