Planimetrics - math word problems - page 179 of 184
Number of problems found: 3667
- Parametrically 6400
Find the angle of the line, which is determined parametrically x = 5 + t y = 1 + 3t z = -2t t belongs to R and the plane, which is determined by the general equation 2x-y + 3z-4 = 0.
- Staircase - escalator
A moving staircase moves downwards at a speed of 0.6 m/s. The staircase makes an angle of 45° with the horizontal. A person weighing 80 kg walks upwards at a speed of 0.9 m/s. Determine the distance covered by the person and the work done by him before he
- The body
The body slides down an inclined plane, forming an angle α = π / 4 = 45° under the action of a horizontal plane under the effect of friction forces with acceleration a = 2.4 m/s². At what angle β must the plane be inclined so that the body slides on it af
- Complex roots
Find the sum of the fourth square root of the number 16.
- Unit circle
In the Cartesian coordinate system, a unit circle is given on which points A and B lie. Point O is the origin and has coordinates (0,0) and point B has coordinates (1,0). The size of angle BOA is 151°. Determine the x-coordinate of point A.
- Difference - altitude
The distance as the crow flies between Dolní and Horní Ves is 3 km, and the steady climb is 5%. What is the height difference between Horní and Dolní Ves rounded to the nearest meter?
- Length of the chord
Calculate the length of the chord in a circle with a radius of 25 cm and a central angle of 26°.
- Space vectors 3D
The vectors u = (1; 3;- 4) and v = (0; 1; 1) are given. Find their sizes, calculate their angles, and determine the distances between them.
- Two artillery
Objective C we observe from two artillery observatories, A and B, which are 975 m apart. The size of the BAC angle is 63°, and the size of ABC is 48°. Calculate the distance of points A and C.
- Straight 21243
The straight railway line has a gradient of 16 permille. What is the size of the pitch angle?
- Rhombus
ABCD is a rhombus, ABD is an equilateral triangle, and AC is equal to 4. Find the area of the rhombus.
- Calculate roots of z
Calculate the ratio of the two fifth roots of the number 32.
- Trapezoid MO
The rectangular trapezoid ABCD with the right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid.
- River
From the observatory 18 m high and 31 m from the riverbank, river width appears in the visual angle φ = 20°. Calculate the width of the river.
- Angle between vectors
Find the angle between the given vectors to the nearest tenth degree. u = (-1, 24) and v = (-8, -21)
- Triangle - many properties
In a right triangle ABC with a right angle at the vertex C, it is given: a = 17cm, Vc = 8 cm. Calculate the length of the sides b, c, its area S, the perimeter o, the length of the radii of the circles of the triangle circumscribed by R and inscribed r an
- Calculate
Calculate the area of triangle ABC if given by alpha = 49°, beta = 31°, and the height on the c side is 9cm.
- Slope
What is the slope of a line with an inclination -325°?
- SSA and geometry
The distance between the points P and Q was 356 m measured in the terrain. The viewer can see the PQ line at a 107°22' viewing angle. The observer's distance from P is 271 m. Find the viewing angle of P and the observer.
- Chord 24
A chord with length t = r times the square root of two divides a circle with radius r into two circular segments. What is the ratio of the areas of these segments?
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