Themes, topics - math word problems
- Copper Cu wire
Copper wire with a diameter of 1 mm and a weight of 350 g is wound on a spool. Calculate its length if the copper density is p = 8.9 g/cm cubic.
- Birthday paradox
How large must the group of people be so that the probability that two people have a birthday on the same day of the year is greater than 90%?
- Cyclist 12
What is the average speed of a cycle traveling at 20 km in 60 minutes in km/h?
- Side lengths
In the triangle ABC, the height to the side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b.
- The farmer
The farmer calculated that the supply of fodder for his 20 cows was enough for 60 days. He decided to sell 2 cows and a third of the feed. How long will the feed for the rest of the peasant's herd last?
- The coal
The coal stock would be enough to heat a larger room for 12 weeks, a smaller one for 18 weeks. It was heated for four weeks in both rooms, then only in a smaller one. How long was the coal stock enough?
- A particle
A particle moves in a straight line so that its velocity (m/s) at time t seconds is given by v(t) = 3t2-4t-4, t>0. Initially the particle is 8 meters to the right of a fixed origin. After how many seconds is the particle at the origin?
The first worker would dig a trench in 6 hours. For the second, the same work would take 4 hours. How long did it take for the trench to be dug if they worked together?
- Closed circuit
In a closed circuit, there is a voltage source with U1 = 12 V and with an internal resistance R1 = 0.2 Ω. The external resistance is R2 = 19.8 Ω. Determine the electric current and terminal voltage.
Seven dwarfs will cut 420 stumps in 15 hours. After five hours, the two dwarves disappear discreetly. How many hours will the remaining dwarves complete the task?
- Energy consumption
The device is connected to 230V and draws 3.5A current. Power consumption is 1932kJ. How many minutes has this device been in operation?
- Two trains
The train runs at speed v1 = 72 km/h. The passenger, sitting in the train, observed that a train long l = 75m in 3 s passed on the other track in the opposite direction. Calculate the speed of this train.
A current of 2A passes through the immersion cooker at a voltage of 230V. What work do the electric field forces in 2 minutes?
- Double probability
The probability of success of the planned action is 60%. What is the probability that success will be achieved at least once if this action is repeated twice?
The first bricklayer would build a wall in 3 days, the second in 4 days. The first bricklayer worked alone for a day, then the second bricklayer came to his aid and they finished the work together. How long did it take to build the wall?
- Water mixing
There are 5 liters of water at 75°C in the pot, how much water at 10°C do we have to add to the resulting temperature of 55°C?
- Working together
Two people will do the work in 12 days. They worked together for 8 days. Then only one worked for 10 days. How many days would each of them do the work if he worked alone?
- The copper wire
The copper wire bundle with a diameter of 2.8mm has a weight of 5kg. How many meters of wire is bundled if 1m3 of copper weighs 8930kg?
- The shooter
The shooter heard the impact of the bullet on the target in one second after the shot. The bullet was moving at an average speed of 500 m/s. Calculate with speed of sound of 340 m/s. Determine the distance of the target.
- Hectares of forest
12 workers plant 24 ha of forest in 6 days. In how many days will 15 people and 12 people plant the same area?