Tangent + equation - practice problems
Number of problems found: 16
- The tangent of the hyperbola
Write the equation of the tangent of the hyperbola 9x²−4y²=36 at the point T =[t1,4]. - Coefficient 81704
In the equation of the line p: ax-2y+1=0, determine the coefficient a so that the line p: a) it formed an angle of 120° with the positive direction of the x-axis, b) passed through point A[3,-2], c) was parallel to the x-axis, d) had a direction of k = 4. - Opposite 78434
We see the tree on the opposite bank of the river at an angle of 15° from a distance of 41m from the river bank. From the bank of the river, we can see at an angle of 31°. How tall is the tree? - Side wall planes
Find the volume and surface of a cuboid whose side c is 30 cm long and the body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls.
- 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. - The tangent line
Find the tangent line of the ellipse 9x² + 16y² = 144 with slope k = -1. - Tangents to ellipse
Find the magnitude of the angle at which the ellipse x² + 5 y² = 5 is visible from the point P[5, 1]. - Calculate 9701
In the triangle, the side length AB = 6 cm, the height per side c = 5 cm, and the angle BCA = 35°. Calculate sides a b. - Equilateral triangle
A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.
- 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? - Clouds
From two points, A and B, on the horizontal plane, a forehead cloud was observed above the two points under elevation angles 73°20' and 64°40'. Points A and B are separated by 2830 m. How high is the cloud? - Sphere in cone
A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions. - Angle
A straight line p given by the equation y = (-8)/(6) x +78. Calculate the size of the angle in degrees between line p and y-axis. - River
From the observatory 11 m high and 24 m from the riverbank, river width appears in the visual angle φ = 13°. Calculate the width of the river.
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