Algebra Answers

assuming you are a researcher tasked to know about some truths in life. you plan to investigate the growth or decay of some things that interest you. you are to report what you have researched and present exponential or logarithmic functions that would model the involved quantities. you also have to present the graph and explain its characteristics or behavior.

Find at least one solution to the following equation:
sin(x^2 − 1)/1 − sin(x^2 − 1) = sin(x) + sin^2(x) + sin^3(x) + sin^4(x) + · · ·

Find all points (x, y) where the functions f(x), g(x), h(x) have the same value:
f(x) = 2^x−5 + 3, g(x) = 2x − 5, h(x) = 8/x+ 10

While grocery shopping, you are trying to decide which orange juice bottle would be the best to buy in terms of how much real juice is in the bottle compared to water. Both bottles each contain 1 Litre of solution. In Bottle 1, there is 5% real juice. In Bottle 2, there is 200mL of real juice. Which bottle of juice would be the best to buy if you wanted a solution that had the highest concentration of real juice.

.Find all points (x, y) where the functions f(x), g(x), h(x) have the same value:
f(x) = 2^x−5 + 3, g(x) = 2x − 5, h(x) = 8/x+ 10

Solve for n in the following equation:

250(1+0.015)n=750

If 5 machine makes 600 part in 2.3hours. How many hours it will take 2 machine to make 600 part

You have given a function λ : R→R with the following properties (x ∈R, n ∈N): λ(n) = 0 , λ(x + 1) = λ(x) , λ(n + 1/ 2)= 1 Find two functions p,q : R→R with q(x) (is not equal to zero)= 0 for all x such that λ(x) = q(x)(p(x) + 1).

Consider the following sequence of successive numbers of the 2^k-th power:
1, 2^2k, 3^2k, 4^2k, 5^2k, ... Show that the difference between the numbers in this sequence is odd for all k ∈N.

Determine the roots of the function f(x) = (5^2x −6)^2 −(5^2x −6)−12.