Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
42401	Find the Roots (Zeros)	x^4+6x^3+7x^2-6x-8	$x^{4} + 6 x^{3} + 7 x^{2} - 6 x - 8$
42402	Find the Roots (Zeros)	x^3-9x^2+31x-39	$x^{3} - 9 x^{2} + 31 x - 39$
42403	Find the Roots (Zeros)	2x^4+14x^3-35x^2	$2 x^{4} + 14 x^{3} - 35 x^{2}$
42404	Find the Roots (Zeros)	2x^3-7x^2-17x+10	$2 x^{3} - 7 x^{2} - 17 x + 10$
42405	Find the Roots (Zeros)	3x^4-x^3-9x^2+159x-52	$3 x^{4} - x^{3} - 9 x^{2} + 159 x - 52$
42406	Find the Roots (Zeros)	x^3+7x^2+7x-15	$x^{3} + 7 x^{2} + 7 x - 15$
42407	Find the Roots (Zeros)	x^3+4x^2+3x-1	$x^{3} + 4 x^{2} + 3 x - 1$
42408	Find the Roots (Zeros)	x^2e^x-49e^x	$x^{2} e^{x} - 49 e^{x}$
42409	Find the Roots (Zeros)	x^2-4x-1	$x^{2} - 4 x - 1$
42410	Solve by Completing the Square	x^2-18x+81=0	$x^{2} - 18 x + 81 = 0$
42411	Find the Other Trig Values in Quadrant III	cos(theta)=-4/9	$\cos (θ) = - \frac{4}{9}$
42412	Find the Other Trig Values in Quadrant III	sec(theta)=-13/5	$\sec (θ) = - \frac{13}{5}$
42413	Find the Other Trig Values in Quadrant II	cos(2theta)=-( square root of 3)/2	$\cos (2 θ) = - \frac{\sqrt{3}}{2}$
42414	Simplify/Condense	log base 3 of 4* log base 4 of 5* log base 5 of 6* log base 6 of 7* log base 7 of 8* log base 8 of 9	$\log_{3} (4) \cdot \log_{4} (5) \cdot \log_{5} (6) \cdot \log_{6} (7) \cdot \log_{7} (8) \cdot \log_{8} (9)$
42415	Simplify/Condense	4 log of x-1/3 log of x^2+1+2 log of x-1	$4 \log (x) - \frac{1}{3} \log (x^{2} + 1) + 2 \log (x - 1)$
42416	Find the Center and Radius	(x-4)^2+(y-7)^2=45	${(x - 4)}^{2} + {(y - 7)}^{2} = 45$
42417	Find the Center and Radius	(x-5)^2+(y+2)^2=81/4	${(x - 5)}^{2} + {(y + 2)}^{2} = \frac{81}{4}$
42418	Find the Center and Radius	(x-5)^2+(y-5)^2=29	${(x - 5)}^{2} + {(y - 5)}^{2} = 29$
42419	Find the Center and Radius	(x-2)^2+(y-3)^2=36	${(x - 2)}^{2} + {(y - 3)}^{2} = 36$
42420	Find the Center and Radius	(x+9)^2+(y-46)^2=123	${(x + 9)}^{2} + {(y - 46)}^{2} = 123$
42421	Find the Center and Radius	(x+3)^2+(y-1)^2=36	${(x + 3)}^{2} + {(y - 1)}^{2} = 36$
42422	Find the Center and Radius	x^2+y^2-3y=0	$x^{2} + y^{2} - 3 y = 0$
42423	Find the Center and Radius	x^2+y^2-4=0	$x^{2} + y^{2} - 4 = 0$
42424	Find the Center and Radius	x^2+y^2-4x+2y-31=0	$x^{2} + y^{2} - 4 x + 2 y - 31 = 0$
42425	Find the Center and Radius	x^2+y^2=2y	$x^{2} + y^{2} = 2 y$
42426	Find the Center and Radius	x^2+y^2-10x-16y=-40	$x^{2} + y^{2} - 10 x - 16 y = - 40$
42427	Find the Center and Radius	x^2+y^2-10x-6y+25=0	$x^{2} + y^{2} - 10 x - 6 y + 25 = 0$
42428	Simplify/Condense	1/4(3 natural log of x+2- natural log of x+4- natural log of x^2+2)	$\frac{1}{4} (3 \ln (x + 2) - \ln (x + 4) - \ln (x^{2} + 2))$
42429	Find the Center and Radius	x^2+y^2-8x+6y+7=0	$x^{2} + y^{2} - 8 x + 6 y + 7 = 0$
42430	Find the Center and Radius	x^2+y^2<=64	$x^{2} + y^{2} \leq 64$
42431	Find the Center and Radius	4x^2+4y^2-64x+48y=0	$4 x^{2} + 4 y^{2} - 64 x + 48 y = 0$
42432	Find the Center and Radius	10x^2+10y^2-160x+120y=0	$10 x^{2} + 10 y^{2} - 160 x + 120 y = 0$
