Road

Between cities A and B is route 13 km long of stúpanie average 7‰. Calculate the height difference of cities A and B.

Correct result:

h =  91 m

Solution:

$$\begin{gathered} s=13\text{ km}\to \text{ m}=13\cdot 1000\text{ m}=13000\text{ m } \\ q=7\mathrm{/}1000={\displaystyle \frac{7}{1000}}=0.007 \\ A={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arctan (q)={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arctan (0.007)\doteq 0.4011^{\circ } \\ h=s\cdot \sin A^{\circ }=s\cdot \sin 0.401063905967^{\circ }=13000\cdot \sin 0.401063905967^{\circ }=13000\cdot 0.007=90.99777=91\text{ m } \\ {h}_1=13\cdot 7=91\text{ m } \\ {h}_1\approx h \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• RC time constant
  You introduced 1 Coulomb worth of electrons into the inner volume of a dielectric material with ϵr=6. 30 minutes later, you found that only 36.79% of the electrons were in the inner volume. Determine the conductivity σ of the dielectric material.
• Decibel
  By what percentage does the sound intensity increase if the sound intensity level increases by 1 dB?
• Natural fertilizer
  The rectangular garden measuring 120m and 60m was fertilized with 16kg of natural fertilizer. Natural fertilizer contains 45% organic matter. How much organic matter falls on 1 m² of garden?
• Sphere in cone
  A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele
• Hiking trip
  Rosie went on a hiking trip. The first day she walked 18kilometers. Each day since she walked 90 percent of what she walked the day before. What is the total distance Rosie has traveled by the end of the 10th day? Round your final answer to the nearest ki
• 2 cyclists and car
  One cyclist rides at a constant speed over a bridge. It is 100 meters long. When he is 40 meters behind him, he meets an oncoming cyclist who is riding at the same speed. The car travels along the bridge in the same direction as the first cyclist at a spe
• Water mixing
  We have 520 ml of hot water and 640 ml of water at 48°C. What is the temperature of approximately hot water when the resulting mixture has a temperature of 65°C?
• 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.
• 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?
• Permille of alcohol
  I have 2 per mille of alcohol in my blood. How many milliliters is it when I have 5 liters of blood?
• Wall thickness
  The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm³.
• What percentage
  What percentage of the Earth’s surface is seen by an astronaut from a height of h = 350 km. Take the Earth as a sphere with the radius R = 6370 km
• Self-oscillation period
  The water in the vessel carried by the boy has a self-oscillation period of 0.8 s. What is the size of the boy's movement speed when the length of the boy's step is 60 cm? Give the result in m/s.
• Power line pole
  From point A, the power line pole is seen at an angle of 18 degrees. From point B to which we get when going from point A 30m away from the column at an angle of 10 degrees. Find the height of the power pole.
• Angled cyclist turn
  The cyclist passes through a curve with a radius of 20 m at 25 km/h. How much angle does it have to bend from the vertical inward to the turn?
• Newtonmeters
  The driver loosened the nut on the car wheel with a wrench that held 20 cm from the axis of the bolt. He acted on the key with a force of 320N. At what moment did he act on the bolt?
• Pool
  How many hl of water is in a cuboid pool (a = 25m, b = 8m) if the area of the wetted walls is 279.2 m²?