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Earth is about 150 million kilometers from the Sun, and the apparent brightness of the Sun in our sky is about 1300 watts/m2. Using these two facts and the inverse square law for light, determine the apparent brightness that we would measure for the Sun if we were located at the following positions.
Half Earth's distance from the Sun.Twice Earth's distance from the Sun.9 times Earth's distance from the Sun.
The three methods of solving linear systems covered are substitution, elimination, and graphing. There are examples posted on the solution field and in the attachment.
In a local election, there are eight candidates for five positions as judges on the Supreme Bench. The number of possible outcomes of the election is:
Suppose that f is continuous on [a,b], f(z) 0. Set z = sup{x: f (t)
Construct the circle through the excenters of triangle ABC. How is its center related to the circumcenter and incenter of triangle ABC?
Find the slope and the equation of the tangent line to the graph of the function at the given value of x.
Prove that the projection onto the plane Y O Z of the intersection curve of an elliptical paraboloid x = y^2 + z^2 with a plane x - 2y + 4z = 0 is a circle of radius R = 3 centered at M (0, 1, -2).
Let L:R^n -->R^n be a linear operator on R^n. suppose that L(x) = 0 for some x does not equal 0. Let A be the matrix representing L with respect to standard basis. Show that matrix A is singular.
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?
Use Gram-Schmidt algorithm to the sequence {x_1,x_2, x_3} to find an orthonormal basis of S. Use the result above to find the QR factorization of the matrix A=(x_1l x_2l x_3).
Show that if n is odd then the set of all n-cycles consists of two conjugacy classes of equal size in An. Let G be a transitive permutation group on the finite set A with |A|>1. Show that there is some g in G such that g(a) is not equal to a for al..
When graphing a linear inequality, how do you select the area (which side of the line) that is being represented (and has to be shaded) by the inequality?
Explain what makes a function a polynomial. Give an example of a function that is a polynomial and a function that is not a polynomial.
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