42433	Find the Center and Radius	5x^2+5y^2=125	$5 x^{2} + 5 y^{2} = 125$
42434	Find the Value Using the Unit Circle	330 degrees	$330 °$
42435	Find the Value Using the Unit Circle	0	$0$
42436	Find the Value Using the Unit Circle	cos(165 degrees )	$\cos (165 °)$
42437	Find the Value Using the Unit Circle	cos(330 degrees )	$\cos (330 °)$
42438	Find the Value Using the Unit Circle	sin(105 degrees )	$\sin (105 °)$
42439	Find the Value Using the Unit Circle	sin(300 degrees )	$\sin (300 °)$
42440	Find the x and y Intercepts	f(x)=3x+1	$f (x) = 3 x + 1$
42441	Find the x and y Intercepts	f(x)=2^(x-1)	$f (x) = 2^{x - 1}$
42442	Find the x and y Intercepts	f(x)=x^3+3x^2-10x-24	$f (x) = x^{3} + 3 x^{2} - 10 x - 24$
42443	Find the x and y Intercepts	f(x)=-x^2-4x+1	$f (x) = - x^{2} - 4 x + 1$
42444	Find the Roots (Zeros)	x^2=8x-16	$x^{2} = 8 x - 16$
42445	Find the Roots (Zeros)	x^3-5x^2+8x-6=0	$x^{3} - 5 x^{2} + 8 x - 6 = 0$
42446	Split Using Partial Fraction Decomposition	(7x-70)/((x-3)^2(x+4))	$\frac{7 x - 70}{{(x - 3)}^{2} (x + 4)}$
42447	Split Using Partial Fraction Decomposition	(6x^2+13x+31)/(x^3+5x^2+4x+20)	$\frac{6 x^{2} + 13 x + 31}{x^{3} + 5 x^{2} + 4 x + 20}$
42448	Split Using Partial Fraction Decomposition	x/((x+2)(x+5))	$\frac{x}{(x + 2) (x + 5)}$
42449	Solve by Substitution	x^2+y^2=128 , x+y=0	$x^{2} + y^{2} = 128$ , $x + y = 0$
42450	Solve by Substitution	x^2+y^2=25x+y=8	$x^{2} + y^{2} = 25 x + y = 8$
42451	Solve by Substitution	2x+4y+z=1x-2y-3z=2x+y-z=-1	$2 x + 4 y + z = 1 x - 2 y - 3 z = 2 x + y - z = - 1$
42452	Solve by Substitution	x^2+y^2=53x-y=5	$x^{2} + y^{2} = 53 x - y = 5$
42453	Solve by Substitution	x=y^2-3x=y^2-3y	$x = y^{2} - 3 x = y^{2} - 3 y$
42454	Solve by Substitution	x=y^2-4yx+y=0	$x = y^{2} - 4 y x + y = 0$
42455	Split Using Partial Fraction Decomposition	(4x-5)/(x(2x^2+1)^2)	$\frac{4 x - 5}{x {(2 x^{2} + 1)}^{2}}$
42456	Split Using Partial Fraction Decomposition	12/(x^2-9)	$\frac{12}{x^{2} - 9}$
42457	Find the Roots/Zeros Using the Rational Roots Test	5x^3-2x^2-10x+4=0	$5 x^{3} - 2 x^{2} - 10 x + 4 = 0$
42458	Complete the Square	y^2-10y	$y^{2} - 10 y$
42459	Complete the Square	y^2+4y	$y^{2} + 4 y$
42460	Find the Roots/Zeros Using the Rational Roots Test	x^4-5x^3+9x^2-7x+2=0	$x^{4} - 5 x^{3} + 9 x^{2} - 7 x + 2 = 0$
42461	Find the Roots/Zeros Using the Rational Roots Test	x^4+2x^3-5x^2-8x+4=0	$x^{4} + 2 x^{3} - 5 x^{2} - 8 x + 4 = 0$
42462	Find the Center	((x-8)^2)/49+((y-2)^2)/9=1	$\frac{{(x - 8)}^{2}}{49} + \frac{{(y - 2)}^{2}}{9} = 1$
42463	Find the Center	(x^2)/81+((y+7)^2)/9=1	$\frac{x^{2}}{81} + \frac{{(y + 7)}^{2}}{9} = 1$
42464	Find the Center	16x^2-9y^2-64x+18y-121=0	$16 x^{2} - 9 y^{2} - 64 x + 18 y - 121 = 0$
42465	Find the End Behavior	f(x)=arctan(x)	$f (x) = \arctan (x)$
42466	Find the Center	x^2-9y^2+2x-54y-80=0	$x^{2} - 9 y^{2} + 2 x - 54 y - 80 = 0$
42467	Solve over the Interval	sin(3x)=1/2 , [0,2pi)	$\sin (3 x) = \frac{1}{2}$ , $[0, 2 π)$
