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Suppose that the three coordinate planes are all mirrored and a light ray given by vector a=(a1,a2,a3) first strikes the xz-plane, then the reflected ray strikes the xy-plane and the reflected ray of this ray strikes the yz-plane. Use the fact that angle of incidence equals the angle of reflection, show that the reflected ray b=(a1,-a2,a3). Deduce that after being reflected by all three mutually perpendicular mirrors, the resulting ray is parallel to the initial ray. Thank you.
the everton college store paid $1824 for an order of 52 calculators. The store paid $ 8 for each scientific calculator. The others, all graphing calculators, cost the store $ 52 each. How many of each type of calculator was ordered?
From the top of a 175 ft lighthouse, the angle of depression to a ship in the ocean is 23°. How far is the ship from the base of the lighthouse? Round your answer to the nearest foot.
why can't I search by subject instead of school? I just want some precalc study resources for my daughter, who is in high school. The organization of this site makes no sense. Isn't there a search box??
The distance in miles an automobile travels is given by the formula D = rt, where r is the rate in miles per hour and t is the time in hours. How far will an automobile travel in 6 hours at a rate of 55 miles per hour?
A thin plate occupies the region x^2/4 + y^2/9 is less than or equal to 1. If the temerature of the plate is T(x,y)= x^2 + y^2 - 5y + 5, find the coldest and hottest points on the plate.
Use the leading coefficient test to determine the behavior of the function.
For the function below, find a) the critical numbers, b) the open intervals where the function is increasing, and c) the open intervals where the function is decreasing.
Ace Industries has current assets equal to $3 million. The company's current ratio is 1.5, and its quick ratio is 1.0. What is the firm's level of current liabilities? What is the firm's level of inventories?
How many days would the company have to operate each factory in order to fill an order for exactly 500 baseline and 325 GT cars?
What would be the null hypothesis for a chi-square test for testing if the claim made in the medical journal is indeed true?
A metal storage tank with a mximum volume of 500 m^3 is to be constructed in the shape of a right circular sylinder surmounted by a hemisphere. What radial and height dimensions will require the least amount of material?
In your own words, describe the process of factoring by grouping. Explain how the distributive property is used in this process. Give a detailed example of this process.
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