Real numbers + planimetrics - practice problems
Number of problems found: 40
- Rail turn
The curve radius on the railway line is 532 m. The length of the rail track on it is 818 m. How many degrees is the angle ASB if A and B are boundary points and S is the center of the arc curve? - Angles
Find the interior angles of a rhombus with area 319.1 cm² and perimeter 72 cm. - Estate
Semicircle estate must be a fence. The straight section has a 26 meters long fence. How many meters of the fence should we buy? - Complex plane mapping
Show that the mapping w = z +c/z, where z = x+iy, w = u+iv, and c is a real number, maps the circle |z| = 1 in the z-plane into an ellipse in the (u, v) plane.
- Quarter circular
The wire hooked around the perimeter of the quarter-circular arc has a length of 5π+20. Determine the radius of the circle arc. - Rectangle SS
The perimeter of a rectangle is 268 cm, and its diagonal is 99.3 cm. Determine the dimensions of the rectangle. - Wire D
Wire length 1 m is bent to form a semicircle circuit (including the diameter). Determine the radius of the semicircle. - Determine 80662
Given the function y = x² - 4x + 3. Determine all real numbers z such that g(x) = g(-2). - 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°.
- 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? - IS triangle
Calculate interior angles of the isosceles triangle with base 40 cm and legs 22 cm long. - Rhombus ABCD
Rhombus ABCD, |AC| = 63 cm, |BD| = 50 cm. Calculate the perimeter of the rhombus ABCD. - Diagonals of the rhombus
Calculate the height of the rhombus whose diagonals are 18 cm and 6 cm. - Trigonometric functions
In the right triangle is: tg α= frac(4) 2 Find the value of s and k: sin α= (s)/(√ 20) cos α= (k)/(√ 20)
- Sea
How far can you see from the ship's mast, whose peak is at 14 meters above sea level? (Earth's radius is 6370 km). - Building
How high is the building that throws horizontal shadow 85.6 m long at angle 34°12'? - Described
Calculate the perimeter of the circle described by a triangle with sides 191, 428, 385. - Square 2
Points D[10,-8] and B[4,5] are opposed vertices of the square ABCD. Calculate the area of the square ABCD. - Triangle TBC
TBC is isosceles triangle with base TB with base angle 63° and legs length |TC| = |BC| = 25. How long is the base TB?
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