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Let be a smooth parametric surface and let P be a point such that each line that starts at P intersects S at most once. The solid angle Ω(S) subtended by S at P is the set of lines starting at P and passing through . Let S(a) be the intersection of Ω(S) with the surface of the sphere with center P and radius a. Then the measure of the solid angle (in steradians) is defined to be
|Ω(s)| = areaf s(a) / a2
Apply the Divergence Theorem to the part of Ω(S) between S(a) and to show that
|Ω(s)| = ∫s∫ (r·n) ds / r3
where is the radius vector from P to any point on S, r = |r|, and the unit normal vector is directed away from P.
The length of one of the equal legs of an isosceles triangle is 8 cm less than 4 times the length of the base. If the perimeter is 29 cm, find the length of one of the equal legs.
Determine the total contribution to profit that lies on the objective function (profit line) as it is plotted on the graph if the company produces a combination of cases of Brand X and Brand Y.
Explain the method use to find the amount of air
on friday a local hamburger shop sold a c ombined total of 426 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. how many hamburgers were sold on friday?
Define Population 1 as this year and Population 2 as last year and use the p-value approach to test this hypothesis with α = 0.05.
the cost varies linearly with the distance and is $366 per month for 300 km driven per month, and $510 per month for 1500 km driven per month. write the equation expressing cost in terms of distance.
The kinetic Energy (K) of a moving object varies jointly with its mass (m) and the square of its velocity (v). If an object has a mass of 22.5 kilograms and moving with a velocity of 20 meters per second has a kinetic energy of 4500 Joules
The region R is bounded by the graphs of x-2y = 3 and x=y^2. Set up (but not evaluate) the integral that gives the volume of the solid obtained by rotating R around the line x=-1.
Use the given information to draw the graph of f(x) on an interval near the indicated point (x=3). If there is not enough information given, then state this fact.
One card will be randomly selected from a standard 52-card deck of cards. What is the probability that it will be the jack of hearts?
A box contains 4 green, 10 red, 6 yellow, and 5 blue marbles. Four marbles are drawn from the box without replacement. What is the probability that you get one marble of each color?
What is the probability it would be a student, a faculty member, an admin staff member, a faculty or admin staff member and anyone except an admin staff member?
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