Absolute value - examples
Triangle KLM is given by plane coordinates of vertices: K[-2, -20] L[4, 1] M[-16, 4]. Calculate its area and itsinterior angles.
- Speed of Slovakian trains
Rudolf decided to take the train from the station 'Trnava' to 'Zemianske Kostoľany'. In the train timetables found train R 725 Remata : km0Bratislava hl.st.12:574Bratislava-Vinohrady13:0113:0219Pezinok13:1213:1346Trnava13:3013:3263Leopoldov13:4514:0168H
The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 43 km/h and ambulance 52 km/h. Calculate such a relative speed of the ambulance moves to the car.
- Airplane navigation
An airplane leaves an airport and flies due west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?
Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
Circle is given by centre on S[-7; 10] and maximum chord 13 long. How many intersect points have circle with the coordinate axes?
- Equilateral cylinder
Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 168 cm3 . Calculate the surface area of the cylinder.
Which of the pairs of numbers on the number line encloses the longest segment: ?
- Goniometric form
Determine goniometric form of a complex number ?.
- Cube - wall
V kocke ABCDEFGH je ?. Aký je povrch kocky?
- Unit vector 2D
Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
Vector a has coordinates (8; 10) and vector b has coordinates (0; 17). If the vector c = b - a, what is the magnitude of the vector c?
- Two cars
Car A1 goes at average speed of 106 km/h and the second car A2 goes at 103 km/h. How many second will it take car A1 to circulate car A2? Assume that both cars are 5 meters long and the safety gap between cars is 1.5 meters.
The sum and the product of three integers is 6. Write largest of them.
- 3d vector component
The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?
For how many integer values of x can 16, 15 and x be the lengths of the sides of triangle?
- Right triangle - leg
Calculate to the nearest tenth cm length of leg in right-angled triangle with hypotenuse length 9 cm and 7 cm long leg.
- Null points
Calculate the roots of the equation: ?
What is the value of ? ?
- Moivre 2
Find the cube roots of 125(cos 288° + i sin 288°).