Questions in mathematics

Questions in mathematics

📝 Answered - Select the correct answer. What are the solutions of this quadratic equation? [tex]x^2+10=0[/tex] A. [tex]z= \pm \sqrt{10}[/tex] B. [tex]z= \pm 5[/tex] C. [tex]z= \pm \sqrt{10} i[/tex] D. [tex]z= \pm 5 i[/tex]

📝 Answered - Find the Wronskian (W) of the fundamental solution of the following differential equation: y'' - 2y' + 1 = (x+1)e^{2x} A. W = e^x B. W = e^{2x} C. W = xe^{2x} D. W = x

📝 Answered - An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

📝 Answered - 1. Which of the following are even numbers? 16, 27, 21, 35, 28, 59, 280, 559 2. Which of the following numbers are prime? 1, 5, 17, 28, 61, 89, 78, 88, 97, 47, 81 3. List all twin-primes between 1 and 50. 4. List all prime numbers between 51 and 100. 5. Give four examples of pairs of co-primes. 6. Write the prime factorization of each of the following numbers using division by prime numbers: a. 30 b. 72 c. 84 d. 210 e. 728 7. Write the prime factorisation of each of the following numbers using factor tree: a. 45 b. 69 c. 96 d. 210 e. 450 8. Which of the following are co-prime numbers? a. 48, 52 b. 33, 51 c. 9, 16 d. 30, 45

📝 Answered - \left(-\frac{11}{2 \sqrt{2}} x\right) \times\left(-x^4+\frac{1}{\sqrt{2}} x^3-\frac{\sqrt{3}}{7} x^2+\frac{2}{5} x-\frac{21}{8}\right)

📝 Answered - A rectangular garden has a length of x meters and a width of (x+4) meters. Express its area as an algebraic expression.

📝 Answered - How does the range of [tex]g(x)=\frac{6}{x}[/tex] compare with the range of the parent function [tex]f(x)=\frac{1}{x}[/tex] ? A. The range of both [tex]f(x)[/tex] and [tex]g(x)[/tex] is all real numbers B. The range of both [tex]f(x)[/tex] and [tex]g(x)[/tex] is all nonzero real numbers C. The range of [tex]f(x)[/tex] is all real numbers, the range of [tex]g(x)[/tex] is all real numbers except 6 D. The range of [tex]f(x)[/tex] is all nonzero real numbers, the range of [tex]g(x)[/tex] is all real numbers except 6

📝 Answered - Danika concludes that the following functions are inverses of each other because [tex]f(g(x))=x[/tex]. Do you agree with Danika? Explain your reasoning. [tex]f(x)=|x|[/tex] [tex]g(x)=-x[/tex]

📝 Answered - Determine the multiplicity of the roots of the function [tex]$k(x)=x(x+2)^3(x+4)^2(x-5)^4$[/tex]. 0 has multiplicity $\square$ -2 has multiplicity $\square$ -4 has multiplicity $\square$ 5 has multiplicity $\square$

📝 Answered - $256^b t^2=4^2-{ }^{2 b}