# Grade - examples - page 170

- Free fall

How long does the stone fall freely into a depth of 80m? What speed will it hit the bottom of the abyss? - Quarters

How many meters is a quarter of a kilometer? How many centimeters is a quarter of a meter, how many cents is a quarter of the euro? - Combinations

How many elements can form six times more combinations fourth class than combination of the second class? - Dividing by five and ten

Number 5040 divide by the number 5 and by number 10: a = 5040: 5 b = 5040: 10 - 3 cats

3 cats eat 3 mice in 3 days. How many mice will eat 10 cats in 10 days? - Diagonals

A diagonal of a rhombus is 20 cm long. If it's one side is 26 cm find the length of the other diagonal. - Cuboids

Two separate cuboids with different orientation in space. Determine the angle between them, knowing the direction cosine matrix for each separate cuboid. u1=(0.62955056, 0.094432584, 0.77119944) u2=(0.14484653, 0.9208101, 0.36211633) - Ratios

Reduce the numbers: 50 in a 1:2 ratio 111 at a ratio of 2:3 70 at 10:50 560 at a ratio of 3:8 - Three painters

The three painters have painted bridge. The first would work done in 5 days, the second in 6 days, and the third in 7.5 days. How long will the bridge work if they work together? - Write decimals

Write in the decimal system the short and advanced form of these numbers: a) four thousand seventy-nine b) five hundred and one thousand six hundred and ten c) nine million twenty-six - 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. - Points on line segment

Points P & Q belong to segment AB. If AB=a, AP = 2PQ = 2QB, find the distance: between point A and the midpoint of the segment QB. - Remainder

A is an arbitrary integer that gives remainder 1 in the division with 6. B is an arbitrary integer that gives remainder 2 the division by. What makes remainder in division by 3 product of numbers A x B ? - Trapezium internal angles

A trapezium where AB is parallel to CD, has angle A : angle D = 4 :5, angle B = 3x-15 and angle C = 4x+20. Find angle A, B, C and D. - 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. - Mushrooms

Eva and Jane collected 114 mushrooms together. Eve found twice as much as Jane. How many mushrooms found each of them? - Embankment

Perpendicular cross-section of the embankment around the lake has the shape of an isosceles trapezoid. Calculate the perpendicular cross-section, where bank is 4 m high the upper width is 7 m and the legs are 10 m long. - Eq1

Solve equation: 4(a-3)=3(2a-5) - Unknown number 17

Milada said, I am thinking of a number such that I evaluate expression x^{1}/3, the value of the expression would be 5. Which number Milada thinking? - Thunder and lightning

There was a glimpse of the sky and we hear a thunder in 4.5 seconds. The light spreads at 300,000 kilometers per second, so we can assume the flash instantly without delay. However, the speed of the sound is much smaller in the air one third of a kilomete

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