Pythagorean theorem + addition - practice problems
Number of problems found: 21
- 11990 perimeter RT
A right triangle has integer side lengths and a perimeter of 11990. In addition, we know that one of its perpendiculars has a prime number length. Find its length. - Recursion squares
In the square, ABCD has inscribed a square so that its vertices lie at the centers of the sides of the square ABCD. The procedure of inscribing the square is repeated this way. The side length of the square ABCD is a = 16 cm. Calculate: a) the sum of peri - Infinite sum of areas
An equilateral triangle A1B1C1 is constructed above the height of the equilateral triangle ABC is constructed as. Above the height of the equilateral triangle A1B1C1 is built triangle A2B2C2, and so on. The procedure is repeated continuously. What is the - Transmitter 34201
A television transmitter 108 m high is anchored at 2/3 of its height (from the ground) by three ropes of equal length. How many meters of rope are needed for anchoring if it is embedded at a distance of 54 m from the foot of the mast, and we count 10% of - 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? - Two forces
Two forces with magnitudes of 25 and 30 pounds act on an object at 10° and 100° angles. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and your final answer. - Graphically 7004
A boatman walks along the ship's deck at a constant speed of 5 km/h in a direction that forms an angle of 60° with the direction of the ship's speed. The boat moves with respect to the lake's calm surface at a constant speed of 10 km/h. Determine graphica - Paratrooper
After the parachute is opened, the paratrooper drops to the ground at a constant speed of 2 m/s, with the sidewinding at a steady speed of 1.5 m/s. Find: a) the magnitude of its resulting velocity concerning the ground, b) the distance of his land from a - Perpendicular 7001
We throw a ball in an express car traveling at a constant speed of 24 m/s, whose initial speed relative to the vehicle is 7 m/s. What is the initial velocity of the ball relative to the surface of the ground if we throw it a) in the direction of travel b) - Crosswind
A plane is traveling 45 degrees N of E at 320 km/h when it comes across a current from S of E at 115 degrees of 20 km/h. What are the airplane's new course and speed? - A man 7
A man wandering in the desert walks 3.8 miles in the direction of S 44° W. He then turns and walks 2.2 miles in the direction of N 55° W. At that time, how far is he from his starting point? (Round your answer to two decimal places.) - Meridian ground speed
The plane flies south at an average speed of 190 km/h, and the wind blows from west to east at a speed of 20 m/s. How fast and in what direction (relative to the meridian) will the plane move relative to the ground? - The bomber
An aircraft flying at an altitude of 1260 m. From what distance in front of the target must a parachute load be dropped from an airplane? The load slopes at a speed of 5.6 m/s and moves in the direction of movement at 12 m/s. What is the direct distance o - Angle ASB
On a circle with a radius of 10 cm and with a center S, the points A, B, and C are given so that the central angle ASB is 60 degrees and the central angle ASC is 90 degrees. Find the length of the circular arc and the amount of AB and AC offsets. - Forces
Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant? - Resultant force
Calculate mathematically and graphically the resultant of three forces with a common center if: F1 = 50 kN α1 = 30° F2 = 40 kN α2 = 45° F3 = 40 kN α3 = 25° - Isosceles 48443
Three equal positive charges Q are located at the vertices of an isosceles right triangle ABC. The right angle is at vertex A. The length of side AB is 1m. What is the electric field strength at the center S of side BC, i.e., what force would act on a pos - Displacement 55871
Assemble the two offsets, d1, and d2, shown by OA and OB oriented lines. The coordinates of the points are O = (0m, 0m), A = (3m, 3m), and B = (5m, 2m). Measure the magnitude of the resulting displacement d. - North + west
Find the magnitude of the resultant of the given vectors: vector 1:2 m/s, north vector 2:7 m/s, west - Vectors abs sum diff
The vectors a = (4,2), b = (- 2,1) are given. Calculate: a) |a+b|, b) |a|+|b|, c) |a-b|, d) |a|-|b|.
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