# 9th grade (14y) + expression of a variable from formula - examples - page 11

- Arithmetic progression

In some AP applies: 5a2 + 7a5 = 90 s3 = 12 Find the first member a =? and difference d = ? - Cylindrical tank

Cylindrical tank holds 600hl water and is deep 2.5 m. Calculate the diameter of the cylinder. - Regular n-gon

In a regular n-angle polygon the internal angle is 144 degrees. Find the number n indicating the number of sides of this polygon. - A mast

A mast 32 meters high was broken by the wind so that its top touches the ground 16 meters from the pole. The still standing part of the mast, the broken part and the ground form a rectangular triangle. At what height was the mast broken? - Rectangular triangle PQR

In the rectangular triangle PQR, the PQ leg is divided by the X point into two segments of which longer is 25cm long. The second leg PR has a length 16 cm. The length of the RX is 20 cm. Calculate the length p of side RQ. The result is round to 2 decimal - Determine AP

Determine the difference of the arithmetic progression if a3 = 7, and a4 + a5 = 71 - Diagonals

Given a rhombus ABCD with a diagonalsl length of 8 cm and 12 cm. Calculate the side length and content of the rhombus. - Red balls

In the bag there are 3 red, 12 blue and 8 green balls. How many red balls we must be attached to the bag if we want the probability of pulling out the red balls was 20%? - Quotient

Determine the quotient and the second member of the geometric progression where a3=10, a1+a2=-1,6 a1-a2=2,4. - Coach

Average age of 24 players and a coach of one team is 24 years. The average age of players without a coach is 23 years. How old is the coach? - Q of GP

Calculate quotient of geometric progression if a1=5 a a1+a2=12. - Chord

It is given to a circle k(r=6 cm) and the points A, B such that / AB / = 8 cm lies on k. Calculate the distance of the center of circle S to the midpoint C of the segment AB. - Coefficient

Determine the coefficient of this sequence: 7.2; 2.4; 0.8 - Inscribed circle

The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c. - Trapezium

The area of trapezium is 35 cm^{2}. Find its altitude if the bases are 6cm and 8 cm. - The rope

A 68 centimetre long rope is used to make a rhombus on the ground. The distance between a pair of opposite side corners is 16 centimetres what is the distance between the other two corners? - Diagonal

he rectangular ABCD trapeze, whose AD arm is perpendicular to the AB and CD bases, has area 15cm square. Bases have lengths AB = 6cm, CD = 4cm. Calculate the length of the AC diagonal. - Area of iso-trap

Find the area of an isosceles trapezoid, if the lengths of its bases are 16 cm, and 30 cm, and the diagonals are perpendicular to each other. - Trapezoid - intersection of diagonals

In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate trapezoid area. - Rhombus

The rhombus has diagonal lengths of 4.2cm and 3.4cm. Calculate the length of the sides of the rhombus and its height

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