Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
601	Find the Equation Using Two Points	(-3,6) , (3,-1)	$(- 3, 6) (3, - 1)$ $(- 3, 6) (3, - 1)$
602	Find the Properties	(x^2)/16+(y^2)/9=1	$\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$ $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$
603	Find the Properties	(x^2)/36-(y^2)/4=1	$\frac{x^{2}}{36} - \frac{y^{2}}{4} = 1$ $\frac{x^{2}}{36} - \frac{y^{2}}{4} = 1$
604	Find the Properties	(x^2)/100+(y^2)/64=1	$\frac{x^{2}}{100} + \frac{y^{2}}{64} = 1$ $\frac{x^{2}}{100} + \frac{y^{2}}{64} = 1$
605	Find the Properties	2x^2+8y^2=16	$2 x^{2} + 8 y^{2} = 16$ $2 x^{2} + 8 y^{2} = 16$
606	Find the Properties	y^2=-4x	$y^{2} = - 4 x$ $y^{2} = - 4 x$
607	Find the Properties	(x^2)/9+(y^2)/25=1	$\frac{x^{2}}{9} + \frac{y^{2}}{25} = 1$ $\frac{x^{2}}{9} + \frac{y^{2}}{25} = 1$
608	Find the Properties	1/2x^2+1/8y^2=1/4	$\frac{1}{2} x^{2} + \frac{1}{8} y^{2} = \frac{1}{4}$ $\frac{1}{2} x^{2} + \frac{1}{8} y^{2} = \frac{1}{4}$
609	Find the Properties	x^2=-24y	$x^{2} = - 24 y$ $x^{2} = - 24 y$
610	Find the Properties	y^2=20x	$y^{2} = 20 x$ $y^{2} = 20 x$
611	Evaluate	e^( natural log of square root of 2)	$e^{ln (\sqrt{2})}$ $e^{\ln (\sqrt{2})}$
612	Evaluate	log base 2 of 0.5	${log}_{2} (0.5)$ $\log_{2} (0.5)$
613	Evaluate	log base 2 of 12	${log}_{2} (12)$ $\log_{2} (12)$
614	Evaluate	log base 5 of 121	${log}_{5} (121)$ $\log_{5} (121)$
615	Evaluate	log base 49 of 1/7	${log}_{49} (\frac{1}{7})$ $\log_{49} (\frac{1}{7})$
616	Evaluate	log base 3 of 1/18	${log}_{3} (\frac{1}{18})$ $\log_{3} (\frac{1}{18})$
617	Evaluate	log base 3 of 100- log base 3 of 18- log base 3 of 50	${log}_{3} (100) - {log}_{3} (18) - {log}_{3} (50)$ $\log_{3} (100) - \log_{3} (18) - \log_{3} (50)$
618	Write in Exponential Form	log base x of 100=2	${log}_{x} (100) = 2$ $\log_{x} (100) = 2$
619	Expand the Logarithmic Expression	natural log of square root of (x^4)/(y^3)	$ln (\sqrt{\frac{x^{4}}{y^{3}}})$ $\ln (\sqrt{\frac{x^{4}}{y^{3}}})$
620	Expand the Logarithmic Expression	log base 5 of (z/25)^3	${log}_{5} ({(\frac{z}{25})}^{3})$ $\log_{5} ({(\frac{z}{25})}^{3})$
621	Expand the Logarithmic Expression	log base 2 of z^3	${log}_{2} (z^{3})$ $\log_{2} (z^{3})$
622	Expand the Logarithmic Expression	log base 5 of 125x	${log}_{5} (125 x)$ $\log_{5} (125 x)$
623	Expand the Logarithmic Expression	log base 8 of x^4	${log}_{8} (x^{4})$ $\log_{8} (x^{4})$
624	Simplify/Condense	log of x-2 log of y+3 log of z	$log (x) - 2 log (y) + 3 log (z)$ $\log (x) - 2 \log (y) + 3 \log (z)$
625	Convert from Radians to Degrees	2pi	$2 π$ $2 π$
626	Simplify/Condense	natural log of e^(6x)	$ln (e^{6 x})$ $\ln (e^{6 x})$
