Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
41801	Find the Behavior (Leading Coefficient Test)	f(x)=-13x^5-4x^4-1	$f (x) = - 13 x^{5} - 4 x^{4} - 1$
41802	Identify the Polar Equation	r=1-2cos(theta)	$r = 1 - 2 \cos (θ)$
41803	Identify the Polar Equation	rsin(theta)=10	$r \sin (θ) = 10$
41804	Find the Roots (Zeros)	x^2e^x-25e^x	$x^{2} e^{x} - 25 e^{x}$
41805	Find the Roots (Zeros)	x^4-256	$x^{4} - 256$
41806	Find the Roots (Zeros)	\|x^2-25\|	$\| x^{2} - 25 \|$
41807	Find the Degree	-6-8i	$- 6 - 8 i$
41808	Find the Domain	f(x) = natural log of 3-x	$f (x) = \ln (3 - x)$
41809	Find the Domain	f(x) = log base 7 of 8x+5	$f (x) = \log_{7} (8 x + 5)$
41810	Find the Other Trig Values in Quadrant I	cos(theta)=5/7	$\cos (θ) = \frac{5}{7}$
41811	Find the Distance Between Two Points	(2,pi/3) , (2,(11pi)/6)	$(2, \frac{π}{3})$ , $(2, \frac{11 π}{6})$
41812	Find the Roots (Zeros)	y=(x+9)(x-9)^2	$y = (x + 9) {(x - 9)}^{2}$
41813	Find the Vertex	f(x)=-x^2-4x+1	$f (x) = - x^{2} - 4 x + 1$
41814	Divide Using Synthetic Division	(x^3-11x+3)/(x-3)	$\frac{x^{3} - 11 x + 3}{x - 3}$
41815	Find the x and y Intercepts	f(x)=4x^3-2x^2+9x+11	$f (x) = 4 x^{3} - 2 x^{2} + 9 x + 11$
41816	Find the Value Using the Unit Circle	tan(-180 degrees )	$\tan (- 180 °)$
41817	Find the Value Using the Unit Circle	cos(90 degrees )	$\cos (90 °)$
41818	Find the Center and Radius	5x^2+5y^2-120x+90y=0	$5 x^{2} + 5 y^{2} - 120 x + 90 y = 0$
41819	Find the Center and Radius	3x^2+3y^2+120x-90y=0	$3 x^{2} + 3 y^{2} + 120 x - 90 y = 0$
41820	Find the Center and Radius	16x^2+16y^2+96x-192y=0	$16 x^{2} + 16 y^{2} + 96 x - 192 y = 0$
41821	Find the Center and Radius	10x^2+10y^2+400x-300y=0	$10 x^{2} + 10 y^{2} + 400 x - 300 y = 0$
41822	Find the Center and Radius	x^2+y^2-9=0	$x^{2} + y^{2} - 9 = 0$
41823	Find the Center and Radius	x^2+y^2-12y+20=0	$x^{2} + y^{2} - 12 y + 20 = 0$
41824	Find the Center and Radius	x^2+y^2-12x+6y+27=0	$x^{2} + y^{2} - 12 x + 6 y + 27 = 0$
41825	Simplify/Condense	log of a+ log of b+ log of c	$\log (a) + \log (b) + \log (c)$
41826	Solve for z	z=2 square root of 2+2 square root of 2i	$z = 2 \sqrt{2} + 2 \sqrt{2 i}$
41827	Solve for t	42000=21000e^(0.045t)	$42000 = 21000 e^{0.045 t}$
41828	Solve for y	e^(y-9)=6	$e^{y - 9} = 6$
41829	Solve for y	8y-3x=1	$8 y - 3 x = 1$
41830	Solve for b	-6*18^(2b-2)-8.4=-76	$- 6 \cdot 18^{2 b - 2} - 8.4 = - 76$
41831	Solve for m	m-3 = square root of 7m-33	$m - 3 = \sqrt{7 m - 33}$
41832	Solve for k	81^(3k)*81^(1-2k)=9	$81^{3 k} \cdot 81^{1 - 2 k} = 9$
41833	Solve for q	square root of 5q-4=4	$\sqrt{5 q - 4} = 4$
