Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
43001	Write in Standard Form	cube root of i	$\sqrt[3]{i}$
43002	Write in Standard Form	1+i square root of 3	$1 + i \sqrt{3}$
43003	Convert to a Simplified Fraction	135 degrees	$135 °$
43004	Combine	sin(pi/3+theta)-cos(pi/6+theta)	$\sin (\frac{π}{3} + θ) - \cos (\frac{π}{6} + θ)$
43005	Combine	cos(2x)+sin(x)	$\cos (2 x) + \sin (x)$
43006	Convert to a Simplified Fraction	square root of 125	$\sqrt{125}$
43007	Convert to a Simplified Fraction	square root of 116	$\sqrt{116}$
43008	Convert to a Simplified Fraction	square root of 106	$\sqrt{106}$
43009	Convert to a Simplified Fraction	square root of 55	$\sqrt{55}$
43010	Convert to a Simplified Fraction	square root of 35	$\sqrt{35}$
43011	Combine	(sin(theta))/(cos(theta))+(cos(theta))/(sin(theta))	$\frac{\sin (θ)}{\cos (θ)} + \frac{\cos (θ)}{\sin (θ)}$
43012	Solve by Completing the Square	4x^2-8x-8=0	$4 x^{2} - 8 x - 8 = 0$
43013	Find the Vertex	f(x)=5x^2-2	$f (x) = 5 x^{2} - 2$
43014	Identify the Conic	16x^2-24xy+9y^2-30x-40y=0	$16 x^{2} - 24 x y + 9 y^{2} - 30 x - 40 y = 0$
43015	Identify the Conic	4x^2+9y^2-8x-32=0	$4 x^{2} + 9 y^{2} - 8 x - 32 = 0$
43016	Identify the Conic	4x^2+7y^2+32x-56y+148=0	$4 x^{2} + 7 y^{2} + 32 x - 56 y + 148 = 0$
43017	Identify the Conic	4x^2-5xy+16y^2-32=0	$4 x^{2} - 5 x y + 16 y^{2} - 32 = 0$
43018	Identify the Conic	4y^2+12x^2=24	$4 y^{2} + 12 x^{2} = 24$
43019	Identify the Conic	x^2+y^2=2y	$x^{2} + y^{2} = 2 y$
43020	Identify the Conic	9y^2+4x^2-108y+24x=-144	$9 y^{2} + 4 x^{2} - 108 y + 24 x = - 144$
43021	Find the Expanded Form	(x+0.09)^2+(y-6)^2=1	${(x + 0.09)}^{2} + {(y - 6)}^{2} = 1$
43022	Find the Derivative - d/d@VAR	f(x)=5x^18	$f (x) = 5 x^{18}$
43023	Find the Derivative - d/d@VAR	f(x)=(4x-3)/(3x+1)	$f (x) = \frac{4 x - 3}{3 x + 1}$
43024	Solve the Triangle	tri{12}{}{}{}{9}{90}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = & 12 \\ c = \\ a = & 9 \end{matrix} & \begin{matrix} A = \\ B = \\ C = & 90 \end{matrix} \end{matrix}$
43025	Find the Roots/Zeros Using the Rational Roots Test	f(x)=x^3+3x^2-219x-221	$f (x) = x^{3} + 3 x^{2} - 219 x - 221$
43026	Split Using Partial Fraction Decomposition	(x-1)/((x-5)(x-3))	$\frac{x - 1}{(x - 5) (x - 3)}$
43027	Split Using Partial Fraction Decomposition	(7x+197)/((x-4)^2(x+5))	$\frac{7 x + 197}{{(x - 4)}^{2} (x + 5)}$
43028	Split Using Partial Fraction Decomposition	(6x-11)/((x-1)^2)	$\frac{6 x - 11}{{(x - 1)}^{2}}$
43029	Split Using Partial Fraction Decomposition	(8x+4)/((x+4)(4x-1))	$\frac{8 x + 4}{(x + 4) (4 x - 1)}$
43030	Split Using Partial Fraction Decomposition	(8x^3+13x)/((x^2+2)^2)	$\frac{8 x^{3} + 13 x}{{(x^{2} + 2)}^{2}}$
43031	Solve by Substitution	5x-2y=2.257x-4y=3	$5 x - 2 y = 2.257 x - 4 y = 3$
43032	Solve by Substitution	4x^2+9y^2=72 , 4x-3y^2=0	$4 x^{2} + 9 y^{2} = 72$ , $4 x - 3 y^{2} = 0$
43033	Solve by Substitution	2x^2+y^2=17 , 3x^2-2y^2=-6	$2 x^{2} + y^{2} = 17$ , $3 x^{2} - 2 y^{2} = - 6$
43034	Solve by Substitution	0.5x-4y=9x-0.5y=3	$0.5 x - 4 y = 9 x - 0.5 y = 3$
43035	Solve by Substitution	x^2-y^2+x+8y-28=6x^2-y^2+41x+8y+52=0	$x^{2} - y^{2} + x + 8 y - 28 = 6 x^{2} - y^{2} + 41 x + 8 y + 52 = 0$
43036	Solve by Substitution	x-0.2y=1-10x+2y=5	$x - 0.2 y = 1 - 10 x + 2 y = 5$
43037	Split Using Partial Fraction Decomposition	1/((2x+1)(x+2))	$\frac{1}{(2 x + 1) (x + 2)}$
43038	Split Using Partial Fraction Decomposition	(3x^2+7x-10)/(x^3+2x^2-4x-8)	$\frac{3 x^{2} + 7 x - 10}{x^{3} + 2 x^{2} - 4 x - 8}$
