Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
401	Use the Rational Roots Test to Find All Possible Roots	f(x)=x^3-10x^2+4x-24	$f (x) = x^{3} - 10 x^{2} + 4 x - 24$
402	Use the Rational Roots Test to Find All Possible Roots	x^3-4x^2-7x+10	$x^{3} - 4 x^{2} - 7 x + 10$
403	Solve Using the Quadratic Formula	x^2+4x+4=0	$x^{2} + 4 x + 4 = 0$
404	Find the x and y Intercepts	y=cot(x)	$y = \cot (x)$
405	Find the x and y Intercepts	y^2=6-x	$y^{2} = 6 - x$
406	Find the Roots (Zeros)	P(x)=x^3+3x^2-4	$P (x) = x^{3} + 3 x^{2} - 4$
407	Solve by Completing the Square	x^2+5x-9=0	$x^{2} + 5 x - 9 = 0$
408	Split Using Partial Fraction Decomposition	4/(x(x-1))	$\frac{4}{x (x - 1)}$
409	Write in Standard Form	(2+i)/(3i)	$\frac{2 + i}{3 i}$
410	Write in Standard Form	7/(4-14i)	$\frac{7}{4 - 14 i}$
411	Write in Standard Form	2/(2-15i)	$\frac{2}{2 - 15 i}$
412	Find the Range	y=sec(x)	$y = \sec (x)$
413	Find the Asymptotes	f(x) = natural log of x+3	$f (x) = \ln (x + 3)$
414	Find the Asymptotes	f(x)=x/(x-1)	$f (x) = \frac{x}{x - 1}$
415	Find the Asymptotes	f(x)=(x^2-9)/(x-3)	$f (x) = \frac{x^{2} - 9}{x - 3}$
416	Find the Asymptotes	f(x)=(3x^2)/(x^2-4)	$f (x) = \frac{3 x^{2}}{x^{2} - 4}$
417	Find the Asymptotes	f(x)=1/(x-3)	$f (x) = \frac{1}{x - 3}$
418	Find the Asymptotes	f(x)=1/(x-4)	$f (x) = \frac{1}{x - 4}$
419	Factor	(a+b)^2-(a-b)^2	${(a + b)}^{2} - {(a - b)}^{2}$
420	Factor	(z+2)^2-5(z+2)	${(z + 2)}^{2} - 5 (z + 2)$
421	Factor	x^3-7x+6	$x^{3} - 7 x + 6$
422	Factor	25-16t^2	$25 - 16 t^{2}$
423	Find the Other Trig Values in Quadrant II	sin(x)=3/4	$\sin (x) = \frac{3}{4}$
424	Find the Other Trig Values in Quadrant III	sin(x)=-5/13	$\sin (x) = - \frac{5}{13}$
425	Find the Asymptotes	y=3^x	$y = 3^{x}$
426	Solve for x	natural log of e^x=4	$\ln (e^{x}) = 4$
427	Solve for X	csc(x)+cot(x)=1	$\csc (x) + \cot (x) = 1$
428	Solve for x	natural log of 2x-1=0	$\ln (2 x - 1) = 0$
429	Solve for x	natural log of x-6+ natural log of x+7=1	$\ln (x - 6) + \ln (x + 7) = 1$
430	Solve for x	x^5-7x^2=0	$x^{5} - 7 x^{2} = 0$
431	Simplify	(1+cot(x))(1-cot(x))-csc(x)^2	$(1 + \cot (x)) (1 - \cot (x)) - \csc^{2} (x)$
432	Simplify	(3y^2)(4y^5)	$(3 y^{2}) (4 y^{5})$
433	Simplify	(3u^3v^3)^2(2u^-2v)^3	${(3 u^{3} v^{3})}^{2} {(2 u^{- 2} v)}^{3}$