41834	Solve for n	6*11^(3n-9)+10=47	$6 \cdot 11^{3 n - 9} + 10 = 47$
41835	Solve for a	1/(2a)+(a-1)/(a^2)=1/a	$\frac{1}{2 a} + \frac{a - 1}{a^{2}} = \frac{1}{a}$
41836	Determine if Odd, Even, or Neither	f(x)=sec(x)	$f (x) = \sec (x)$
41837	Find the Eccentricity	9x^2+4y^2-54x+40y+37=0	$9 x^{2} + 4 y^{2} - 54 x + 40 y + 37 = 0$
41838	Find the Roots (Zeros)	f(x)=x^3-10x^2+44x-69	$f (x) = x^{3} - 10 x^{2} + 44 x - 69$
41839	Find the Trig Value	cos(theta)=24/25 , 270 degrees <theta<360 degrees	$\cos (θ) = \frac{24}{25}$ , $270 ° < θ < 360 °$
41840	Find the Domain and Range	1/(x-4)	$\frac{1}{x - 4}$
41841	Find the Trig Value	tan(theta)=12/5	$\tan (θ) = \frac{12}{5}$
41842	Find the Trig Value	sin(theta)=-1/5 , pi<theta<(3pi)/2 , cos(theta)	$\sin (θ) = - \frac{1}{5}$ , $π < θ < \frac{3 π}{2}$ , $\cos (θ)$
41843	Find the Domain and Range	3^x-3	$3^{x} - 3$
41844	Find the Domain and Range	-3x^2+6x-2	$- 3 x^{2} + 6 x - 2$
41845	Find the Vertex Form	7x^2-y^2-7=9	$7 x^{2} - y^{2} - 7 = 9$
41846	Expand Using Pascal's Triangle	(x-8)^5	${(x - 8)}^{5}$
41847	Expand Using Pascal's Triangle	(6v+s)^5	${(6 v + s)}^{5}$
41848	Expand Using Pascal's Triangle	(1/2x-4y)^5	${(\frac{1}{2} x - 4 y)}^{5}$
41849	Find the Vertex	y=x^2+11x-2	$y = x^{2} + 11 x - 2$
41850	Find the Vertex	y^2-2x+4y-2=0	$y^{2} - 2 x + 4 y - 2 = 0$
41851	Find the Vertex	y^2-2x-18y+69=0	$y^{2} - 2 x - 18 y + 69 = 0$
41852	Find the Vertex	y=3x^2+12x+17	$y = 3 x^{2} + 12 x + 17$
41853	Find the Vertex	x=1/4(y^2+2y+33)	$x = \frac{1}{4} (y^{2} + 2 y + 33)$
41854	Find the Vertex	x=6y^2	$x = 6 y^{2}$
41855	Find the Vertex	x^2-12y-6x+5=0	$x^{2} - 12 y - 6 x + 5 = 0$
41856	Find the Vertex	-1/3(x-3)=(y+5)^2	$- \frac{1}{3} (x - 3) = {(y + 5)}^{2}$
41857	Find the Vertex	x^2+10x-2y+9=0	$x^{2} + 10 x - 2 y + 9 = 0$
41858	Find the Vertex	(y^2)/4-(x^2)/12=1	$\frac{y^{2}}{4} - \frac{x^{2}}{12} = 1$
41859	Find the Center	9x^2+16y^2+54x-32y-47=0	$9 x^{2} + 16 y^{2} + 54 x - 32 y - 47 = 0$
41860	Find the Determinant	[[1,5,-2],[7,4,1],[-3,1,6]]	$[\begin{array}{c} 1 & 5 & - 2 \\ 7 & 4 & 1 \\ - 3 & 1 & 6 \end{array}]$
41861	Write in Standard Form	x^2-4x	$x^{2} - 4 x$
41862	Write in Standard Form	1/(3- square root of -4)	$\frac{1}{3 - \sqrt{- 4}}$
41863	Convert to a Simplified Fraction	square root of 68	$\sqrt{68}$
41864	Find the x and y Intercepts	4(x-3)^2+4y^2=16	$4 {(x - 3)}^{2} + 4 y^{2} = 16$
41865	Transpose	[[1,2],[3,5]]	$[\begin{array}{c} 1 & 2 \\ 3 & 5 \end{array}]$
41866	Find the Degree	cos(theta)=8/15	$\cos (θ) = \frac{8}{15}$
41867	Convert to Logarithmic Form	(1/3)^8=1/6561	${(\frac{1}{3})}^{8} = \frac{1}{6561}$
