# Examples for secondary school students - page 62

- Prove

Prove that k1 and k2 is the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x^{2}+y^{2}+2x+4y+1=0 k2: x^{2}+y^{2}-8x+6y+9=0 - Vector 7

Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|. - Equation with abs

Solve this equation with absolute value member: ? - Dice

We throw five times the dice. What is the probability that six fits exactly twice? - Two people

Two straight lines cross at right angles. Two people start simultaneously at the point of intersection. John walking at the rate of 4 kph in one road, Jenelyn walking at the rate of 8 kph in the other road. How long will it take for them to be 20√5 km apar - Average speed 4

Starting at home Tony traveled uphill to the store for 45 minutes at 8 miles per hour. he then traveled back home on the same path at a speed of 24 miles per hour. what is his average speed for the entire trip? - Basket of fruit

In six baskets, the seller has fruit. In individual baskets, there are only apples or just pears with the following number of fruits: 5,6,12,14,23 and 29. "If I sell this basket," the salesman thinks, "then I will have just as many apples as a pear." Which - Flying

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? - Sphere equation

Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1). - Two workers

Two workers should fulfill certain task together for 5 days. If the first worker increased their performance twice and second twice fell, it took them just four days. For how many days would handle the entire task first worker himself? - Decagon

Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m - Sequence 11

What is the nth term of this sequence 1,1/2,1/3,1/4,1/5 ? - Tractors

Two tractors plow the field in 4 hours together. If the first tractor plow half of the field and then the second tractor completed the job, it would take 9 hours. How many hours does the field plow for each tractor separately? - ABCD square

In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment? - Angle of diagonal

Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume. - Dice

We throw 10 times a play dice, what is the probability that the six will fall exactly 4 times? - Boys and girls

There are eight boys and nine girls in the class. There were six children on the trip from this class. What is the probability that left a) only boys b) just two boys - Fruit tea

Tea contains 7% of fruit components and 12% of sugar in this component. How many percents of sugar is represented in the whole tea? - Performance

Two masons with the same performance would have made of plaster for 6 days. One of them, however, has increased its daily performance by 50%. How long would take they now to make plaster together? - Cube, cuboid, and sphere

Volumes of a cube and a cuboid are in ratio 3: 2. Volumes of sphere and cuboid are in ratio 1: 3. In what ratio are the volumes of cube, cuboid, and sphere?

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