627	Simplify/Condense	natural log of e^5	$ln (e^{5})$ $\ln (e^{5})$
628	Simplify/Condense	natural log of e^(5x)	$ln (e^{5 x})$ $\ln (e^{5 x})$
629	Simplify/Condense	natural log of e^6	$ln (e^{6})$ $\ln (e^{6})$
630	Convert from Degrees to Radians	61	$61$ $61$
631	Convert from Radians to Degrees	(19pi)/24	$\frac{19 π}{24}$ $\frac{19 π}{24}$
632	Evaluate the Summation	sum from n=1 to 8 of 5(r)^(n-1)	$8 \sum n = 1 5 {(r)}^{n - 1}$ $\sum_{n = 1}^{8} 5 {(r)}^{n - 1}$
633	Convert from Radians to Degrees	(31pi)/18	$\frac{31 π}{18}$ $\frac{31 π}{18}$
634	Convert from Radians to Degrees	-1.75	$- 1.75$ $- 1.75$
635	Evaluate the Summation	sum from k=1 to 8 of 4(2/3)^(k-1)	$8 \sum k = 1 4 {(\frac{2}{3})}^{k - 1}$ $\sum_{k = 1}^{8} 4 {(\frac{2}{3})}^{k - 1}$
636	Evaluate the Summation	sum from k=1 to 5 of 6k	$5 \sum k = 1 6 k$ $\sum_{k = 1}^{5} 6 k$
637	Evaluate the Summation	sum from k=1 to 4 of 2k	$4 \sum k = 1 2 k$ $\sum_{k = 1}^{4} 2 k$
638	Evaluate the Limit	limit as x approaches infinity of (x^2(1-4x^3))/(x^4(2x+1))	$lim x \to \infty \frac{x^{2} (1 - 4 x^{3})}{x^{4} (2 x + 1)}$ $lim_{x \to \infty} \frac{x^{2} (1 - 4 x^{3})}{x^{4} (2 x + 1)}$
639	Simplify the Matrix	[[11],[4]]	$[\begin{matrix} 114 \end{matrix}]$ $[\begin{array}{c} 11 \\ 4 \end{array}]$
640	Evaluate	log base 8 of 0.125	${log}_{8} (0.125)$ $\log_{8} (0.125)$
641	Evaluate	log base a of x	${log}_{a} (x)$ $\log_{a} (x)$
642	Evaluate	natural log of 1/(e^6)	$ln (\frac{1}{e^{6}})$ $\ln (\frac{1}{e^{6}})$
643	Evaluate	natural log of 1/(e^7)	$ln (\frac{1}{e^{7}})$ $\ln (\frac{1}{e^{7}})$
644	Evaluate	log of log of 10^100000	$log (log (10^{100000}))$ $\log (\log (10^{100000}))$
645	Evaluate	natural log of 25.3	$\ln (25.3)$
646	Evaluate	natural log of 54.6	$\ln (54.6)$
647	Evaluate	log of 1/( square root of 10)	$\log (\frac{1}{\sqrt{10}})$
648	Find Amplitude, Period, and Phase Shift	y=arccos(x)	$y = \arccos (x)$
649	Find Amplitude, Period, and Phase Shift	y=cos(-6x)	$y = \cos (- 6 x)$
650	Find the Reference Angle	1589	$1589$
651	Find Amplitude, Period, and Phase Shift	y=1.5sin(4x)	$y = 1.5 \sin (4 x)$
652	Verify the Identity	(tan(x))/(1-cos(x))=csc(x)(1+sec(x))	$\frac{\tan (x)}{1 - \cos (x)} = \csc (x) (1 + \sec (x))$
653	Find the Exact Value	cos(-105)	$\cos (- 105)$
654	Find the Exact Value	cos(arctan(4/3))	$\cos (\arctan (\frac{4}{3}))$
655	Find the Exact Value	cos((41pi)/12)	$\cos (\frac{41 π}{12})$
656	Find the Exact Value	arccos(cos((17pi)/6))	$\arccos (\cos (\frac{17 π}{6}))$
657	Find the Exact Value	arccos(pi)	$\arccos (π)$
658	Expand the Trigonometric Expression	sin(x-y)	$\sin (x - y)$
659	Expand the Trigonometric Expression	(x-4)^2	${(x - 4)}^{2}$
