Planimetry - math word problems - page 151 of 187
Number of problems found: 3739
- The tangent of the hyperbola
Write the equation of the tangent of the hyperbola 9x²−4y²=36 at the point T =[t1,4]. - Point construction
Given an isosceles right triangle ABS with base AB. On a circle centered at point S and passing through points A and B, point C lies such that triangle ABC is isosceles. Determine how many points C satisfy the given conditions and construct all such point - Diagonal in rectangle
In the ABCD rectangle is the center of BC, point E, and point F is the center of the CD. Prove that the lines AE and AF divide diagonal BD into three equal parts. - construction triangle problem
Construct the vertices C of all triangles ABC, if given side AB, height vb on side b, and length of line tc on side c. Build all the solutions. Mark the vertices C1, C2,. .. - MO8-Z8-I-5 2017
Identical rectangles ABCD and EFGH are positioned such that their sides are parallel to the same. The points I, J, K, L, M, and N are the intersections of the extended sides, as shown. The area of the BNHM rectangle is 12 cm², the rectangle MBCK area is 6 - The tangent line
Find the tangent line of the ellipse 9x² + 16y² = 144 with slope k = -1. - Engine pulley
The engine has a 1460 rev/min (RPM). The disc diameter is 350 mm. What will be the peripheral disc speed in RPM? Pulleys on the engine have a diameter of 80 mm, and a disc has a diameter of 160 mm. - Train
The train is running at speeds of 98 km/h. From the beginning of braking to full stop, the train runs for 2 minutes. If the train slows the braking equally, calculate the distance from the location where you need to start to brake. - Ten points
There are ten arbitrary points in the plane. How many circles can we make from them? - Z6–I–2
Mr. Kockorád owned a rectangular-shaped garden, on which he gradually paved paths from one side to the other. The paths were equally wide, crossed each other at two places, and the already paved area was skipped when paving further. When Mr. Kockorád pave - Body collision momentum
A body with a mass of 4 kg hits an obstacle at a speed of 10 m/s. After the collision, the body continued to move at a speed of 6 m/s, while the direction of this speed was perpendicular to the direction of the speed before the collision. Find: a) change - 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. - 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 - Square grid
A square grid consists of a square with sides of a length of 1 cm. Draw at least three patterns, each with an area of 6 cm² and a circumference of 12 cm, and their sides in a square grid. - Motorcyclist and a car
The passenger car left at 7:00 and was heading east at a speed of 60 km/h. A motorcyclist left the same place and headed north at 40 km/h. What will be their air distance at ten o'clock? - Triangle from sticks
Bob the boulder has many sticks of lengths 3.5 and 7. He wants to form triangles, each of whose edges consists of exactly one stick. How many non-congruent triangles can be formed with the sticks? - Circle line tangent
Given a circle k(O; 2.5 cm), a line p: /Op/=4 cm, a point T: T belongs to p and at the same time /OT/=4.5 cm. We must find all the circles that will touch the circle k and the line p at point T. - Triangle construction
Construct a triangle ABC, given the lengths of the sides: c = 8 cm, a = 5 cm and height length hc = 3.5 cm. Perform an analysis, write down the design procedure, perform it, and determine the number of solutions. - Perpendicular diameters
Draw a circle k/S; 4.5 cm/. Next, draw: a/two mutually perpendicular diameters AB and CD b/two radii SA and SE which form an angle of 75 degrees c/chord/KL/= 4 cm d/chord/MN/, which is perpendicular to KL - Fitness floor cost
The plan of the fitness center is made on a scale of 1:150. The rectangular fitness center has 5 cm and 6 cm dimensions on the plan. How many euros will we pay to cover the fitness studio with a floating floor if we pay 12 euros for 1 m² of floating floor
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