# Examples for secondary school students - page 69

- Diagonals of pentagon

Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm. - Progression

12, 60, -300,1500 need next 2 numbers of pattern - Mast shadow

Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines. - The swimmer

The swimmer swims at a constant speed of 0.85 m/s relative to water flow. The current speed in the river is 0.40 m/s, the river width is 90 m. a) What is the resulting speed of the swimmer with respect to the tree on the riverbank when the swimmer motion - Barrel with water

The water barrel has a weight of 52 kg. When we pour a quarter of the water, the weight of the barrel is reduced to 40 kg. Determine the weight of the empty barrel. - Expressions 3

If k(x+6)= 4x^{2}+ 20, what is k(10)=? - Axial cut of a rectangle

Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long. - SSA and geometry

The distance between the points P and Q was 356 m measured in the terrain. The PQ line can be seen from the viewer at a viewing angle of 107° 22 '. The observer's distance from P is 271 m. Determine the viewing angle of P and observer. - Bridge cards

How many bridge hands are possible containing 4 spades,6 diamonds, 1 club, and 2 hearts? - Find two

Find two consecutive natural numbers whose product is 1 larger than their sum. Searched numbers expressed by a fraction whose numerator is the difference between these numbers and the denominator is their sum. - Rectangle - area, perimeter

The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle. - Integer

Find the integer whose distance on the numerical axis from number 1 is two times smaller as the distance from number 6. - Points collinear

Show that the point A(-1,3), B(3,2), C(11,0) are col-linear. - Company and employees

There are 370 employees in the company - women are 15% less than men. How many men work in the company? - Depth angle

From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff? - Reciprocal equation 2

Solve this equation: x + 5/x - 6 = 4/11 - Resistance

A resistor having an electrical resistance of 1.5 k ohms passes an electrical current of 0.1 A. Calculate what voltage is between the terminals of the resistor. - Pavement

Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if distance the pavement from the center is 15 m. - Practice

How many ways can you place 20 pupils in a row when starting on practice? - Inverted nine

In the hotel,, Inverted nine" each hotel room number is divisible by 6. How many rooms we can count with three-digit number registered by digits 1,8,7,4,9?

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