Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
153901	Verify the Identity	(cos(x))/(1-sin(x))-(cos(x))/(1+sin(x))=2tan(x)	$\frac{\cos (x)}{1 - \sin (x)} - \frac{\cos (x)}{1 + \sin (x)} = 2 \tan (x)$
153902	Find the Inverse	A=[[3,2],[8,5]]	$A = [\begin{array}{c} 3 & 2 \\ 8 & 5 \end{array}]$
153903	Find the Inverse	C=[[12,-20],[36,-52]]	$C = [\begin{array}{c} 12 & - 20 \\ 36 & - 52 \end{array}]$
153904	Find the Inverse	[[9,-10],[-7,3]]	$[\begin{array}{c} 9 & - 10 \\ - 7 & 3 \end{array}]$
153905	Find the Inverse	[[9,-5],[7,-4]]	$[\begin{array}{c} 9 & - 5 \\ 7 & - 4 \end{array}]$
153906	Find the Inverse	[[6,-5],[-5,4]]	$[\begin{array}{c} 6 & - 5 \\ - 5 & 4 \end{array}]$
153907	Find the Inverse	[[6,4],[3,2]]	$[\begin{array}{c} 6 & 4 \\ 3 & 2 \end{array}]$
153908	Find the Inverse	[[-7,1,-10],[4,-1,8],[-3,0,-5]]	$[\begin{array}{c} - 7 & 1 & - 10 \\ 4 & - 1 & 8 \\ - 3 & 0 & - 5 \end{array}]$
153909	Find the Inverse	[[6,-9],[-4,6]]	$[\begin{array}{c} 6 & - 9 \\ - 4 & 6 \end{array}]$
153910	Find the Inverse	[[7,6],[8,7]]	$[\begin{array}{c} 7 & 6 \\ 8 & 7 \end{array}]$
153911	Find the Inverse	[[7,5],[3,2]]	$[\begin{array}{c} 7 & 5 \\ 3 & 2 \end{array}]$
153912	Find the Inverse	[[7,8],[6,7]]	$[\begin{array}{c} 7 & 8 \\ 6 & 7 \end{array}]$
153913	Find the Inverse	[[8,-4],[-8,4]]	$[\begin{array}{c} 8 & - 4 \\ - 8 & 4 \end{array}]$
153914	Find the Inverse	[[6,3],[22,11]]	$[\begin{array}{c} 6 & 3 \\ 22 & 11 \end{array}]$
153915	Find the Inverse	[[4,2],[3,2]]	$[\begin{array}{c} 4 & 2 \\ 3 & 2 \end{array}]$
153916	Find the Inverse	[[4,2],[5,3]]	$[\begin{array}{c} 4 & 2 \\ 5 & 3 \end{array}]$
153917	Find the Inverse	[[3,7],[5,-4]]	$[\begin{array}{c} 3 & 7 \\ 5 & - 4 \end{array}]$
153918	Find the Inverse	[[3,9],[1,-10]]	$[\begin{array}{c} 3 & 9 \\ 1 & - 10 \end{array}]$
153919	Find the Inverse	[[-1,-3],[4,5]]	$[\begin{array}{c} - 1 & - 3 \\ 4 & 5 \end{array}]$
153920	Find the Inverse	[[-1,-2],[-5,-10]]	$[\begin{array}{c} - 1 & - 2 \\ - 5 & - 10 \end{array}]$
153921	Find the Inverse	[[1,-2],[3,4]]	$[\begin{array}{c} 1 & - 2 \\ 3 & 4 \end{array}]$
153922	Find the Inverse	[[11,-3],[-7,2]]	$[\begin{array}{c} 11 & - 3 \\ - 7 & 2 \end{array}]$
153923	Find the Inverse	[[2,1,3],[1,2,3],[4,2,1]]	$[\begin{array}{c} 2 & 1 & 3 \\ 1 & 2 & 3 \\ 4 & 2 & 1 \end{array}]$
153924	Find the Inverse	[[2,0,5],[0,-1,0],[3,3,7]]	$[\begin{array}{c} 2 & 0 & 5 \\ 0 & - 1 & 0 \\ 3 & 3 & 7 \end{array}]$
153925	Find the Inverse	[[3,2,-1],[1,4,3],[2,0,5]]	$[\begin{array}{c} 3 & 2 & - 1 \\ 1 & 4 & 3 \\ 2 & 0 & 5 \end{array}]$
153926	Find the Inverse	[[3,-3,1],[-2,2,-1],[-4,5,-2]]	$[\begin{array}{c} 3 & - 3 & 1 \\ - 2 & 2 & - 1 \\ - 4 & 5 & - 2 \end{array}]$
153927	Find the Inverse	[[3,4],[6,8]]	$[\begin{array}{c} 3 & 4 \\ 6 & 8 \end{array}]$
153928	Find the Inverse	[[3,6,3],[-3,3,3]]	$[\begin{array}{c} 3 & 6 & 3 \\ - 3 & 3 & 3 \end{array}]$
153929	Find the Inverse	[[3,6,9],[2,4,8]]	$[\begin{array}{c} 3 & 6 & 9 \\ 2 & 4 & 8 \end{array}]$
153930	Find the Inverse	[[3,6],[4,8]]	$[\begin{array}{c} 3 & 6 \\ 4 & 8 \end{array}]$
153931	Find the Inverse	[[2,4],[x,3]]=-10	$[\begin{array}{c} 2 & 4 \\ x & 3 \end{array}] = - 10$
