# The most difficult problems

- Kostka

Kostka je vepsána do koule o poloměru r = 6 cm. Kolik procent tvoří objem kostky z objemu koule? - Bent scale

Monica weighed 52 kg. Sara 54 kg. Together they weighed 111 kg. They noticed that the weight on the scale was bent. How much did they really weigh? - A swiming

A swiming pool holds 30000lt of water. How many gallons does it hold? 1 gallon= 4.55lt - Compute 4

Compute the exact value of the area of the triangle with sides 14 mi, 12 mi, and 12 mi long. - The freezer

1. The temperature inside a freezer is minus 23 degree Celsius. The temperature falls by a further 12 degree degree Celsius. What is the new temperature? 2. What is the difference between temperatures of 12 degree Celsius and 210 degree Celsius? - Decide 2

Decide whether points A[-2, -5], B[4, 3] and C[16, -1] lie on the same line - Prescription

Jannin knows that Mr. Robinson needs 14 tablets for a week's supply of an anti-inflammatory drug Mr. Robinson is going to vacation and needs a four week supply. How many tablets does Johnny need to fill his prescription? - Chord BC

A circle k has the center at the point S = [0; 0]. Point A = [40; 30] lies on the circle k. How long is the chord BC if the center P of this chord has the coordinates: [- 14; 0]? - Vector perpendicular

Find the vector a = (2, y, z) so that a⊥ b and a ⊥ c where b = (-1, 4, 2) and c = (3, -3, -1) - Vector equation

Let’s v = (1, 2, 1), u = (0, -1, 3) and w = (1, 0, 7) . Solve the vector equation c1 v + c2 u + c3 w = 0 for variables c1 c2, c3 and decide weather v, u and w are linear dependent or independent - Five-gon

Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm. - Fall sum or same

Find the probability that if you roll two dice, it will fall the sum of 10, or the same number will fall on both dice. - Annulus

Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n. - Coordinates of a centroind

Let’s A = [3, 2, 0], B = [1, -2, 4] and C = [1, 1, 1] be 3 points in space. Calculate the coordinates of the centroid of △ABC (the intersection of the medians). - A library

A library has 12,500 fiction books and 19,000 non fiction books. Currently 2/5 of the fiction books are checked out. Currently 2/5 of the non fiction books are checked out. Of the books checked out, only 1/10 are due back this week. How many books are due - What percentage

What percentage of the Earth’s surface is seen by an astronaut from a height of h = 350 km. Take the Earth as a sphere with the radius R = 6370 km - Tropics and polar zones

What percentage of the Earth’s surface lies in the tropical, temperate and polar zone? Individual zones are bordered by tropics 23°27' and polar circles 66°33' - Tetrahedral pyramid 8

Let’s all side edges of the tetrahedral pyramid ABCDV be equally long and its base let’s be a rectangle. Determine its volume if you know the deviations A=40° B=70° of the planes of adjacent sidewalls and the plane of the base and the height h=16 of the p - Runners

If John has a running speed of 3.5miles per hour and Lucy has a speed of 5 miles per hour. If John starts running at 10:00 am and Lucy starts running at 10:30 am, at what time will they meet? (as soon as possible) - Adding

Divide number 135 into two additions so that one adds 30 more than 2/5 of the other add. Write the bigger one.

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