The square root of an unknown number equals the square of 2. a) What is the volume of a cube? b) How many centimeters measure its edge?ĭetermine the distance of a stationary satellite from the Earth's surface. The glass cube dives into the aquarium, which has a length of 25 cm, a width of 20 cm, and a height of 30 cm. Calculate the surface wetted with water if we poured into the funnel 7.1 liters of water. The funnel has the shape of an equilateral cone. c) Both are positive, and the product of one with the other power of the other is maximal. b) The product of one with the cube of the other is maximal. Find these numbers if: a) The sum of their third powers is minimal. The first is 1.5 times larger than the second number, and the third is 3.5 times larger than the second number. How many pages does the book have if the last page's number is steam? If we multiply the numbers of the last three pages of the book on pyramids, we get the product 23639616. The lengths of edges from the same vertex are in a ratio of 2:3:5. Calculate the surface of the cylinder if its volume is 2 m³.Ī cuboid has a volume of 810 cm³. The diameter of the cylinder is one-third the length of the height of the cylinder. How long must the cube's edge be in which the volume should be twice the volume of the original cube?ĭetermine the sum of the three-third roots of the number 64.įind the smallest natural x such that 2x is the square and 3x is the third power of a natural number. 1331įrom how many elements can we create 13,800 variations of the 3rd class without repeating? Which of the following number is not a perfect cube? a. The sum of three numbers in GP (geometric progression) is 21, and the sum of their squares is 189. Since 2^10=1024, that adds an extra bit of significance that we have to remove from the possible power of 5.Calculate the cube's surface, which is composed of 64 small cubes with an edge 1 cm long. Return mantissa=pow(5.0, possible_10_exponent) Mantissa*= pow(2.0, exponent - possible_10_exponent) Study with Quizlet and memorize flashcards containing terms like 10 to the Nth power 1 and N zeros to the left or the right., 10 Ten., 100. Int possible_10_exponent= (exponent - exponent_adjustment)/3 Luckily, 5^22 also only has 52 significant bits, so we can determine if a double is (2*5)^n for n= : bool is_pow10(double value)ĭouble mantissa= frexp(value, &exponent) Note that the comparison to 0.0 is exact rather than within a particular epsilon since you want to ensure that log10_value is an integer.ĮDIT: Since this sparked a bit of controversy due to log10 possibly being imprecise and the generic understanding that you shouldn't compare doubles without an epsilon, here's a more precise way of determining if a double is a power of 10 using only properties of powers of 10 and IEEE 754 doubles.įirst, a clarification: a double can represent up to 1E22, as 1e22 has only 52 significant bits. There are mathematical libraries available with BigInt implementations or you can roll your own (though efficiency is difficult to achieve).Ī variant of this one: double log10_value= log10(value) ĭouble fractional_value= modf(log10_value, &integer_value) If you really need this precision, my suggestion is not to use a floating point number. you can't test it for being a power of ten. So normally you should be able to represent integers from 0 to 10 14 faithfully.įinally some platforms may have a long long type with an ever greater precision.īut anyway, as soon as your value exceed the number of digits available to be converted back to an integer without loss. You can of course use a much more precise representation, like double which has 15 digits of precision. So if you represent 10 9 as a float chances are it will be converted back as 1 000 000 145 or something like that: nothing guarantees what the last digits will be, they are off the precision. There is no way to cast down a very large or very small floating point number to a BigInt class because you lost precision when using the small floating point number.įor example float only has 6 digits of precision. I am afraid you're in for a world of hurt.
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