153932	Find the Inverse	[[-2,-4],[4,8]]	$[\begin{array}{c} - 2 & - 4 \\ 4 & 8 \end{array}]$
153933	Find the Inverse	[[20,-15,17],[1,-1,1],[12,-9,10]]	$[\begin{array}{c} 20 & - 15 & 17 \\ 1 & - 1 & 1 \\ 12 & - 9 & 10 \end{array}]$
153934	Find the Inverse	[[2,1],[6,3]]	$[\begin{array}{c} 2 & 1 \\ 6 & 3 \end{array}]$
153935	Find the Inverse	[[2,3],[5,8]]	$[\begin{array}{c} 2 & 3 \\ 5 & 8 \end{array}]$
153936	Find the Inverse	[[1,0],[0,2]]	$[\begin{array}{c} 1 & 0 \\ 0 & 2 \end{array}]$
153937	Find the Inverse	[[0,-3,5],[0,1,2]]	$[\begin{array}{c} 0 & - 3 & 5 \\ 0 & 1 & 2 \end{array}]$
153938	Find the Inverse	1/2=[[12,-20],[36,-52]]	$\frac{1}{2} = [\begin{array}{c} 12 & - 20 \\ 36 & - 52 \end{array}]$
153939	Factor over the Complex Numbers	x^4-625	$x^{4} - 625$
153940	Factor over the Complex Numbers	x^3-2x^2+x-2	$x^{3} - 2 x^{2} + x - 2$
153941	Verify the Identity	1+cos(6x)=2sin(3x)^2	$1 + \cos (6 x) = 2 \sin^{2} (3 x)$
153942	Verify the Identity	1+cos(6x)=3cos(2x)	$1 + \cos (6 x) = 3 \cos (2 x)$
153943	Verify the Identity	1+cos(6x)=3sin(2x)	$1 + \cos (6 x) = 3 \sin (2 x)$
153944	Verify the Identity	1+cos(2a)=2/(1+tan(a)^2)	$1 + \cos (2 a) = \frac{2}{1 + \tan^{2} (a)}$
153945	Verify the Identity	(tan(x))/( square root of 1+tan(x)^2)=sin(x)	$\frac{\tan (x)}{\sqrt{1 + \tan^{2} (x)}} = \sin (x)$
153946	Verify the Identity	(tan(y))/(csc(y))=1/(cos(y))-1/(sec(y))	$\frac{\tan (y)}{\csc (y)} = \frac{1}{\cos (y)} - \frac{1}{\sec (y)}$
153947	Verify the Identity	(cos(x)-sin(x))/(cos(x)+sin(x))=sec(2x)-tan(2x)	$\frac{\cos (x) - \sin (x)}{\cos (x) + \sin (x)} = \sec (2 x) - \tan (2 x)$
153948	Verify the Identity	2sin(x)^2=cos(x)(sin(x))	$2 \sin^{2} (x) = \cos (x (\sin (x)))$
153949	Verify the Identity	cot(theta)=cos(theta)csc(theta)	$\cot (t h e t a) = \cos (t h e t a) \csc (t h e t a)$
153950	Verify the Identity	cos(0)*tan(0)=sin(0)	$\cos (0) \cdot \tan (0) = \sin (0)$
153951	Verify the Identity	csc(x)^2-sec(x)^2=cot(x)^2-tan(x)^2	$\csc^{2} (x) - \sec^{2} (x) = \cot^{2} (x) - \tan^{2} (x)$
153952	Verify the Identity	sin(pi/6-x)=1/2( square root of 3cos(x)-sin(x))	$\sin (\frac{π}{6} - x) = \frac{1}{2} (\sqrt{3} \cos (x) - \sin (x))$
153953	Verify the Identity	tan(x)^2=(1+cos(2x))/(1-cos(2x))	$\tan^{2} (x) = \frac{(1 + \cos (2 x))}{1 - \cos (2 x)}$
153954	Verify the Identity	tan(x)^2=(1-cos(2x))/(1+cos(2x))	$\tan^{2} (x) = \frac{(1 - \cos (2 x))}{1 + \cos (2 x)}$
153955	Verify the Identity	tan(x+pi/6)=( square root of 3tan(x)+1)/( square root of 3-tan(x))	$\tan (x + \frac{π}{6}) = \frac{\sqrt{3} \tan (x) + 1}{\sqrt{3} - \tan (x)}$
153956	Factor over the Complex Numbers	-16i	$- 16 i$
153957	Factor over the Complex Numbers	2i(2i-i^3)	$2 i (2 i - i^{3})$
153958	Factor over the Complex Numbers	5+9i	$5 + 9 i$
153959	Factor over the Complex Numbers	3-77i	$3 - 77 i$
153960	Factor over the Complex Numbers	9-8i	$9 - 8 i$
153961	Factor over the Complex Numbers	7+9i	$7 + 9 i$
153962	Factor over the Complex Numbers	-9i	$- 9 i$
153963	Factor over the Complex Numbers	a^2+4b^2	$a^{2} + 4 b^{2}$
