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Question: An object at a distance p from a thin glass lens produces an image at a distance q from the lens, where
(1/p) + (1/q) = (1/f)
The constant f is called the focal length of the lens. Suppose an object is moving at 3 mm per second toward a lens of focal length 15 mm. How fast and in what direction is the image moving at the moment at which the object is 35 mm from the lens?
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 ..
In a cube with side length 6, what is the volume of the tetrahedron formed by any vertex and the three vertices connected to that vertex by edges of the cube?
What radius produces such a disk?
a flashlight flashes every 2 minutes a second light flashes every 3.5 minutes and a third light flashes every 4
A 9kg mass on a slope which is at an angle of 15 degrees is attached via a an inextensible string over a fixed, frictionless pulley to a 5kg mass.
If the temperature is 35oF, what wind speed makes it feel like 25oF? If the temperature is 25oF, what wind speed makes it feel like 12oF?
Describe the adjacency matrix of a graph with n connected components when the vertices of the graph are listed so that vertices in each connected component are listed successively.
What is the probability that among the 12 months of the year there are 3 non necessarily consecutive months containing exactly 4 birthdays?
Find the centroid of the region bounded by 3x - 10y = -56, x - 10y = 28, x = -2, and x = 8. You should enter the coordinates of your answer either as decimals or fractions. Find the fifth Maclaurin polynomial for f(x) = x3 cos (Sx).
Let R ba a partial order on S, and suppose that x is a unique minimal element in S. Prove that S is finite, then xRy for all s in S
Estimate the probability that a randomly generated simple graph with n vertices is connected for each positive integer n not exceeding ten by generating.
The 2010 Census determined the population of the US was 308.75 million on April 1, 2010. If the population was increasing exponentially at a rate of 2.85.
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