Themes, topics - math word problems - page 35 of 169

Number of problems found: 3370

Integer part system
In the field of real numbers, solve the system of equations: 2x + ⌊y⌋ = 2022, 3y + ⌊2x⌋ = 2023. (⌊a⌋ denotes the (lower) integer part of the real number a, i.e., the largest integer not greater than a., E.g., ⌊1.9⌋ = 1 and ⌊−1.1⌋ = −2.)
Triangle circle proof
Given is an acute-angled triangle ABC. On the half lines opposite to BA and CA lie successively the points D and E such that |BD| = |AC| and |CE| = |AB|. Prove that the center of the circle circumscribing triangle ADE lies on the circle circumscribing tri
Mountain climbing
Ken and his brother decided to go on mountain climbing 8 miles from their house to Mt. Daraitan at a rate of x mph (miles per hour). For the return trip, it was 2 mph faster. It took them 6 hours for the entire round trip. What is the x?
Grandmother house distance
Little Red Riding Hood walked through the forest from her house to her grandmother's house. She walked at an average speed of 0.75 m/s. She left her house at 11:30 and reached her grandmother exactly at noon. How far from her house does her grandmother li
The electric motor
The electric motor winding's copper wire (alpha=4*10^-3 1/K) has a resistance of 42 ohms at a temperature of 18 degrees. What is its resistance at an operating temperature of 50 degrees?
Nikelin and brass
Calculate the length of brass wire (ró=0.08 microohm m) and nickel (ró=0.4 microohm m) with a diameter of 0.5 mm, which has a resistance of 1 ohm
Cooker wire resistivity
The heating coil of the cooker has a resistance of 70.5 ohms and is made of a wire with a diameter of 0.30 mm and a length of 9.8 m. Determine the resistivity of the material from which it is made.
Glass sheet weight
What is the weight of a sheet of glass 75 cm x 120 cm and 2 mm thick if one cubic meter of glass weighs 2500 kilograms?
Wire charge current
A constant current of 80mA passes through the wire. What charge passes through the conductor in 1 h?
Source voltage resistance
Determine the source voltage to which we must connect a 1k ohm resistance wire if a current of 40 mA is to flow through it.
Bulb filament resistance
A current of 0.2 A flows through a light bulb connected to a voltage of 6 V. What is the resistance of the red-hot filament?
LED resistor current
Calculate the current I that would race through resistor R5 (720 ohms), resistor R2 (220 ohms), and an LED (U=2V) at a DC 6V source. The resistors are connected in series.
Tourist group distance
A group of tourists split up at the intersection of two perpendicular paths. One group walked at a speed of 5.3 km/h. Second group 4.1km/h. How far were the two groups from each other after 1h 25min?
Cycling trip fractions
The Malíkova family plans a 120 km cycling trip for 4 days. They want to cover a quarter of the entire route on the first day. The second day, 2/15, and the third day, 7/20, will cover the entire length of the trip. What part of the trip will they cover i
Instructor team pursuit
On the school ski trip, the team set off from hut A at 9:30 a.m. to hut B at a speed of 2 m/s. Fifteen minutes later, the instructor followed them at a speed of 3 m/s. At what time and distance from cabin A will the instructor catch up with the team? Plea
Almond fat daily
The daily need for fat for a person is 80g on average. Almonds contain 45% fat. How many grams of almonds would a person have to eat if he wanted to cover his daily need for fats by eating only almonds?
Milk butter fat
Cow's milk contains an average of 3.6% fat. How many liters of milk are needed to make 250g of butter? Butter contains 82% fat.
Bread apple carbohydrate
Bread contains an average of 52% carbohydrates, and apples have 12% carbohydrates. How many apples weighing 220g would you have to eat to get as much carbohydrate as 150g of bread?
To convert
To convert from a Celsius temperature to a Fahrenheit temperature, multiply the Celsius temperature by 9/5 and add 32. Which is the Fahrenheit temperature corresponding to - 30 degrees Celsius?
Square diagonal drawing
Draw a square EFIJ if EI is equal to 7cm.

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