Algebra - problems
- Geometric progression
In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is: sn≤217.
The children of the tennis school received 64 white and 48 yellow balls from the sponsor. When asked about how many balls they could take, they were answered: "You have so many that none of you will have more than 10 balls and all will have the same number
- 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?
- The sides
The sides of a rectangle are in a ratio of 2:3, and its perimeter is 1 1/4 inches. What are the lengths of its side? Draw it.
Alice spent 5/11 of her money on a back pack. She has $42 dollars left. How much was her back pack?
- Diamond diagonals
Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm.
Each box has the same number of soaps. A quarter of all boxes contain only white soaps, and in each of the remaining 120 boxes there are always half the white soaps and half the green. White soaps total 1200. (a) the number of all soap boxes; (b) the sma
- Two equations
Solve equations (use adding and subtracting of linear equations): -4x+11y=5 6x-11y=-5
- Largest angle of the triangle
Calculate the largest angle of the triangle whose sides have the sizes: 2a, 3/2a, 3a
- A bridge
A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. H
- Train speed
Two guns were fired from the same place at an interval of 10 minutes and 30 seconds, but a person in a train approaching the place hears second shot 10 minutes after the first. The speed of the train (in km/hr), supposing that sound travels at 340 m/s is:
It rains at night. On 1 m2 of lake will drop 60 liters of water. How many cm will the lake level rise?
- Average age
The company of five people has an average age of 46 years. The average age of the first four is 43 years. How many years has the fifth member of this company?
- Simple sequence
Continue with this series of numbers: 1792,448, 112, _, _
- A residential
A residential colony has a population of 5400 and 60 litres of water is required per person per day. For the effective utilization of rain water, they constructed a water reservoir measuring 48m × 27m × 25m to collect the rain water. For how many days, the
More than 30 and less than 60 dinosaurs have met at the pond. A quarter of them bathed and 1/7 saws and the rest gripped. How many were at the pond? How many were there?
- Equilateral triangle
Calculate the area of an equilateral triangle with circumference 72cm.
Calculate the length of a side of the equilateral triangle with an area of 50cm2.
- A candle
A candle shop sells scented candles for $16 each and unscented candles for $10 each. The shop sells 28 candles today and makes $400. a. Write a system of linear equations that represents the situation. b. Solve the system to answer the questions: How m