Let f(x) = x^{2004} + 2x^{2003} + 3x^{2002} + \dots + 2004x + 2005 and z = cos(pi/1003) + sin (pi/1003). the number [n = f(z)f(z^2) \dotsm f(z^{2005})] can be written in the form a^b, where a and b are positive integers and a is as small as possible. find the remainder when a + b is divided by 1000.

Hillel is juggling flaming torches to raise money for charity. his initial appearance raises $500\$500 $500 , and he raises $15\$15 $15 for each minute of juggling performance. the amount rr r of money hillel raises is a function of tt t , the length of his performance in minutes. write the function's formula.

The length and width of a rectangle are consecutive even integers the area of the rectangle is 120 squares units what are the length and width of the rectangle

Someone answer this asap rn for ! a discount store’s prices are 25% lower than department store prices. the function c(x) = 0.75x can be used to determine the cost c, in dollars, of an item, where x is the department store price, in dollars. if the item has not sold in one month, the discount store takes an additional 20% off the discounted price and an additional $5 off the total purchase. the function d(y) = 0.80y - 5 can be used to find d, the cost, in dollars, of an item that has not been sold for a month, where y is the discount store price, in dollars. create a function d(c(x)) that represents the final price of an item when a costumer buys an item that has been in the discount store for a month. d(c(x)) =