Log and Exponential Functions
Hi I tried some old test problems but I don’t have any feedback as to whether I’m doing it right could anybody check my solutions begin{align} log_{3}(x+4) – log_{3}left(frac{1}{x-2}right) & = ln e...
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One cake requires $150$gm flour and $50$gm fat and other requires $75$gm flour and $75$ gm fat. Amara wants to make as many cakes as possible when $1.5$kg flour and $0.6$kg fat are available. How many...
View ArticleRates of change between $x = 2$ and $x = 2 + h$ for $x^2$ and $1/x$
What is the simplified average rate of change between $x = 2$ and $x = 2 + h$ for the function: (Enter your expression as you would enter an equation in Winplot) a. $f(x) = x^2= 4+h$ b. $(x) =...
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What's wrong with my solution of inequality?
Question: solve the following inequality: $frac{x}{2} geq frac{5}{x + 1} + 4$ My solution: $frac{x}{2} – frac{5}{x + 1} + 4 geq 0$ $=> frac{x(x + 1) – 10(x + 1) – 8(x + 1)}{(x + 1) 2} geq 0$ $=>...
View ArticleIs this function increasing/decreasing and convex/concave?
The function is: $$y= 3x + lnleft(frac {3x – 4}{x – 1}right)$$ After differentiating I got: $$y’ = 3 + frac 1{3x^2 – 7x + 4};;;;; ;;; y”= – frac {6x – 7}{(3x^2 – 7x + 4)^2}$$ If you can’t find any...
View Article$x,|, x$ is a positive integer number such that $x^{2} = 4$. [on hold]
Is the answer $2$? I have guessed that the value of $x$ is $2$ since $2^2 = 4$. Can it be so simple?
View ArticleA human way to simplify $ frac{((sqrt{a^2 – 1} – a)^2 – 1)^2}{(sqrt{a^2 – 1}...
I end up with simplifying the following fraction when I tried to calculate an integral(*) with the residue theory in complex analysis: $$ frac{((sqrt{a^2 – 1} – a)^2 – 1)^2}{(sqrt{a^2 – 1} – a)^22...
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Solving $f(x) – g(x) = 0$, where $f(x) = e^x – 2.4$ and the graph of $g(x)$...
I’m doing a practice test for my EOC which is coming up soon and I can’t solve this (and I don’t know what to search). How can I solve this? Solve $f(x) – g(x) = 0$, to the nearest tenth, where $f(x) =...
View ArticleWhy does squaring an expression with 2 subtracting terms work?
This expression can be simplified as: $$sqrt{(x-frac32)^2} = x – frac32$$ Even though: $$k^2 = m^2 + n^2 to sqrt{k^2} = sqrt{m^2 + n^2} to k = pmsqrt{m^2 + n^2}$$ You can not remove the right-hand...
View ArticleHow would I solve this quadratic equation? [on hold]
I don’t know whether I should do completing the square or use the quadratic formula for this problem: $$x^2+5x-20/x+3$$
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