153964	Factor over the Complex Numbers	sin(arcsin(u)+arctan(v))	$\sin (\arcsin (u) + \arctan (v))$
153965	Factor over the Complex Numbers	x^2+27	$x^{2} + 27$
153966	Factor over the Complex Numbers	x^2+2x-8	$x^{2} + 2 x - 8$
153967	Find the Cosine Given the Point	(-24/145,143/145)	$P (- \frac{24}{145}, \frac{143}{145})$
153968	Find the Cosine Given the Point	(40/41,-9/41)	$p (\frac{40}{41}, - \frac{9}{41})$
153969	Factor over the Complex Numbers	square root of -100-84	$\sqrt{- 100 - 84}$
153970	Factor over the Complex Numbers	square root of 7+5i	$\sqrt{7} + 5 i$
153971	Factor over the Complex Numbers	13-2i	$13 - 2 i$
153972	Find the Cosine Given the Point	p(-1/2,( square root of 3)/2)	$p (- \frac{1}{2}, \frac{\sqrt{3}}{2})$
153973	Factor over the Complex Numbers	1/8x^3-1/27y^3	$\frac{1}{8} x^{3} - \frac{1}{27} y^{3}$
153974	Factor over the Complex Numbers	(3+2i)(17+7i)	$(3 + 2 i) (17 + 7 i)$
153975	Factor over the Complex Numbers	(3-2i)/(5i)	$\frac{3 - 2 i}{5 i}$
153976	Factor over the Complex Numbers	(-3-8i)+(-5-7i)	$(- 3 - 8 i) + (- 5 - 7 i)$
153977	Factor over the Complex Numbers	(4-3i)/(-1-4i)	$\frac{4 - 3 i}{- 1 - 4 i}$
153978	Factor over the Complex Numbers	(x-7+11i)	$(x - 7 + 11 i)$
153979	Factor over the Complex Numbers	(aaaaaaa)/(aaaaa*a)	$\frac{a \cdot a \cdot a \cdot a \cdot a \cdot a \cdot a}{a \cdot a \cdot a \cdot a \cdot a \cdot a}$
153980	Find the Maximum Number of Real Roots	f(x)=x^3-x	$f (x) = x^{3} - x$
153981	Find the Maximum Number of Real Roots	P(x)=2x^5-3x^4-5x^2-2	$P (x) = 2 x^{5} - 3 x^{4} - 5 x^{2} - 2$
153982	Simplify the Matrix	8[[7,-4],[-3,0]]	$8 [\begin{array}{c} 7 & - 4 \\ - 3 & 0 \end{array}]$
153983	Simplify the Matrix	-9[[7,-4],[-3,0]]	$- 9 [\begin{array}{c} 7 & - 4 \\ - 3 & 0 \end{array}]$
153984	Write as a Set of Linear Factors	x^3+x^2-21x-45	$x^{3} + x^{2} - 21 x - 45$
153985	Graph the Line Segment	(5,-2) , (-3,4)	$(5, - 2) (- 3, 4)$
153986	Find the Sum of the Series	-5+-10+-15+-20	$- 5 + - 10 + - 15 + - 20$
153987	Find the Sum of the Series	7+28+112+448	$7 + 28 + 112 + 448$
153988	Find the Sum of the Series	3+7+11+15+19	$3 + 7 + 11 + 15 + 19$
153989	Find the Sum of the Series	3+9+27+81	$3 + 9 + 27 + 81$
153990	Find the Sum of the Series	4 , 12 , 36 , 108 , 324 , 972 , 2916	$4$ , $12$ , $36$ , $108$ , $324$ , $972$ , $2916$
153991	Find the Sum of the Series	1+3+9+27+81	$1 + 3 + 9 + 27 + 81$
153992	Find the Sum of the Series	-1/2+1/4-1/6+1/8-1/10+1/12	$- \frac{1}{2} + \frac{1}{4} - \frac{1}{6} + \frac{1}{8} - \frac{1}{10} + \frac{1}{12}$
153993	Solve Using a Matrix by Row Operations	3x-y+4z=1x-y+z=-12x+y-z=12	$3 x - y + 4 z = 1 x - y + z = - 12 x + y - z = 12$
153994	Solve Using a Matrix by Row Operations	p+q+r=32p-r=42p+q=36	$p + q + r = 32 p - r = 42 p + q = 36$
153995	Find the Sum of the Functions	f(x)=3x^2+2x+1g(x)=x^2-6x+3	$f (x) = 3 x^{2} + 2 x + 1 g (x) = x^{2} - 6 x + 3$
153996	Round to the Nearest Hundredth	7.51	$7.51$
153997	Round to the Nearest Hundredth	7.07106	$7.07106$
153998	Round to the Nearest Hundredth	8.075	$8.075$
153999	Round to the Nearest Hundredth	8.2	$8.2$
154000	Round to the Nearest Hundredth	8.3	$8.3$