Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
42801	Find the Sine Given the Point	(-24/25,-7/25)	$(- \frac{24}{25}, - \frac{7}{25})$
42802	Find the Sine Given the Point	(-12/13,5/13)	$(- \frac{12}{13}, \frac{5}{13})$
42803	Expand Using De Moivre's Theorem	(1-i)^8	${(1 - i)}^{8}$
42804	Expand Using De Moivre's Theorem	(5+5i)^3	${(5 + 5 i)}^{3}$
42805	Expand Using De Moivre's Theorem	(5+5i)^5	${(5 + 5 i)}^{5}$
42806	Expand Using De Moivre's Theorem	(2(cos(pi/3)+isin(pi/3)))^12	${(2 (\cos (\frac{π}{3}) + i \sin (\frac{π}{3})))}^{12}$
42807	Expand Using De Moivre's Theorem	( square root of 3(cos((5pi)/12)+isin((5pi)/12)))^4	${(\sqrt{3} (\cos (\frac{5 π}{12}) + i \sin (\frac{5 π}{12})))}^{4}$
42808	Expand Using De Moivre's Theorem	( square root of 2(cos(20 degrees )+isin(20 degrees )))^6	${(\sqrt{2} (\cos (20 °) + i \sin (20 °)))}^{6}$
42809	Find the Dimensions	[[2.3,3.6],[1.4,5]]	$[\begin{array}{c} 2.3 & 3.6 \\ 1.4 & 5 \end{array}]$
42810	Determine if Odd, Even, or Neither	square root of x	$\sqrt{x}$
42811	Determine if Odd, Even, or Neither	cube root of x	$\sqrt[3]{x}$
42812	Find the Inverse	x+8	$x + 8$
42813	Find the Inverse	g^-1(x)	$g^{- 1} (x)$
42814	Find the Axis of Symmetry	f(x)=x^2-6x-7	$f (x) = x^{2} - 6 x - 7$
42815	Solve the Matrix Equation	-1/3x-[[3,6,2],[9,1,7]]=[[-8,3,-1],[12,-4,-3]]	$- \frac{1}{3} x - [\begin{array}{c} 3 & 6 & 2 \\ 9 & 1 & 7 \end{array}] = [\begin{array}{c} - 8 & 3 & - 1 \\ 12 & - 4 & - 3 \end{array}]$
42816	Find the Center	((x+3)^2)/16+((y-5)^2)/25=1	$\frac{{(x + 3)}^{2}}{16} + \frac{{(y - 5)}^{2}}{25} = 1$
42817	Find the Center	((x+3)^2)/25+((y-1)^2)/16=1	$\frac{{(x + 3)}^{2}}{25} + \frac{{(y - 1)}^{2}}{16} = 1$
42818	Find the Center	((x+4)^2)/16+((y-1)^2)/36=1	$\frac{{(x + 4)}^{2}}{16} + \frac{{(y - 1)}^{2}}{36} = 1$
42819	Find the Center	-((x+5)^2)/(9^2)+((y-7)^2)/(13^2)=1	$- \frac{{(x + 5)}^{2}}{9^{2}} + \frac{{(y - 7)}^{2}}{13^{2}} = 1$
42820	Find the Center	x^2-4y^2-4x+8y-4=0	$x^{2} - 4 y^{2} - 4 x + 8 y - 4 = 0$
42821	Find the Center	x^2+9y^2+16x-54y+136=0	$x^{2} + 9 y^{2} + 16 x - 54 y + 136 = 0$
42822	Find the Center	9x^2-y^2=324	$9 x^{2} - y^{2} = 324$
42823	Find the Center	x^2+4x+4y^2-8y+4=0	$x^{2} + 4 x + 4 y^{2} - 8 y + 4 = 0$
42824	Find the Reciprocal	(3pi)/4	$\frac{3 π}{4}$
42825	Find the Reciprocal	(5pi)/4	$\frac{5 π}{4}$
42826	Find the Inverse	[[-7,33],[4,-19]]	$[\begin{array}{c} - 7 & 33 \\ 4 & - 19 \end{array}]$
42827	Find the Inverse	[[-2,6],[-1,3]]	$[\begin{array}{c} - 2 & 6 \\ - 1 & 3 \end{array}]$
42828	Find the Cosine Given the Point	(-12/13,5/13)	$(- \frac{12}{13}, \frac{5}{13})$
42829	Factor over the Complex Numbers	2x^4-13x^3-16x^2+243x-116	$2 x^{4} - 13 x^{3} - 16 x^{2} + 243 x - 116$
42830	Factor over the Complex Numbers	square root of 3-i	$\sqrt{3} - i$
42831	Convert to Interval Notation	(x+5)(x+3)(x-7)>0	$(x + 5) (x + 3) (x - 7) > 0$
