Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
43801	Find the Domain	log of x^2-8x+15	$\log (x^{2} - 8 x + 15)$
43802	Find the Domain	log of x^2-25	$\log (x^{2} - 25)$
43803	Find the Domain	log base 4 of x^2-4	$\log_{4} (x^{2} - 4)$
43804	Find the Domain	log base 4 of x^2-9	$\log_{4} (x^{2} - 9)$
43805	Find the Domain	log base 6 of 9-3x	$\log_{6} (9 - 3 x)$
43806	Find the Domain	square root of 12-2x	$\sqrt{12 - 2 x}$
43807	Find the Domain	square root of 14-2x	$\sqrt{14 - 2 x}$
43808	Find the Domain	square root of 7x+5	$\sqrt{7 x + 5}$
43809	Find the Domain	square root of 4x-2	$\sqrt{4 x - 2}$
43810	Find the Domain	( square root of x-1)/( square root of x-2)	$\frac{\sqrt{x - 1}}{\sqrt{x - 2}}$
43811	Find the Domain	-x/(4x-25)	$- \frac{x}{4 x - 25}$
43812	Find the Sine Given the Point	(( square root of 5)/5,-(2 square root of 5)/5)	$(\frac{\sqrt{5}}{5}, - \frac{2 \sqrt{5}}{5})$
43813	Find the Sine Given the Point	(( square root of 77)/9,2/9)	$(\frac{\sqrt{77}}{9}, \frac{2}{9})$
43814	Find the Maximum/Minimum Value	y=1/2sin(2x)	$y = \frac{1}{2} \sin (2 x)$
43815	Find the Maximum/Minimum Value	y=4sin(x)	$y = 4 \sin (x)$
43816	Find the Sine Given the Point	(-20,-21)	$t (- 20, - 21)$
43817	Determine if Odd, Even, or Neither	g(x)=x^6-3x	$g (x) = x^{6} - 3 x$
43818	Determine if Odd, Even, or Neither	g(x)=tan(x)	$g (x) = \tan (x)$
43819	Solve Using the Quadratic Formula	3x^2+12x+6=0	$3 x^{2} + 12 x + 6 = 0$
43820	Solve Using the Quadratic Formula	x^2-10x+89=0	$x^{2} - 10 x + 89 = 0$
43821	Find the Eccentricity	9x^2+4y^2-36x+32y-44=0	$9 x^{2} + 4 y^{2} - 36 x + 32 y - 44 = 0$
43822	Find the Eccentricity	4x^2+25y^2+16x-150y+141=0	$4 x^{2} + 25 y^{2} + 16 x - 150 y + 141 = 0$
43823	Find the Eccentricity	12x^2+20y^2-12x+40y-37=0	$12 x^{2} + 20 y^{2} - 12 x + 40 y - 37 = 0$
43824	Determine if Odd, Even, or Neither	f(x)=2x-x^2	$f (x) = 2 x - x^{2}$
43825	Determine if Odd, Even, or Neither	f(x)=5x^2-x	$f (x) = 5 x^{2} - x$
43826	Determine if Odd, Even, or Neither	f(x)=\|x-2\|	$f (x) = \| x - 2 \|$
43827	Find the Eccentricity	x^2+9y^2=81	$x^{2} + 9 y^{2} = 81$
43828	Determine if Odd, Even, or Neither	f(x)=x^4-2x	$f (x) = x^{4} - 2 x$
43829	Determine if Odd, Even, or Neither	f(x)=sin(x)+cos(x)	$f (x) = \sin (x) + \cos (x)$
43830	Determine if Odd, Even, or Neither	f(x)=x^2+2x	$f (x) = x^{2} + 2 x$
43831	Find the Vertex	f(x)=(x-5)^2-1	$f (x) = {(x - 5)}^{2} - 1$
43832	Find the Vertex	f(x)=3x^2+12x+5	$f (x) = 3 x^{2} + 12 x + 5$
43833	Find the Vertex	f(x)=x^2+2x-4	$f (x) = x^{2} + 2 x - 4$
43834	Find the Vertex	f(x)=x^2+3x-4	$f (x) = x^{2} + 3 x - 4$
43835	Find the Vertex	f(x)=5x^2-6x+4	$f (x) = 5 x^{2} - 6 x + 4$
43836	Find the Vertex	f(x)=x^2+10x-9	$f (x) = x^{2} + 10 x - 9$
43837	Find the Vertex	f(x)=x^2+10x	$f (x) = x^{2} + 10 x$