41868	Find the Difference Quotient	f(x)=5/x	$f (x) = \frac{5}{x}$
41869	Find the Vertex Form	x=2y^2-4y-6	$x = 2 y^{2} - 4 y - 6$
41870	Find the Asymptotes	(x^2-9)/(x+3)	$\frac{x^{2} - 9}{x + 3}$
41871	Find the Asymptotes	x/(x^2-1)	$\frac{x}{x^{2} - 1}$
41872	Find the Asymptotes	(x^2+5x+6)/(x^2+3x+2)	$\frac{x^{2} + 5 x + 6}{x^{2} + 3 x + 2}$
41873	Find the Asymptotes	(6x^2+1)/(2x^2+3x-2)	$\frac{6 x^{2} + 1}{2 x^{2} + 3 x - 2}$
41874	Expand Using De Moivre's Theorem	( square root of 3+i)^5	${(\sqrt{3} + i)}^{5}$
41875	Plot	r=4sin(theta)	$r = 4 \sin (θ)$
41876	Plot	(2,(3pi)/4)	$(2, \frac{3 π}{4})$
41877	Write in Standard Form	4x^2-25y^2=100	$4 x^{2} - 25 y^{2} = 100$
41878	Write in Standard Form	3x^2+35y^2-60x+140y-85=0	$3 x^{2} + 35 y^{2} - 60 x + 140 y - 85 = 0$
41879	Write in Standard Form	16x^2-y^2+64x-2y+67=0	$16 x^{2} - y^{2} + 64 x - 2 y + 67 = 0$
41880	Write in Standard Form	9y^2-16x^2=144	$9 y^{2} - 16 x^{2} = 144$
41881	Write in Standard Form	9x^2-4y^2-18x+45=0	$9 x^{2} - 4 y^{2} - 18 x + 45 = 0$
41882	Write in Standard Form	9x^2+4y^2-72x+16y+124=0	$9 x^{2} + 4 y^{2} - 72 x + 16 y + 124 = 0$
41883	Write in Standard Form	9x^2+25y^2-36x+100y-89=0	$9 x^{2} + 25 y^{2} - 36 x + 100 y - 89 = 0$
41884	Write in Standard Form	4y^2-16y-9x^2-36x-164=0	$4 y^{2} - 16 y - 9 x^{2} - 36 x - 164 = 0$
41885	Write in Standard Form	-9x^2+16y^2+90x+64y-305=0	$- 9 x^{2} + 16 y^{2} + 90 x + 64 y - 305 = 0$
41886	Write in Standard Form	x^2+4y^2-6x+20y-2=0	$x^{2} + 4 y^{2} - 6 x + 20 y - 2 = 0$
41887	Write in Standard Form	x^2+y^2+10y=39	$x^{2} + y^{2} + 10 y = 39$
41888	Write in Standard Form	x^2+9y^2-14x+36y+49=0	$x^{2} + 9 y^{2} - 14 x + 36 y + 49 = 0$
41889	Write in Standard Form	x^2+y^2-4x-6y+8=0	$x^{2} + y^{2} - 4 x - 6 y + 8 = 0$
41890	Write in Standard Form	x^2+y^2-12x+4y-9=0	$x^{2} + y^{2} - 12 x + 4 y - 9 = 0$
41891	Write in Standard Form	x^2-4y^2-4x=0	$x^{2} - 4 y^{2} - 4 x = 0$
41892	Write in Standard Form	y^2-4x+12y+40=0	$y^{2} - 4 x + 12 y + 40 = 0$
41893	Write in Standard Form	y^2+2x+8y+12=0	$y^{2} + 2 x + 8 y + 12 = 0$
41894	Write in Standard Form	-y^2+x+8y-17=0	$- y^{2} + x + 8 y - 17 = 0$
41895	Write in Standard Form	y^2+4y-8x+4=0	$y^{2} + 4 y - 8 x + 4 = 0$
41896	Write in Standard Form	y=3(x-1)(x+6)	$y = 3 (x - 1) (x + 6)$
41897	Factor over the Complex Numbers	2-2 square root of 3i	$2 - 2 \sqrt{3} i$
41898	Convert to Interval Notation	((x+11)(x-9))/(x-1)>=0	$\frac{(x + 11) (x - 9)}{x - 1} \geq 0$
41899	Convert to Interval Notation	(x+2)(x-3)(x+8)>0	$(x + 2) (x - 3) (x + 8) > 0$
41900	Convert to Interval Notation	(x^2-9)/(x^2+x-12)<0	$\frac{x^{2} - 9}{x^{2} + x - 12} < 0$