42468	Solve the Matrix Equation	X+[[2,-2,6],[-8,17,9]]=[[-13,24,24],[24,13,12]]	$X + [\begin{array}{c} 2 & - 2 & 6 \\ - 8 & 17 & 9 \end{array}] = [\begin{array}{c} - 13 & 24 & 24 \\ 24 & 13 & 12 \end{array}]$
42469	Solve the Matrix Equation	[[16,5],[3,2]]-x=[[31,9],[19,-6]]	$[\begin{array}{c} 16 & 5 \\ 3 & 2 \end{array}] - x = [\begin{array}{c} 31 & 9 \\ 19 & - 6 \end{array}]$
42470	Solve the Matrix Equation	1/5x+[[4,7],[2,1],[8,6]]=[[9,-4],[-2,8],[-3,7]]	$\frac{1}{5} x + [\begin{array}{c} 4 & 7 \\ 2 & 1 \\ 8 & 6 \end{array}] = [\begin{array}{c} 9 & - 4 \\ - 2 & 8 \\ - 3 & 7 \end{array}]$
42471	Convert to Interval Notation	x^3-6x^2<0	$x^{3} - 6 x^{2} < 0$
42472	Convert to Interval Notation	x^3-x^2-4x+4<0	$x^{3} - x^{2} - 4 x + 4 < 0$
42473	Convert to Interval Notation	x^4-80x^2+1024<0	$x^{4} - 80 x^{2} + 1024 < 0$
42474	Solve the System of @WORD	\|3x+16\|<8	$\| 3 x + 16 \| < 8$
42475	Convert to Interval Notation	x(x+5)^2(x-8)<0	$x {(x + 5)}^{2} (x - 8) < 0$
42476	Convert to Interval Notation	x^3-12x^2<0	$x^{3} - 12 x^{2} < 0$
42477	Convert to Interval Notation	x^3+5x^2<x+5	$x^{3} + 5 x^{2} < x + 5$
42478	Convert to Interval Notation	(x-5)/(x-4)<=0	$\frac{x - 5}{x - 4} \leq 0$
42479	Convert to Interval Notation	(x+5)(x^2-9)(1-x)>=0	$(x + 5) (x^{2} - 9) (1 - x) \geq 0$
42480	Convert to Interval Notation	(x+4)/(x+5)<=0	$\frac{x + 4}{x + 5} \leq 0$
42481	Convert to Interval Notation	(4x-2)/(x+3)<=3	$\frac{4 x - 2}{x + 3} \leq 3$
42482	Factor over the Complex Numbers	tan(arccos(w))	$\tan (\arccos (w))$
42483	Factor over the Complex Numbers	8-8i	$8 - 8 i$
42484	Find the Inverse	[[7,9],[1,1]]	$[\begin{array}{c} 7 & 9 \\ 1 & 1 \end{array}]$
42485	Find the Inverse	(x-5)^3	${(x - 5)}^{3}$
42486	Expand Using De Moivre's Theorem	(4(cos(15 degrees )+isin(15 degrees )))^4	${(4 (\cos (15 °) + i \sin (15 °)))}^{4}$
42487	Expand Using De Moivre's Theorem	(2+2i)^6	${(2 + 2 i)}^{6}$
42488	Find the Domain	(1/( square root of x))/(x^2-4)	$\frac{(\frac{1}{\sqrt{x}})}{x^{2} - 4}$
42489	Find the Domain	( square root of x-4)/(x^2-2x-8)	$\frac{\sqrt{x - 4}}{x^{2} - 2 x - 8}$
42490	Find the Roots (Zeros)	f(x)=x^3+9x^2+23x+15	$f (x) = x^{3} + 9 x^{2} + 23 x + 15$
42491	Find the Roots (Zeros)	f(x)=x^3+6x^2-3x-18	$f (x) = x^{3} + 6 x^{2} - 3 x - 18$
42492	Find the Roots (Zeros)	f(x)=x^3+7x^2+14x+8	$f (x) = x^{3} + 7 x^{2} + 14 x + 8$
42493	Find the Roots (Zeros)	p(x)=2x^3-x^2-4x+2	$p (x) = 2 x^{3} - x^{2} - 4 x + 2$
42494	Find the Roots (Zeros)	p(x)=x^4-1	$p (x) = x^{4} - 1$
42495	Determine if Proper or Improper	g(x)=(x^3-x^2-12x)/(x^4+x-21)	$g (x) = \frac{x^{3} - x^{2} - 12 x}{x^{4} + x - 21}$
42496	Find the Roots (Zeros)	f(x) = square root of 3csc(x)-2	$f (x) = \sqrt{3} \csc (x) - 2$
42497	Find the Roots (Zeros)	f(x)=(x-5i)(x+5i)	$f (x) = (x - 5 i) (x + 5 i)$
42498	Find the Roots (Zeros)	f(x)=3x^4-19x^3-27x^2+359x-116	$f (x) = 3 x^{4} - 19 x^{3} - 27 x^{2} + 359 x - 116$
42499	Find the Roots (Zeros)	f(x)=4x^4+5x^3+9x^2+10x+2	$f (x) = 4 x^{4} + 5 x^{3} + 9 x^{2} + 10 x + 2$
42500	Find the Roots (Zeros)	f(x)=x^2e^x-16e^x	$f (x) = x^{2} e^{x} - 16 e^{x}$