Need ONE of these figured out..
try doing as many as possible...
Let p(x) be a polynomial such that its leading coefficient is 1 and 27(x – 1)p(x) = (x – 27)p(3x) for all real numbers x. Find p(4).
For any positive integer n, let a(n) be the remainder when 7^n is divided by 100. Find the value of a(1) + a(2) + a(3) ... + a(100).
Let f and g be two polynomials such that f(x +g(y)) = 3x + y + 4 for all real numbers x and y. Find the value of g(8 + f(3)).
Let f(x) be a rational function such that f(x) + f((x – 1)/x) = 1 + x for any real number x ≠ 0, 1. Find the value of f(10).
ABCD is a square-shaped piece of paper of area 81 sq cm. A square of area 1 sq cm with one vertex at A and sides parallel to those of ABCD is removed from ABCD. If the remaining part is cut into k congruent triangles,
what is the smallest possible value of k?
try doing as many as possible...
Let p(x) be a polynomial such that its leading coefficient is 1 and 27(x – 1)p(x) = (x – 27)p(3x) for all real numbers x. Find p(4).
For any positive integer n, let a(n) be the remainder when 7^n is divided by 100. Find the value of a(1) + a(2) + a(3) ... + a(100).
Let f and g be two polynomials such that f(x +g(y)) = 3x + y + 4 for all real numbers x and y. Find the value of g(8 + f(3)).
Let f(x) be a rational function such that f(x) + f((x – 1)/x) = 1 + x for any real number x ≠ 0, 1. Find the value of f(10).
ABCD is a square-shaped piece of paper of area 81 sq cm. A square of area 1 sq cm with one vertex at A and sides parallel to those of ABCD is removed from ABCD. If the remaining part is cut into k congruent triangles,
what is the smallest possible value of k?
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Well this will take some time to do all of them. For the first one, p(x) = x³ - 39x² + 351x - 729, so that p(4) = 115. Leave this one open a little bit.
The second is 25(7 + 49 + 43 + 1) = 2500.
The third, f(x) = 3x, and g(y) = (1/3)y + (4/3), so that g(8 + f(3)) = 7
The second is 25(7 + 49 + 43 + 1) = 2500.
The third, f(x) = 3x, and g(y) = (1/3)y + (4/3), so that g(8 + f(3)) = 7
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Hey you closed this out too quick
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