42832	Convert to Interval Notation	(x-3)/(x+3)<2	$\frac{x - 3}{x + 3} < 2$
42833	Convert to Interval Notation	\|2x+5\|>=9	$\| 2 x + 5 \| \geq 9$
42834	Convert to Interval Notation	(x-4)(x-5)(x-7)<=0	$(x - 4) (x - 5) (x - 7) \leq 0$
42835	Convert to Interval Notation	x^3<2x^2+3x	$x^{3} < 2 x^{2} + 3 x$
42836	Convert to Interval Notation	x^2+2x>=8	$x^{2} + 2 x \geq 8$
42837	Convert to Interval Notation	6x<36/(x+5)	$6 x < \frac{36}{x + 5}$
42838	Convert to Interval Notation	4x^3>-12x^2	$4 x^{3} > - 12 x^{2}$
42839	Convert to Interval Notation	\|x-8.2\|-1.5<=0	$\| x - 8.2 \| - 1.5 \leq 0$
42840	Solve the System of @WORD	(3x-1)/4-(x-5)/5>-2	$\frac{3 x - 1}{4} - \frac{x - 5}{5} > - 2$
42841	Solve the System of @WORD	\|2x-1\|-5<=6	$\| 2 x - 1 \| - 5 \leq 6$
42842	Solve the System of @WORD	0<=theta<2pi	$0 \leq θ < 2 π$
42843	Convert to Interval Notation	x-9<-15	$x - 9 < - 15$
42844	Convert to Interval Notation	y^2(5y+3)(y-6)>0	$y^{2} (5 y + 3) (y - 6) > 0$
42845	Convert to Interval Notation	x^4>16x^2	$x^{4} > 16 x^{2}$
42846	Convert to Interval Notation	x^3-2x^2-80x<0	$x^{3} - 2 x^{2} - 80 x < 0$
42847	Convert to Interval Notation	x^3-34x>0	$x^{3} - 34 x > 0$
42848	Convert to Interval Notation	x^3-3x^2-54x<0	$x^{3} - 3 x^{2} - 54 x < 0$
42849	Convert to Interval Notation	x^3-8x^2<=-15x	$x^{3} - 8 x^{2} \leq - 15 x$
42850	Solve the System of @WORD	x-6/x<=-1	$x - \frac{6}{x} \leq - 1$
42851	Solve the System of @WORD	5<3x-1<14	$5 < 3 x - 1 < 14$
42852	Find the Inverse	[[0,-5],[-6,-6]]	$[\begin{array}{c} 0 & - 5 \\ - 6 & - 6 \end{array}]$
42853	Find the Inverse	[[0,-1],[-1,0]]	$[\begin{array}{c} 0 & - 1 \\ - 1 & 0 \end{array}]$
42854	Identify the Zeros and Their Multiplicities	f(x)=2x^4-5x^3-20x^2+115x-52	$f (x) = 2 x^{4} - 5 x^{3} - 20 x^{2} + 115 x - 52$
42855	Identify the Zeros and Their Multiplicities	y=x^2-144	$y = x^{2} - 144$
42856	Identify the Zeros and Their Multiplicities	x^3-x^2-17x-15	$x^{3} - x^{2} - 17 x - 15$
42857	Find the Tangent Given the Point	(-60/61,-11/61)	$(- \frac{60}{61}, - \frac{11}{61})$
42858	Find the Tangent Given the Point	((3 square root of 13)/13,-(2 square root of 13)/13)	$(\frac{3 \sqrt{13}}{13}, - \frac{2 \sqrt{13}}{13})$
42859	Find the Domain	4x-2	$4 x - 2$
42860	Find the Domain	(x+8)/(4x^2-5x+1)	$\frac{x + 8}{4 x^{2} - 5 x + 1}$
42861	Find the Domain	log base 2 of 4x-3	$\log_{2} (4 x - 3)$
42862	Find the Domain	square root of 12-3x	$\sqrt{12 - 3 x}$
42863	Find the Domain	log base 5 of x^2-1	$\log_{5} (x^{2} - 1)$
42864	Find the Domain	log base 7 of 8x+5	$\log_{7} (8 x + 5)$
42865	Find the Domain	square root of 1-7x	$\sqrt{1 - 7 x}$
42866	Find the Domain	2/( square root of 5x-3)+1/(x^2-9)	$\frac{2}{\sqrt{5 x - 3}} + \frac{1}{x^{2} - 9}$
42867	Find the Domain	x/(x^3-125)	$\frac{x}{x^{3} - 125}$
