Basic operations and concepts - math word problems - page 319 of 322

Number of problems found: 6438

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.
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?
Cablecar
Funicular on Petrin (Prague) was 408 meters long and overcame the difference of 106 meters in altitude. Calculate the angle of the climb.
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?
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.
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.
Right
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: 2a +5b = 5.283c
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?
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?
Wheel gear
A drive wheel of radius two is connected to a drive wheel of radius one by a pulley of length 17. What is the distance between the wheel axles?
Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
Perimeter - ASA theorem
Calculate the perimeter of the triangle ABC if a = 12 cm, the angle beta is 38 degrees, and the gamma is 92 degrees.
Triangle area and angle
Calculate the area of the triangle ABC, in which you know the side c=5 cm, the angle at the vertex A= 70 degrees, and the ratio of the segments cut by the height to the side c is 1:3 .
Intersect of 10 lines
At how many points do ten lines intersect if no two are parallel?
Ratio iso triangle
The ratio of the sides of an isosceles triangle is 7:6:7. Find the base angle to the nearest answer correct to 3 significant figures.
Triangle in circle
The vertices of the triangle ABC lie on a circle with a radius 3, which is divided into three parts in the ratio 4:4:4. Calculate the circumference of the triangle ABC.

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