Physical quantities - math word problems - page 277 of 296
Number of problems found: 5915
- Observation tower
At the top of the hill, there is a 30-meter-high observation tower. We can see its heel and shelter from a certain point in the valley at elevation angles a=28°30" and b=30°40". How high is the top of the hill above the horizontal plane of the observation - Seats on carousel
There are 12 seats evenly distributed on the children's carousel in the shape of a circle. How long is the arm of the carousel (connecting the center of the carousel to the seat) if the distance between the two seats is 1.5 m? - Altitude angle
In complete winds-free weather, the balloon took off and remained standing exactly above the place from which it took off. It is 250 meters away from us. How high did the balloon fly when we saw it at an altitude angle of 25°? - The rescue helicopter
The rescue helicopter is above the landing site at a height of 180 m. The rescue operation site can be seen from here at a depth angle of 52°40'. How far will the helicopter land from the rescue site? - Right triangle trigonometrics
Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60°, and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent) - The volleyball ball
The volleyball ball can have a circumference of at least 650 max 750 mm after inflation. What air volume can this ball hold if its circumference is the average of the minimum and maximum inflation of the ball? - In the desert
A man wondering in the desert walks 5.7 miles in the direction S 26° W. He then turns 90° and walks 9 miles in the direction N 49° W. At that time, how far is he from his starting point, and what is his bearing from his starting point? - ABS, ARG, CONJ, RECIPROCAL
Let z=-√2-√2i where i2 = -1. Find |z|, arg(z), z* (where * indicates the complex conjugate), and (1/z). Where appropriate, write your answers in the form a + i b, where both a and b are real numbers. Indicate the positions of z, z*, and (1/z) on an Argand - A rhombus 4
A rhombus has a side length of 10 cm. Find the angles at each vertex of the rhombus if the shorter diagonal measures 7 cm. Give your answers to the nearest degree and provide clear geometric reasoning at each step. - Distance Between Boats
An observer watches two boats at depth angles of 64° and 48° from the top of the hill, which is 75 m above the lake level. Determine the distance between the boats if both boats and the observer are in the same vertical plane. - Tank water height
The tank has the shape of a rotating cylinder with a base radius of 6 m reach. Water flows at a speed of 2 liters per second for 3 hours. To what height does the water in the tank? - Cylindrical magnets
Calculate the magnetic field energy of a cylindrical coil with 400 turns, a length of 0.4 m, and a radius of 20 mm. A current of 3 A passes through the coil. (µo = 4π 10-7 H/m) - Brass sphere
Find the weight of a brass ball with an outer radius of 12 cm and a wall thickness of 20 mm if the brass's density is 8.5 g/cm³. - Gorilla fruit supply
At the Prague Zoo, they need to know how long the fruit will last for the gorillas. The stock in the warehouse would last the female Kamba for 25 days, the male Richard for 20 days, and the little Nura even for 40 days. How long will the supply last if ev - Steps
Find the height between the two floors if you know that the number of steps between the two floors is 18, the gradient is 30º, and the step length is 28.6 cm. Report the result in centimeters to the nearest centimeter. - Average speed
At what average speed would you have to travel around the world in 80 days? (Assume a path along the equator; round to km/h.) - Performance
Two masons with the same performance would have been made of plaster for six days. One of them, however, has increased its daily performance by 50%. How long would it take them now to make plaster together? - Cyclist
A cyclist rides 7 km uphill in 46.9 minutes and the same distance downhill in 15.4 minutes, applying the same force to the pedals throughout. How long would it take to cycle the same 7 km on flat ground? - 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 - In mass
In the mass production of a product, the average dimension is 250 mm, whereas the dimensions of individual products due to inaccuracies in the production fluctuate around this mean value. The dimension of the products has a normal distribution with standa
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