Questions in mathematics

Questions in mathematics

📝 Answered - By setting t=0 in \[ f(t) = \frac{\pi^2}{6} + \sum_{n=1}^{\infty} -\frac{\pi}{n^2} (\cos(n\pi) + 1) \cos(nt) \] show that \[ f(t) = \frac{\pi^2}{6} = \sum_{n=1}^{\infty} \frac{1}{n^2} \] where \[ f(t) = t^2 - \pi t, \quad 0 < t < \pi \]

📝 Answered - Evaluate \(\sqrt{\frac{s^2 - (b+c)s + bc}{bc}}\) when \(b=25\), \(c=7\), and \(s=30\).

📝 Answered - It is given that G = {apple, orange, banana, grape, durian, pear} and H = {apple, banana, grape, strawberry}. (i) Draw a Venn diagram to represent the sets G and H. (ii) From the Venn diagram, list all the elements in G ∪ H in set notation.

📝 Answered - Solve and check the linear equation. [tex]4(x-2)+15=3(x+4)[/tex] What is the solution? Select the correct choice below and, if necessary, fill in the answer. A. The solution set is {$\square$} B. The solution set is {[tex]x | x[/tex] is a real number}. C. The solution set is $\varnothing$.

📝 Answered - Fifteen percent of an employee's taxable income is collected each paycheck. Before taxes are removed from each paycheck, $350 of tax-exempt expenses is taken out. If the variable $x$ represents the employee's pay before tax-exempt expenses and taxes are removed, which expression represents the employee's take-home pay after these deductions? A. $0.15(x-350)$ B. $x-0.15-350$ C. $0.85(x-350)$ D. $x-0.85-350

📝 Answered - If $y$ varies directly as $x$, and $y$ is 6 when $x$ is 72, what is the value of $y$ when $x$ is $8$?

📝 Answered - Solve the system by using Gaussian elimination or Gauss-Jordan elimination. [tex] \begin{aligned} -2 x-5 y+6 z & = -33 \\ x+3 y+5 z & = 27 \\ 5 x+4 y-5 z & =50 \end{aligned} [/tex] The solution set is { $\square$, $\square$, $\square$ }

📝 Answered - What is $24 x^2+14 x$ in factored form?

📝 Answered - Find the unknown value in the proportion [tex]2.3 / 6.7=4.6 / x[/tex]. A. 3.4 B. 13.4 C. 1.6 D. 20.1

📝 Answered - Simplify: [tex]$\frac{6 x^5-2 x-4}{2 x}$[/tex]