434	Simplify	square root of 5a^3b* square root of 10ab	$\sqrt{5 a^{3} b} \cdot \sqrt{10 a b}$
435	Solve for x	(x+1)^(2/3)=4	${(x + 1)}^{\frac{2}{3}} = 4$
436	Solve for x	(2^x-2^(-x))/3=4	$\frac{2^{x} - 2^{- x}}{3} = 4$
437	Solve for x	square root of 5x+4-1=2x	$\sqrt{5 x + 4} - 1 = 2 x$
438	Solve for ?	cot(x)=- square root of 3	$\cot (x) = - \sqrt{3}$
439	Solve for ?	cos(x)=sin(x)	$\cos (x) = \sin (x)$
440	Solve for ?	2sin(x)- square root of 3=0	$2 \sin (x) - \sqrt{3} = 0$
441	Solve for x	x^3-9x^2+20x-12=0	$x^{3} - 9 x^{2} + 20 x - 12 = 0$
442	Solve for x	2e^(12x)=17	$2 e^{12 x} = 17$
443	Solve for x	4+3 log of 2x=16	$4 + 3 \log (2 x) = 16$
444	Solve for x	3 natural log of 4x=13	$3 \ln (4 x) = 13$
445	Solve for x	3 natural log of 5x=10	$3 \ln (5 x) = 10$
446	Solve for x	square root of x^2+15-4=0	$\sqrt{x^{2} + 15} - 4 = 0$
447	Solve for x	log base 4 of x-3=3	$\log_{4} (x - 3) = 3$
448	Solve for x	log base 4 of 16=x	$\log_{4} (16) = x$
449	Solve for x	log base 3 of x=-3	$\log_{3} (x) = - 3$
450	Solve for x	log base 3 of 3x-2=2	$\log_{3} (3 x - 2) = 2$
451	Solve for x	log base 6 of x=-2	$\log_{6} (x) = - 2$
452	Solve for x	e^x-30e^(-x)-1=0	$e^{x} - 30 e^{- x} - 1 = 0$
453	Solve for x	e^x-9=19	$e^{x} - 9 = 19$
454	Solve for x	e^(2x)-e^x-12=0	$e^{2 x} - e^{x} - 12 = 0$
455	Solve for x	7^(2x)+7^x-6=0	$7^{2 x} + 7^{x} - 6 = 0$
456	Solve for x	3^(2x)+3^x-30=0	$3^{2 x} + 3^{x} - 30 = 0$
457	Solve for x	3^(2x)+3^x-6=0	$3^{2 x} + 3^{x} - 6 = 0$
458	Solve for x	3^(2x)+3^(x+1)-4=0	$3^{2 x} + 3^{x + 1} - 4 = 0$
459	Solve for x	4^(7-3x)=1/16	$4^{7 - 3 x} = \frac{1}{16}$
460	Solve for x	5^x=8	$5^{x} = 8$
461	Solve for x	5^(x-2)=3^(3x+2)	$5^{x - 2} = 3^{3 x + 2}$
462	Solve for x	50/(1+e^(-x))=4	$\frac{50}{1 + e^{- x}} = 4$
463	Simplify	(x^4y^3)/(x^2y^5)	$\frac{x^{4} y^{3}}{x^{2} y^{5}}$
464	Simplify	u^(3/2)u^(2/7)	$u^{\frac{3}{2}} u^{\frac{2}{7}}$
465	Simplify	(x+2)/(x-1)-2/(x+6)-14/(x^2+5x-6)	$\frac{x + 2}{x - 1} - \frac{2}{x + 6} - \frac{14}{x^{2} + 5 x - 6}$
466	Simplify	1/(cot(x))	$\frac{1}{\cot (x)}$
467	Simplify	1/x+1/(x^2)+1/(x^3)	$\frac{1}{x} + \frac{1}{x^{2}} + \frac{1}{x^{3}}$
468	Simplify	5/(2x-3)-3/((2x-3)^2)	$\frac{5}{2 x - 3} - \frac{3}{{(2 x - 3)}^{2}}$
