Absolute value - examples
Triangle KLM is given by plane coordinates of vertices: K[-19, -8] L[8, -12] M[2, -6]. Calculate its area and itsinterior angles.
- Speed of Slovakian trains
Rudolf decided to take the train from the station 'Nová Baňa' to 'Gelnica'. In the train timetables found train R 371 Horehronec : km0Břeclav os.n.05:268Lanžhot05:3205:3214Brodské05:3705:3818Kúty05:4205:4344Malacky05:5906:0082Bratislava hl.st.06:2606:37
The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 45 km/h and ambulance 58 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 23.32°W. How far is the plane from the airport (round to the nearest mile)?
Calculate length of the vector v⃗ = (-2.5, 6.25, -4.25).
Circle is given by centre on S[-9; 4] and maximum chord 20 long. How many intersect points have circle with the coordinate axes?
Which of the pairs of numbers on the number line encloses the longest segment: ?
- Equilateral cylinder
Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 221 cm3 . Calculate the surface area of the cylinder.
- 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[19; 10], B[-12; -6].
Vector a has coordinates (7; 16) and vector b has coordinates (15; -7). If the vector c = b - a, what is the magnitude of the vector c?
- Two cars
Car A1 goes at average speed of 133 km/h and the second car A2 goes at 128 km/h. How many second will it take car A1 to circulate car A2? Assume that both cars are 4.7 meters long and the safety gap between cars is 2.7 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 8, 11 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°).