660	Expand the Trigonometric Expression	(x-3)^2	${(x - 3)}^{2}$
661	Find the Exact Value	tan(165 degrees )	$\tan (165 °)$
662	Find the Exact Value	sin(arcsin(6))	$\sin (\arcsin (6))$
663	Find the Exact Value	sin(arctan(7/24))	$\sin (\arctan (\frac{7}{24}))$
664	Find the Exact Value	sin(arccos(-2/3))	$\sin (\arccos (- \frac{2}{3}))$
665	Find the Exact Value	tan(arcsin(5/8))	$\tan (\arcsin (\frac{5}{8}))$
666	Solve for y	log base 4 of y=2	$\log_{4} (y) = 2$
667	Simplify	square root of 121(z-2)^14	$\sqrt{121 {(z - 2)}^{14}}$
668	Simplify	square root of 4x	$\sqrt{4 x}$
669	Simplify	square root of x^2-25	$\sqrt{x^{2} - 25}$
670	Divide Using Long Polynomial Division	(6x^3+10x^2+x+8)/(2x^2+1)	$\frac{6 x^{3} + 10 x^{2} + x + 8}{2 x^{2} + 1}$
671	Divide Using Synthetic Division	(5x^3+6x+8)/(x+2)	$\frac{5 x^{3} + 6 x + 8}{x + 2}$
672	Simplify	( square root of a-b)( square root of a+b)	$(\sqrt{a} - b) (\sqrt{a} + b)$
673	Simplify	square root of 20x^16	$\sqrt{20 x^{16}}$
674	Simplify	cot(- square root of 3)	$\cot (- \sqrt{3})$
675	Simplify	(1/( square root of 4+h)-1/2)/h	$\frac{\frac{1}{\sqrt{4 + h}} - \frac{1}{2}}{h}$
676	Find the Domain	2/x	$\frac{2}{x}$
677	Find the Domain	f(x) = square root of 4-x^2	$f (x) = \sqrt{4 - x^{2}}$
678	Find the Domain	square root of x^2-2x-8	$\sqrt{x^{2} - 2 x - 8}$
679	Find the Domain	square root of x^2-36	$\sqrt{x^{2} - 36}$
680	Find the Domain	log base 2 of x	$\log_{2} (x)$
681	Find the Domain	4/x	$\frac{4}{x}$
682	Find the Domain	square root of 1-x^2	$\sqrt{1 - x^{2}}$
683	Find the Domain	y=1/x	$y = \frac{1}{x}$
684	Find the Domain	f(x)=(x+4)/(x^2-9)	$f (x) = \frac{x + 4}{x^{2} - 9}$
685	Find the Domain	f(x)=(x+1)/(x^2-1)	$f (x) = \frac{x + 1}{x^{2} - 1}$
686	Find the Domain	x=y^2	$x = y^{2}$
687	Find the Domain	natural log of x-2	$\ln (x - 2)$
688	Split Using Partial Fraction Decomposition	1/(x^2-1)	$\frac{1}{x^{2} - 1}$
689	Split Using Partial Fraction Decomposition	(x^2)/(x^2+14x+49)	$\frac{x^{2}}{x^{2} + 14 x + 49}$
690	Split Using Partial Fraction Decomposition	(4x^2+2x-1)/(x^2(x+1))	$\frac{4 x^{2} + 2 x - 1}{x^{2} (x + 1)}$
691	Find the Domain	y=csc(x)	$y = \csc (x)$
692	Find the Domain	y = log base a of x	$y = \log_{a} (x)$
693	Find the Domain	square root of 6-x^2	$\sqrt{6 - x^{2}}$
694	Find the Domain	3/(x^2-2x-15)	$\frac{3}{x^{2} - 2 x - 15}$
695	Find the Domain	square root of x^2-1	$\sqrt{x^{2} - 1}$
696	Find the Domain	8	$8$
697	Find the Domain	x/( square root of x-4)	$\frac{x}{\sqrt{x - 4}}$
698	Find the Domain	square root of 7-3x	$\sqrt{7 - 3 x}$
699	Find the Domain	square root of 25-x^2	$\sqrt{25 - x^{2}}$
700	Find the Domain	square root of 2x-4	$\sqrt{2 x - 4}$