42868	Find the Domain	x/(x^3-216)	$\frac{x}{x^{3} - 216}$
42869	Determine if Proper or Improper	g(x)=(x^3-2x-5)/(x^2+5x-7)	$g (x) = \frac{x^{3} - 2 x - 5}{x^{2} + 5 x - 7}$
42870	Find the Roots (Zeros)	F(x)=x^3+6x^2-2x-12	$F (x) = x^{3} + 6 x^{2} - 2 x - 12$
42871	Find the Roots (Zeros)	f(x)=x^3+5x^2-2x-10	$f (x) = x^{3} + 5 x^{2} - 2 x - 10$
42872	Find the Roots (Zeros)	f(x)=x^3+3x^2-219x-221	$f (x) = x^{3} + 3 x^{2} - 219 x - 221$
42873	Find the Roots (Zeros)	f(x)=7x^4-x^3-21x^2+367x-52	$f (x) = 7 x^{4} - x^{3} - 21 x^{2} + 367 x - 52$
42874	Find the Roots (Zeros)	f(x)=sin(2x)+sin(x)	$f (x) = \sin (2 x) + \sin (x)$
42875	Find the Roots (Zeros)	f(x)=10x^3-33x^2+8x+3	$f (x) = 10 x^{3} - 33 x^{2} + 8 x + 3$
42876	Find the Roots (Zeros)	f(x)=csc(x)+ square root of 2	$f (x) = \csc (x) + \sqrt{2}$
42877	Find the Perfect Square Trinomial	y^2-4y	$y^{2} - 4 y$
42878	Find the Roots (Zeros)	g(x)=10x^3-33x^2+8x+3	$g (x) = 10 x^{3} - 33 x^{2} + 8 x + 3$
42879	Find the Roots (Zeros)	f(x)=x^4-7x^3+8x^2+28x-48	$f (x) = x^{4} - 7 x^{3} + 8 x^{2} + 28 x - 48$
42880	Find the Roots (Zeros)	g(x)=2x^3-3x^2-32x-15	$g (x) = 2 x^{3} - 3 x^{2} - 32 x - 15$
42881	Find the Roots (Zeros)	f(x)=x^4-32x^2-144	$f (x) = x^{4} - 32 x^{2} - 144$
42882	Find the Roots (Zeros)	h(x)=2x^3-3x^2-32x-15	$h (x) = 2 x^{3} - 3 x^{2} - 32 x - 15$
42883	Find the Roots (Zeros)	f(x)=x^4+40x^2-441	$f (x) = x^{4} + 40 x^{2} - 441$
42884	Find the Roots (Zeros)	f(x)=x^4+2x^3+46x^2+98x-147	$f (x) = x^{4} + 2 x^{3} + 46 x^{2} + 98 x - 147$
42885	Find the Roots (Zeros)	f(x)=x^4-10x^2+9	$f (x) = x^{4} - 10 x^{2} + 9$
42886	Find the Roots (Zeros)	f(x)=x^4+6x^3-11x^2-24x+28	$f (x) = x^{4} + 6 x^{3} - 11 x^{2} - 24 x + 28$
42887	Find the Roots (Zeros)	p(x)=x^4-4x^3+3x^2	$p (x) = x^{4} - 4 x^{3} + 3 x^{2}$
42888	Find the Roots (Zeros)	p(x)=x^4-x^3-2x-4	$p (x) = x^{4} - x^{3} - 2 x - 4$
42889	Find the Roots (Zeros)	r(x)=(xe^x+2e^x)/((1+e^(2x))^3)	$r (x) = \frac{x e^{x} + 2 e^{x}}{{(1 + e^{2 x})}^{3}}$
42890	Find the Roots (Zeros)	f(x)=x^3-5x^2+25x-125	$f (x) = x^{3} - 5 x^{2} + 25 x - 125$
42891	Find the Roots (Zeros)	f(x)=x^3-10x^2+9x-24	$f (x) = x^{3} - 10 x^{2} + 9 x - 24$
42892	Find the Roots (Zeros)	f(x)=x^3-25x	$f (x) = x^{3} - 25 x$
42893	Determine if Odd, Even, or Neither	g(x)=-6x^5+7x^3	$g (x) = - 6 x^{5} + 7 x^{3}$
42894	Solve Using the Quadratic Formula	9x^2+24x+32=0	$9 x^{2} + 24 x + 32 = 0$
42895	Find the Eccentricity	(x^2)/64+(y^2)/81=1	$\frac{x^{2}}{64} + \frac{y^{2}}{81} = 1$
42896	Find the Eccentricity	6x^2-12x+54y^2+108y-426=0	$6 x^{2} - 12 x + 54 y^{2} + 108 y - 426 = 0$
42897	Determine if Odd, Even, or Neither	f(x)=4x-4	$f (x) = 4 x - 4$
42898	Find the Trig Value	tan(theta)=-3/5	$\tan (θ) = - \frac{3}{5}$
42899	Find the Trig Value	tan(theta)=-2/7	$\tan (θ) = - \frac{2}{7}$
42900	Find the Trig Value	sin(15 degrees )	$\sin (15 °)$