Triangle + maximum - practice problems
Number of problems found: 19
- Base and longest side
The base of a right-angled triangle is 10 centimeters, and the longest side is 26 centimeters. What is the area of the triangle? - 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. - A missile
A missile is fired with a speed of 100 fps in a direction 30° above the horizontal. Determine the maximum height to which it rises. Fps foot per second. - Circumference 9811
Kristýna chose a certain odd natural number divisible by three. Jakub and David then examined triangles with a circumference in millimeters equal to the number selected by Kristýna and whose sides have lengths in millimeters expressed by different integer
- Traffic laws
Under traffic regulations, car lights can illuminate the road up to a maximum of 30 m. To check the reach of the dipped-beam lights of their car, Peter stopped the car at 1.5 m from the wall. The dipped beam headlights are 60 cm high. At what height on th - Carpet
The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make a rectangular cut of a roll. That piece of carpet will be the longest possible and will fit into the room. How long is a piece of carpet? Note: The carpet will not be parallel w - An equilateral
An equilateral triangle with a side of 10 m represents a wooden platform standing on a lawn. A goat is tied to a corner with a 15 m rope. What is the maximum amount of grazing area available to the goat? - Martians
A sphere-shaped spaceship with a diameter of 6 m landed in the meadow. To avoid attracting attention, the Martians covered it with a roof in the shape of a regular cone. How high will this roof be so that the consumption of roofing is minimal? - Coefficient 82566
What is the maximum angle at which the tram can go downhill to still be able to stop? The coefficient of shear friction is f =0.15.
- Reflector
The circular reflector throws a light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane? - Right-angled 78394
A right-angled triangle was inscribed in a circle with a diameter of 20 cm, whose hypotenuse is the circle's diameter and has the largest possible area. Calculate the area of this triangle. - Hypotenuse - RT
A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle? - Confectionery 7318
The confectioner needs to carve a cone-shaped decoration from a ball-shaped confectionery mass with a radius of 25 cm. Find the radius of the base of the ornament a (and the height h). He uses as much material as possible is used to make the ornament. - Dimensions 81670
A wooden crate with dimensions d=3m, e=4m, and f=3m was placed in a transport container with dimensions a=10 m, b=4m, and c=3m. What is the maximum length of a straight, rigid rod of negligible diameter that can still be placed in the container in this si
- Closest 82051
On the line p: 2x + y + 1 = 0, find the point A ∈ p that is closest to the point P =(1,0) - Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base of 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure. - Ladder
A 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall? - Quadrilateral 8405
Calculate the magnitude of the largest inner angle and the deviation of the diagonals in the quadrilateral, whose vertices correspond to points 1, 5, 8, and 12 on the dial. - Maximum of volume
The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum?
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