Basic operations and concepts - math word problems - page 319 of 323
Number of problems found: 6445
- Railway
The railway line had a 5.8 km segment climb nine permille. How many meters does the track ascent? - Chimney height calculation
The heating plant sees the observer standing 26 m from the bottom of the chimney and seeing the top at an angle of 67 °. Thus, the chimney of the heating plant is how high? - Height difference
What height difference is overcome if we pass a road 1 km long with a pitch of 21 per mille? - Road
Between cities, A and B is a route 9 km long of average 9‰ klesanie. Calculate the height difference between cities A and B. - 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. - 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? - 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. - Cablecar
Funicular on Petrin (Prague) was 408 meters long and overcame the difference of 106 meters in altitude. Calculate the angle of the climb. - Function x*tanx
Functions: f(x)=xtanx f(x)=(e^x)/((e^x)+1) Find; i)vertical and horizontal asymptotes iii)the interval of decrease and increase iii)Local maxima and local minima iv)interval of concavity and inflection. And sketch the graph. - Calculate
Calculate the area of triangle ABC if given by alpha = 49°, beta = 31°, and the height on the c side is 9cm. - Clouds
We see the cloud under an angle of 26°10' and the Sun at an angle of 29°15'. The shade of the cloud is 92 meters away from us. Approximately at what height is the cloud? - Four sides of trapezoid
In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles. - The tower
The observer sees the tower's base 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands? - Right
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: 2a +5b = 5.283c - Traffic sign
There is a traffic sign for climbing on the road with an angle of 7%. Calculate at what angle the road rises (falls). - Altitude difference
Between the resorts is 15 km, and the climb is 13 permille. What is the height difference? - Angle of inclination
What percentage of the gradient should be indicated on the mark if the angle of inclination of the road is 6°25'? - Lift
The largest angle at which the lift rises is 16°31'. Give climb angle in permille. - Rhombus 48
A rhombus consists of four identical rhombuses with an area of 42 m². The angle alpha of each rhombus is 60°. What is its perimeter? - Depth angles
At the top of the mountain stands a castle with a tower 30 meters high. We see the crossroad at a depth angle of 32°50' and the heel at 30°10' from the top of the tower. How high is the top of the mountain above the crossroad?
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