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Questions in mathematics

📝 Answered - Mandy takes out a ten-year loan of R80 000. She repays the loan by means of equal monthly payments starting four months after the granting of the loan. The interest rate is 12% per annum compounded monthly. Calculate the monthly payments.

📝 Answered - If [tex]A=\left[\begin{array}{cc}2 & 3 \\ 10 & 15\end{array}\right][/tex] and [tex]B=\left[\begin{array}{cc}4 & 7 \\ 8 & 24\end{array}\right][/tex], find [tex]A+B[/tex], [tex]A-B[/tex], [tex]2A+3B[/tex], and [tex]B[/tex].

📝 Answered - 10 - x + y ÷ 2; x = 5 & y = 2

📝 Answered - What two operations do you need to use to find the temperature at noon? A. addition and subtraction B. addition and multiplication C. division and addition D. multiplication and subtraction

📝 Answered - Find the equation of the line that is perpendicular to $y=-4 x+3$ and contains the point $(8,1)$. $y=\frac{[?]}{[]} x+[]$

📝 Answered - Solve $2 x^2+20 x+8=0$ by completing the square. A. $x=5+\sqrt{17}, x=5-\sqrt{17}$ B. $x=5+\sqrt{21}, x=5-\sqrt{21}$ C. $x=-5+\sqrt{21}, x=-5-\sqrt{21}$ D. $x=-5+\sqrt{17}, x=-5-\sqrt{17}$

📝 Answered - The mass of the part of a metal rod that lies between its left end and a point [tex]$x$[/tex] meters to the right is [tex]$s = 4x^2$[/tex]. Find the linear density when [tex]$x$[/tex] is 3 m.

📝 Answered - Let $f$ be a function defined on $[0, \infty)$. Then the function $F$ defined by $F(s)=\int_0^{\infty} e^{-s t} f(t) d t$ is said to be the Laplace transform of $f$. The domain of $F(s)$ is the set of values of $s$ for which the given improper integral converges. Use the definition of a Laplace transform to find $L \{f(t)\}$. (Write your answer as a function of $s$.) $\begin{array}{r} f(t)=\left\{\begin{array}{lr} 0, & 0 \leq t<\pi / 2 \\ \cos (t), & t \geq \pi / 2 \end{array}\right. \\ L \{f(t)\}=\square \\ x \end{array}$

📝 Answered - Which is the simplified form of $\left(\frac{2 a b}{a^{-5} b^2}\right)^{-3}$ ? Assume $a \neq 0, b \neq 0$. A. $\frac{b^3}{8 a^{18}}$ B. $\frac{b^2}{8 a^{45}}$ C. $\frac{a^6}{4 b}$ D. $\frac{2 a^6}{b^5}$

📝 Answered - Evaluate [tex] \int \sin ^2 x \cos x dx [/tex]