469	Simplify	((3p^3q^-1)/(9p^2q^-2))^2	${(\frac{3 p^{3} q^{- 1}}{9 p^{2} q^{- 2}})}^{2}$
470	Simplify	cos(pi/4)+cos(pi/6)	$\cos (\frac{π}{4}) + \cos (\frac{π}{6})$
471	Simplify	sin(x)csc(-x)	$\sin (x) \csc (- x)$
472	Simplify	(7x^2)/(x^3)	$\frac{7 x^{2}}{x^{3}}$
473	Simplify	cot(x)sin(x)-sin(pi/2-x)+cos(x)	$\cot (x) \sin (x) - \sin (\frac{π}{2} - x) + \cos (x)$
474	Simplify	csc(t)cos(t)	$\csc (t) \cos (t)$
475	Simplify	cos(x)+tan(x)sin(x)	$\cos (x) + \tan (x) \sin (x)$
476	Simplify	cos(x)(tan(x)+cot(x))	$\cos (x) (\tan (x) + \cot (x))$
477	Simplify	cos(75)	$\cos (75)$
478	Solve for x	(3x-1)/4-(x-5)/5>-2	$\frac{3 x - 1}{4} - \frac{x - 5}{5} > - 2$
479	Simplify	(2x(x+6)^4-x^2*4(x+6)^3)/((x+6)^8)	$\frac{2 x {(x + 6)}^{4} - x^{2} \cdot 4 {(x + 6)}^{3}}{{(x + 6)}^{8}}$
480	Solve for x	\|x-3\|<7	$\| x - 3 \| < 7$
481	Find the Domain	fourth root of x	$\sqrt[4]{x}$
482	Find the Domain	x^2-1	$x^{2} - 1$
483	Split Using Partial Fraction Decomposition	1/(x(x^2+1))	$\frac{1}{x (x^{2} + 1)}$
484	Find the Domain	y=arccos(x)	$y = \arccos (x)$
485	Find the Domain	x=-3	$x = - 3$
486	Find the Domain	( square root of 4-x^2)/(x-3)	$\frac{\sqrt{4 - x^{2}}}{x - 3}$
487	Find the Domain	(2x+1)/(x-4)	$\frac{2 x + 1}{x - 4}$
488	Find the Domain	1/( square root of x-1)	$\frac{1}{\sqrt{x - 1}}$
489	Find the Domain	( square root of x+3)/(x-4)	$\frac{\sqrt{x + 3}}{x - 4}$
490	Simplify	sin(arccos(( square root of 3)/2))	$\sin (\arccos (\frac{\sqrt{3}}{2}))$
491	Simplify	( square root of h^2+1+1)( square root of h^2+1-1)	$(\sqrt{h^{2} + 1} + 1) (\sqrt{h^{2} + 1} - 1)$
492	Simplify	square root of 81x^2+81	$\sqrt{81 x^{2} + 81}$
493	Simplify	( square root of 125x^5y^6)/( square root of 5x^3y^10)	$\frac{\sqrt{125 x^{5} y^{6}}}{\sqrt{5 x^{3} y^{10}}}$
494	Simplify	square root of 36x^2+36y^2	$\sqrt{36 x^{2} + 36 y^{2}}$
495	Divide Using Synthetic Division	(5x^3+18x^2+7x-6)/(x+3)	$\frac{5 x^{3} + 18 x^{2} + 7 x - 6}{x + 3}$
496	Simplify	fourth root of b^5 square root of b	$\sqrt[4]{b^{5}} \sqrt{b}$
497	Simplify	fourth root of 16a^4b^5	$\sqrt[4]{16 a^{4} b^{5}}$
498	Solve for y	square root of y+2=3	$\sqrt{y + 2} = 3$
499	Find the Exact Value	tan(-315)	$\tan (- 315)$
500	Find the Exact Value	tan(255)	$\tan (255)$