# Examples for secondary school students - page 20

- Numbers

How many different 7 digit natural numbers in which no digit is repeated, can be composed from digits 0,1,2,3,4,5,6? - Hairs

Suppose the length of the hair is affected by only the α-keratin synthesis, which is the major component. This synthesis takes place in the epithelial cells of the hair bulb. The structure of α-keratin is made up of α-helix, wherein in one revolution it is - Biquadratic

By introducing a new variable solve biquadratic equation: ? - The cone

The lateral surface area of the cone is 4 cm^{2}, the area of the base of the cone is 2 cm^{2}. Determine the angle in degrees (deviation) of the cone sine and the cone base plane. (Cone side is the segment joining the vertex cone with any point of the base ci - Two valves

Water fill the pool by two valves for 11 days. After 7 days the first valve was stopped and the second valve fill pool for 7 days. How many days took to fill the pool each of the valves individually? - Toys

3 children pulled 12 different toys from a box. Many ways can be divided toys so that each children had at least one toy? - Vertical prism

The base of vertical prism is a right triangle with leg a = 5 cm and a hypotenuse c = 13 cm. The height of the prism is equal to the circumference of the base. Calculate the surface area and volume of the prism - Segments

Which of the pairs of numbers on the number line encloses the longest segment: ? - Mushrooms

Fresh mushrooms contain 94% water, dried 14%. How many kg of fresh mushrooms is needed to collect to get 10 kg dried? - Sun rays

If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current hei - Leg

Determine the area of a trapezoid with bases 71 and 42 and height is 4 shorter than the its leg. - Funnel

The funnel has the shape of an equilateral cone. Calculate the surface wetted with water if we poured into the funnel 7.1 liters of water. - Fire tank

Whole fire tank was discharged once in 5 days by first out by second in $n days. Once firefighters pumped out 6/13 of water out from the tank and then let the water flow out both drain. How long take empty the tank? - Diagonals in the diamond

The length of one diagonal in diamond is 24 cm greater than the length of the second diagonal and diamond area is 50 m^{2}. Determine the sizes of the diagonals. - Triangle SAA

The triangle has one side long 71 m and its two internal angles is 60°. Calculate the perimeter and area of the triangle. - Chord AB

What is the length of the chord AB if its distance from the center S of the circle k(S, 92 cm) is 10 cm? - Family

What is the probability that a family with 7 childrens have: exactly 5 girls? 7 girls and 0 boys? Consider the birth probability of a girl is 48.69% and boy 51.31%. - Line

Line p passing through A[-10, 6] and has direction vector v=(3, 2). Is point B[7, 30] on the line p? - Loan

Apply for a $ 59000 loan, the loan repayment period is 8 years, the interest rate 7%. How much should I pay for every month (or every year if paid yearly). Example is for practise geometric progression and/or periodic payment for an annuity. - Chemical parison

The blown parison (with shape of a sphere) have a volume 1.5 liters. What is its surface?

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