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An air ambulance is travelling from Barrie to Toronto. Toronto is located 90 km [S5°E] of Barrie. If the wind is blowing from the South with a velocity of 62 km/h, and the plane's air speed is 375 km/h, what direction must the pilot fly to make it to Toronto?
evaluate approximately the ratio of the mass of the sun to that of the earth. lunar month 27.3 days, mean radii of the earth's orbit 149000000 km and that of moon's orbit 380000 km.
The width of a rectangle is 9 less than twice its length. If the area of the rectangle is 173 cm, what is the length of the diagonal?
A volcano fills the volume between the graphs z=0 and z=1/(x^2+y^2)^23 , and outside the cylinder x^2+y^2=1. Find the volume of this volcano.
A 25.5 foot ladder rests against the side of a house at . a point 24.1 feet above the ground. The foot of the ladder. is x feet from the house. Find the value of x to one decimal place.
Find the volume of the solid whose base is the region bounded by y=x^{6}, y=1, and the y-axis and whose cross-sections perpendicular to the y axis are equilateral triangles.
In R2, let triangle ABC be a right triangle with right angle at angle C. Consider the altitude CH (it meets AB perpendicularly). Prove that |CH|^2 = |AH| * |BH|.
Find the amount of work in joules required to empty the trough by pumping the water over the top. (Note: Use as the acceleration due to gravity.)
money is deposited into the account at a continuous rate of $2000 p.a at a continuous rate of 8% p.a compounded quarterly. Express the amount as an exponential function of time hence find the amount in the account after 5 years.
A woman w = 6 ft tall is standing near a street lamp that is s = 14 ft tall. Find a function that models the length L of her shadow in terms of her distance d from the base of the lamp.
A straight line moves in such a way that the sum of the reciprocals of the intercepts of the axes is equal to 1/k , where k is a constant. Prove that the line will pass through a fixed point.
Using the definition of the derivative and any standard limiting theorems, show that the derivative of (sinx)^2 is sin(2x).
a number has 3 digits. it is an even square number less than 500.the product of its digits is evenly divisible by 15. what is the number?
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