The airplane from Prague to Bratislava was flying at a speed of 60 km/h less and back by 70 km/h greater than the original speed. What was the original speed if the plane returned to Prague according to the timetable?
- Exponential warm
Suppose that a body with temperature T1 is placed in surroundings with temperature T0 different from that of T1. The body will either cool or warm to temperature T(t) after time t, in minutes, where T(t)=T0 + (T1-T0)e^(-kt) . If jello salad with 30 degre
- What is
What is the value of the smaller of a pair of numbers for which their sum is 78 and their division quotients are 0.3?
We throw five times the dice. What is the probability that six fits exactly twice?
- Rhombus 29
One of the diagonals of a rhombus is equal to a side of the rhombus. Find the angles of the rhombus.
- Diagonal to area
Calculate the area of a rectangle in which the length of the diagonal is 10 cm.
- Map scale
The rectangular plot has in a scale of 1: 10000 area 3 cm2 on the map. What content does this plot have on a 1:5000 scale map?
Six of the painters paint 90 m of fence in five hours. For how long would the 4 painters paint a 45 meter fence? How many meters fence painted painters 5 for two hours?
- 13 tickets
A short and long sightseeing tour is possible at the castle. Ticket for a short sightseeing circuit costs CZK 60, for a long touring circuit costs CZK 100. So far, 13 tickets have been sold for 1140 CZK. How much did you pay for tickets for a short tour?
- Three points 2
The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.
- A rectangular
A rectangular garden 40 m long and 30 m wide is to be fenced with fence posts at each corner. All the other posts will be 5 meters a part. How many posts will be needed to fence in the garden.
- Find the 2
Find the term independent of x in the expansion of (4x3+1/2x)8
- Curve and line
The equation of a curve C is y=2x² -8x+9 and the equation of a line L is x+ y=3 (1) Find the x co-ordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
- Perimeter of a rectangle
If the perimeter of a rectangle is 114 meters and the length is twice the width plus 6 meters, what are the length and width?
The sum of the lengths of the three edges of the cuboid that originate from one vertex is 210 cm. Edge length ratio is 7: 5: 3. Calculate the length of the edges.
How long have we trained on the pitch when we know that the warm-up took 10 minutes, we trained passes for one-third of the time and we played football half the time?
- Radioactive material
A radioactive material loses 10% of its mass each year. What proportion will be left there after n=10 years?
1000$ is invested at 10% compound interest. What factor is the capital multiplied by each year? How much will be there after n=12 years?
- A number
A number increased by 7.9 is 8.3
- Percentage 10
52 shorts and missed 13. Calculate percentage