43838	Find Amplitude, Period, and Phase Shift	h(x)=tan(2x+pi)	$h (x) = \tan (2 x + π)$
43839	Find Amplitude, Period, and Phase Shift	g(x)=2/5sin((2x)/5-1/3)	$g (x) = \frac{2}{5} \sin (\frac{2 x}{5} - \frac{1}{3})$
43840	Find Amplitude, Period, and Phase Shift	G(x)=csc(3x-3pi)	$G (x) = \csc (3 x - 3 π)$
43841	Find Amplitude, Period, and Phase Shift	G(x)=5sin(3x-3pi)	$G (x) = 5 \sin (3 x - 3 π)$
43842	Find Amplitude, Period, and Phase Shift	f(x)=9cos(pi/5x+pi)+3	$f (x) = 9 \cos (\frac{π}{5} x + π) + 3$
43843	Find Amplitude, Period, and Phase Shift	f(x)=2sin(pi/3x-pi)+4	$f (x) = 2 \sin (\frac{π}{3} x - π) + 4$
43844	Find the Maximum/Minimum Value	c(h)=(2h^2+5h)/(h^3+8)	$c (h) = \frac{2 h^{2} + 5 h}{h^{3} + 8}$
43845	Find the Maximum/Minimum Value	C(t)=t/(3t^2+1)	$C (t) = \frac{t}{3 t^{2} + 1}$
43846	Find the Maximum/Minimum Value	f(x)=(x-2)^2+5	$f (x) = {(x - 2)}^{2} + 5$
43847	Find the Maximum/Minimum Value	f(x)=-2x^2+8x-3	$f (x) = - 2 x^{2} + 8 x - 3$
43848	Find the Vertex	f(x)=x^2+5x+6	$f (x) = x^{2} + 5 x + 6$
43849	Find the Vertex	f(x)=x^2+4x-3	$f (x) = x^{2} + 4 x - 3$
43850	Find the Vertex	f(x)=x^2-12x+35	$f (x) = x^{2} - 12 x + 35$
43851	Find the Vertex	f(x)=x^2-2	$f (x) = x^{2} - 2$
43852	Find the Vertex	f(x)=x^2+8x+13	$f (x) = x^{2} + 8 x + 13$
43853	Find Amplitude, Period, and Phase Shift	f(x)=-1/5sin(2/3x-pi/2)	$f (x) = - \frac{1}{5} \sin (\frac{2}{3} x - \frac{π}{2})$
43854	Find Amplitude, Period, and Phase Shift	f(x)=3/4sin(2/3x-pi/6)	$f (x) = \frac{3}{4} \sin (\frac{2}{3} x - \frac{π}{6})$
43855	Simplify/Condense	cos(x)+tan(x)sin(x)	$\cos (x) + \tan (x) \sin (x)$
43856	Simplify/Condense	natural log of 12+5 natural log of x-8 natural log of y	$\ln (12) + 5 \ln (x) - 8 \ln (y)$
43857	Simplify/Condense	log base 4 of 10+3 log base 4 of 11+6 log base 4 of 3	$\log_{4} (10) + 3 \log_{4} (11) + 6 \log_{4} (3)$
43858	Simplify/Condense	sin(a)^4-cos(a)^4+cos(a)^2	$\sin^{4} (a) - \cos^{4} (a) + \cos^{2} (a)$
43859	Simplify/Condense	sin(x)(cos(x)cot(x)-sin(x))	$\sin (x (\cos (x) \cot (x) - \sin (x)))$
43860	Simplify/Condense	6 natural log of y	$6 \ln (y)$
43861	Simplify/Condense	9 natural log of x-1/8 natural log of y	$9 \ln (x) - \frac{1}{8} \ln (y)$
43862	Simplify/Condense	cos(theta)^4-sin(theta)^4	$\cos^{4} (θ) - \sin^{4} (θ)$
43863	Simplify/Condense	3 natural log of x- natural log of x+3+2 natural log of y	$3 \ln (x) - \ln (x + 3) + 2 \ln (y)$
43864	Find the Inverse	y=9-x^2	$y = 9 - x^{2}$
43865	Find the Inverse	y=3x+6	$y = 3 x + 6$
43866	Find the Inverse	y=50+2.3(x-60)	$y = 50 + 2.3 (x - 60)$
43867	Find the Inverse	y=6x-7	$y = 6 x - 7$
43868	Find the Points of Intersection	x^2+y^2=49 , (x^2)/4+(y^2)/25=1	$x^{2} + y^{2} = 49$ , $\frac{x^{2}}{4} + \frac{y^{2}}{25} = 1$
