Questions in mathematics

Questions in mathematics

[Free] Use the following to answer the next 4 questions. Let the universal set be the natural numbers from 40 to 60 inclusive. The universal set contains the following subsets: - [tex]F=\{\text{multiples of 6}\}[/tex] - [tex]T=\{\text{multiple of 2}\}[/tex] True or False. [tex]T I=\{m \mid m=2 x, 20 \leq x \leq 30, x \in R\} ??[/tex]

[Free] An arc on a circle measures $125^{\circ}$. The measure of the central angle, in radians, is within which range? A. 0 to $\frac{\pi}{2}$ radians B. $\frac{\pi}{2}$ in $\pi$ radians C. $\pi$ to $\frac{3 \pi}{2}$ radians D. $\frac{3 \pi}{2}$ to $2 \pi$ radians

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

[Free] Multiply: [tex]$\sqrt[4]{x} \cdot \sqrt[4]{y^3}$[/tex] Rewrite the expression using rational exponents with a common denominator. [tex]$x^{-6} \cdot y^{\frac{3}{4}}$[/tex] [tex]$x^{\frac{2}{12}} \cdot y^{\frac{9}{12}}$[/tex] [tex]$x y^{\frac{11}{12}}$[/tex]

[Free] What is the greatest common factor of [tex]$42 a^5 b^3, 35 a^3 b^4$[/tex], and [tex]$42 a b^4 ?$[/tex]

[Free] Find the domain of the function. [tex]f(x)=\sqrt{\frac{3}{x+7}}[/tex] Write your answer as an interval or union of intervals.

[Free] The multiplication theorem for Kummer's function [tex]{_1F_1}(a;x)[/tex] involves the product of: A. [tex]{_1F_1}(a; x) {_1F_1}(b; x)[/tex] B. [tex]{_1F_1}(a; x) {_1F_1}(a+b; x)[/tex] C. [tex]{_1F_1}(a; x) {_1F_1}(a-b; x)[/tex] D. [tex]{_1F_1}(a; x) {_1F_1}(2a; x)[/tex]

[Free] Consider the boundary value problem [tex]y'' + \lambda y = 0, x \in [0, \pi], y(0) = 0, y(\pi) = 0[/tex] Let [tex]S_\lambda = {y_\lambda(x) | y_\lambda(x)[/tex] is an eigenfunction corresponding to [tex] \lambda}[/tex]. Then which of the following is/are FALSE? (a) [tex]S_\lambda[/tex] is linearly independent (L.I.). (b) The number of linearly independent functions in [tex]S_\lambda[/tex] is exactly one. (c) If [tex]y_1(x) \in S_{\lambda_1}[/tex] and [tex]y_2(x) \in S_{\lambda_2}[/tex], where [tex] \lambda_1 \neq \lambda_2[/tex], then [tex]y_1[/tex] and [tex]y_2[/tex] are linearly independent. (d) There exists [tex]\lambda[/tex] such that the number of linearly independent functions in [tex]S_\lambda[/tex] is more than one.

[Free] Angie is working on solving the exponential equation [tex]$23^x=6$[/tex]; however, she is not quite sure where to start. Solve the equation and use complete sentences to describe the steps to solve. Hint: Use the change of base formula: [tex]$\log _0 y=\frac{\log y}{\log b}$[/tex].

[Free] Determine whether the graph of the equation is symmetric with respect to the $y$-axis, the $x$-axis, the origin, more than one of these, or none of these. $y^2=x^2+17$ Select all that apply. x-axis y-axis origin none of these