Square root + real numbers - practice problems
Number of problems found: 31
- ABS, ARG, CONJ, RECIPROCAL
Let z=-√2-√2i where i2 = -1. Find |z|, arg(z), z* (where * indicates the complex conjugate), and (1/z). Where appropriate, write your answers in the form a + i b, where both a and b are real numbers. Indicate the positions of z, z*, and (1/z) on an Argand - Infinitely 3818
We have 2 numbers. If we multiplied the first number's third root by the second number's square root, we would get the number 18. Determine these 2 numbers. Calculate only the integer solution if the problem has infinitely many solutions in the set of rea - Equation: 3726
Determine the real root of the equation: x^-3: x^-8 = 32 - Triangle ABC
Calculate the sides of triangle ABC with area 1404 cm², and if a: b: c = 12:7:18 - Rectangle
The rectangle is 21 cm long and 38 cm wide. Find the radius of the circle circumscribing the rectangle. - Garden
The square garden area is 2/9 of triangle garden with sides 160 m, 100 m, and 100 m. How many meters of fencing need to fence a square garden? - Rhombus ABCD
Rhombus ABCD, |AC| = 63 cm, |BD| = 50 cm. Calculate the perimeter of the rhombus ABCD. - Short cut
Imagine that you are going to a friend. That path has a length 120 meters. Then turn doprava and go other 630 meters, and you are at a friend's. The question is, how much will the journey be shorter if you go direct across the field? - Cube in a sphere
The cube is inscribed in a sphere with a volume 7253 cm³. Determine the length of the edges of a cube. - Area 4gon
Calculate the area of 4-gon, two, and the two sides are equal and parallel with lengths 11, 5, 11, and 5. Inner angles are 45°, 135°,45°, 135°. - Right Δ
A right triangle has the length of one leg 72 cm and the hypotenuse 90 cm size. Calculate the height of the triangle. - Area of RT
Calculate the right triangle area that hypotenuse has length 14, and one hypotenuse segment has length 5. - Movement
From the crossing of two perpendicular roads started two cyclists (each on a different road). One runs at an average speed of 28 km/h, and the second 24 km/h. Determine the distance between them after 45 minutes of cycling. - Area of RT
The right triangle has orthogonal projections of legs to the hypotenuse lengths 15 cm and 9 cm. Determine the area of this triangle. - Square 2
Points D[10,-8] and B[4,5] are opposed vertices of the square ABCD. Calculate the area of the square ABCD. - Square
Points A[9,9] and B[-4,1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD. - Cubes
One cube is an inscribed sphere, and the other one is described. Calculate the difference of volumes of cubes if the difference of surfaces in 231 cm². - Forces
In point, O acts three orthogonal forces: F1 = 20 N, F2 = 7 N, and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2, and F3. - Axial section
The axial section of the cone is an equilateral triangle with an area 208 m². Calculate the volume of the cone. - Rotation
The right triangle with legs 11 cm and 18 cm rotates around the longer leg. Calculate the volume and surface area of the formed cone.
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