Expression of a variable from formula - problems
- A rectangle
A rectangle has an area of 36 cm2. What could the length and width of rectangle be?
Klara and Jitka went on a hiking trip at 13 o'clock at speed 5km/h. At 14 o'clock, Tomas ride on the bike at an average speed of 28 km/h. How many hours and at what distance from the beginning of the road Tomáš caught the two girls?
- Evaluation of expressions
If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3
The boys and girls in the class formed without the rest of the fives, 2 girls and 3 boys. There are 6 girls missing to create mixed pairs (1 boy and 1 girl). How many girls are in the classroom?
- Expression with powers
If x-1/x=5, find the value of x4+1/x4
- Speed of car
The car went to a city that was 240 km away. If his speed increased by 8 km/h, it would reach the finish one hour earlier. Determine its original speed.
- The tourist
The tourist came started from the hostel at an average speed of 5km/h. Half an hour later, the bicyclist started along the same route at a speed of 20km/h. How many minutes will a cyclist catch up and how many kilometers will he go?
- Three painters
The three painters have painted bridge. The first would work done in 5 days, the second in 6 days, and the third in 7 days. How long will the bridge work if they work together?
The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height
- Paul earned
Paul earned 300 Kč in one hour, Václav 1/3 more than Paul. Václav worked 60 hours, which is 1/3 fewer hours than Paul worked. How many percents less earned Paul an hour than Václav? How many hours did Paul more than Václav? How much did Paul earn more t
- Ratio of sides
The triangle has a circumference of 21 cm and the length of its sides is in a ratio of 6: 5: 3. Find the length of the longest side of the triangle in cm.
- Solutions, mixtures
How many liters of 70% solution we must add to 5 liters of 30% solution to give us a 60% solution?
Two workers will construct the stage at the festival in 54 hours. Organizers need to shorten the assembly time by 42 hours. How many workers must the assembly company send?
- Quadrangular pyramid
Given is a regular quadrangular pyramid with a square base. The body height is 30 cm and volume V = 1000 cm³. Calculate its side a and its surface area.
- A box
A box is 15 centimeters long, 4 centimeters wide, and 3 centimeters tall what is the diagonal S of the bottom side? What is the length of the body diagnol R?
- Geometric progression
In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.
- A cylinder
A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the cylinder's top and bottom. (forming a spiral around the cylinder). How long is the string in cm?
- Regular quadrangular pyramid
The height of the regular quadrangular pyramid is 6 cm, the length of the base is 4 cm. What is the angle between the ABV and BCV planes?
- Diamond diagonals
Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm.
- Three pumps
The water tank is emptied with the first pump in 6 hours, with the second pump in 2 hours. In order to be emptied in 1 hour, all three pumps had to be started at once. How long will take tank be emptied by only the third pump?