43869	Find the Points of Intersection	x^2+y^2=64 , (x^2)/16+(y^2)/9=1	$x^{2} + y^{2} = 64$ , $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$
43870	Find the Inverse	x=y^2-4y	$x = y^{2} - 4 y$
43871	Find the Inverse	y=(x-6)^2	$y = {(x - 6)}^{2}$
43872	Simplify/Condense	(cos(x))/(sec(x)-tan(x))	$\frac{\cos (x)}{\sec (x) - \tan (x)}$
43873	Use the Rational Roots Test to Find All Possible Roots	f(x)=2x^3-4x^2-38x+76	$f (x) = 2 x^{3} - 4 x^{2} - 38 x + 76$
43874	Find the Inverse	[[-5,9],[1,9]]	$[\begin{array}{c} - 5 & 9 \\ 1 & 9 \end{array}]$
43875	Find the Inverse	[[8,4],[12,6]]	$[\begin{array}{c} 8 & 4 \\ 12 & 6 \end{array}]$
43876	Find the Inverse	[[-3,-7],[2,5]]	$[\begin{array}{c} - 3 & - 7 \\ 2 & 5 \end{array}]$
43877	Find the Inverse	[[4,1],[1,1]]	$[\begin{array}{c} 4 & 1 \\ 1 & 1 \end{array}]$
43878	Find the Inverse	[[3,-2],[1,2]]	$[\begin{array}{c} 3 & - 2 \\ 1 & 2 \end{array}]$
43879	Find the Inverse	[[2,-2],[7,9]]	$[\begin{array}{c} 2 & - 2 \\ 7 & 9 \end{array}]$
43880	Find the Inverse	[[2,3,-1],[-1,0,4],[0,1,1]]	$[\begin{array}{c} 2 & 3 & - 1 \\ - 1 & 0 & 4 \\ 0 & 1 & 1 \end{array}]$
43881	Find the Cosine Given the Point	(( square root of 5)/5,-(2 square root of 5)/5)	$(\frac{\sqrt{5}}{5}, - \frac{2 \sqrt{5}}{5})$
43882	Find the Cosine Given the Point	(2/5,-( square root of 21)/5)	$(\frac{2}{5}, - \frac{\sqrt{21}}{5})$
43883	Find the Cosine Given the Point	(21/29,-20/29)	$(\frac{21}{29}, - \frac{20}{29})$
43884	Factor over the Complex Numbers	64+64 square root of 3i	$64 + 64 \sqrt{3} i$
43885	Factor over the Complex Numbers	cos(arcsin(x)-arctan(y))	$\cos (\arcsin (x) - \arctan (y))$
43886	Factor over the Complex Numbers	-8-8 square root of 3i	$- 8 - 8 \sqrt{3 i}$
43887	Factor over the Complex Numbers	x^4-81	$x^{4} - 81$
43888	Factor over the Complex Numbers	x^3-27	$x^{3} - 27$
43889	Factor over the Complex Numbers	3i	$3 i$
43890	Factor over the Complex Numbers	1+ square root of 3i	$1 + \sqrt{3} i$
43891	Convert to Interval Notation	(4x-5)/(x+2)<=3	$\frac{4 x - 5}{x + 2} \leq 3$
43892	Convert to Interval Notation	(4x-3)/(x+4)<=3	$\frac{4 x - 3}{x + 4} \leq 3$
43893	Convert to Interval Notation	(4x-4)/(x+2)<=3	$\frac{4 x - 4}{x + 2} \leq 3$
43894	Convert to Interval Notation	(8x-3)/(5x-3)<=2	$\frac{8 x - 3}{5 x - 3} \leq 2$
43895	Convert to Interval Notation	(6x-2)/(x+2)<=5	$\frac{6 x - 2}{x + 2} \leq 5$
43896	Convert to Interval Notation	( square root of x^2-1)/(x+1)>=0	$\frac{\sqrt{x^{2} - 1}}{x + 1} \geq 0$
43897	Convert to Interval Notation	((x-7)(x+7))/x<=0	$\frac{(x - 7) (x + 7)}{x} \leq 0$
43898	Convert to Interval Notation	(x+4)(x-3)(x-5)<=0	$(x + 4) (x - 3) (x - 5) \leq 0$
43899	Convert to Interval Notation	(x^2+x-12)/(x^2-4x+4)>0	$\frac{x^{2} + x - 12}{x^{2} - 4 x + 4} > 0$
43900	Convert to Interval Notation	(x-3)/(x-6)>0	$\frac{x - 3}{x - 6} > 0$