43039	Split Using Partial Fraction Decomposition	(3x+50)/((x-9)(x+2))	$\frac{3 x + 50}{(x - 9) (x + 2)}$
43040	Split Using Partial Fraction Decomposition	(5x^2-18x+1)/(x^3-x^2-8x+12)	$\frac{5 x^{2} - 18 x + 1}{x^{3} - x^{2} - 8 x + 12}$
43041	Find the Difference Quotient	f(x)=4x-9	$f (x) = 4 x - 9$
43042	Find the Difference Quotient	f(x)=x^2-7	$f (x) = x^{2} - 7$
43043	Find the Asymptotes	natural log of x	$\ln (x)$
43044	Find the Vertex Form	y=-4x^2-72x-315	$y = - 4 x^{2} - 72 x - 315$
43045	Find the Vertex Form	-x^2+10x+y-21=0	$- x^{2} + 10 x + y - 21 = 0$
43046	Find the Vertex Form	x=y^2-4y+7	$x = y^{2} - 4 y + 7$
43047	Find the Asymptotes	(x^4-81)/(x^2-3x)	$\frac{x^{4} - 81}{x^{2} - 3 x}$
43048	Find the Asymptotes	(x^2)/(x^2-25)	$\frac{x^{2}}{x^{2} - 25}$
43049	Find the Asymptotes	(x^2+x-2)/(x^2-3x-4)	$\frac{x^{2} + x - 2}{x^{2} - 3 x - 4}$
43050	Find the Asymptotes	(x^2+x-72)/(x^2-x-56)	$\frac{x^{2} + x - 72}{x^{2} - x - 56}$
43051	Find the Asymptotes	1/(x+3)	$\frac{1}{x + 3}$
43052	Find the Asymptotes	(-4x^2-8x+5)/(2x+1)	$\frac{- 4 x^{2} - 8 x + 5}{2 x + 1}$
43053	Find the Slope and y-intercept	4x-11y=32	$4 x - 11 y = 32$
43054	Find the Slope and y-intercept	3x+2y=5	$3 x + 2 y = 5$
43055	Find the Sum of the Infinite Geometric Series	9 , -6 , 4 , -8/3	$9$ , $- 6$ , $4$ , $- \frac{8}{3}$
43056	Find the Sum of the Infinite Geometric Series	1 , 1/8 , 1/64 , 1/512	$1$ , $\frac{1}{8}$ , $\frac{1}{64}$ , $\frac{1}{512}$
43057	Expand the Trigonometric Expression	cot(90 degrees -theta)	$\cot (90 ° - θ)$
43058	Expand the Trigonometric Expression	sin(4theta)cos(2theta)	$\sin (4 θ) \cos (2 θ)$
43059	Expand the Trigonometric Expression	sin(theta/2)	$\sin (\frac{θ}{2})$
43060	Determine if Odd, Even, or Neither	y=sec(x)	$y = \sec (x)$
43061	Find the Slope of a Perpendicular Line	y=5x+4	$y = 5 x + 4$
43062	Determine if Odd, Even, or Neither	y=(sec(x))/x	$y = \frac{\sec (x)}{x}$
43063	Evaluate the Derivative at x=11	f(x)=-5/x x=11	$f (x) = - \frac{5}{x}$ $x = 11$
43064	Find the Degree	rst+r^2s^2+r^3s^2	$r s t + r^{2} s^{2} + r^{3} s^{2}$
43065	Convert to Radical Form	64^(1/4)	$64^{\frac{1}{4}}$
43066	Convert to Radical Form	7e^((5pi)/6i)	$7 e^{\frac{5 π}{6} i}$
43067	Convert to Radical Form	i^(1/4)	$i^{\frac{1}{4}}$
43068	Plot	(2,pi/6)	$(2, \frac{π}{6})$
43069	Plot	theta=(11pi)/6	$θ = \frac{11 π}{6}$
43070	Solve for a	(9/4)^a=81/16	${(\frac{9}{4})}^{a} = \frac{81}{16}$
43071	Solve for b	(4pi)/3=(2pi)/b	$\frac{4 π}{3} = \frac{2 π}{b}$
43072	Solve for b	(2pi)/b=5	$\frac{2 π}{b} = 5$
43073	Solve for b	1/4=b^-2	$\frac{1}{4} = b^{- 2}$
43074	Solve for p	15/p+(7p-9)/(p+3)=7	$\frac{15}{p} + \frac{(7 p - 9)}{p + 3} = 7$
43075	Solve for p	4p=8	$4 p = 8$
43076	Solve for P	P(3)=1800e^(0.11(3))	$P (3) = 1800 e^{0.11 (3)}$
43077	Solve for r	rsin(theta)=4	$r \sin (θ) = 4$
43078	Solve for r	12^r=13	$12^{r} = 13$
43079	Solve for r	r=8sin(theta)	$r = 8 \sin (θ)$
43080	Solve for r	S=a/(1-r)	$S = \frac{a}{1 - r}$
43081	Solve for r	r=4	$r = 4$
43082	Solve for r	r=8cos(theta)	$r = 8 \cos (θ)$
43083	Solve for t	28.3=23.1e^(0.0152t)	$28.3 = 23.1 e^{0.0152 t}$
43084	Solve for m	2m^2-5m-25=0	$2 m^{2} - 5 m - 25 = 0$
43085	Solve for k	k=( natural log of 0.54/0.60)/30	$k = \frac{\ln (\frac{0.54}{0.6})}{30}$
43086	Solve for m	F=G(mM)/(r^2)	$F = G \frac{m M}{r^{2}}$
43087	Solve for n	2 log base 12 of n-3=6	$2 \log_{12} (n - 3) = 6$
43088	Solve for n	square root of 3n=n	$\sqrt{3 n} = n$
43089	Solve for n	122=6+(n-1)*4	$122 = 6 + (n - 1) \cdot 4$
43090	Solve for n	1+ square root of 6-2n = square root of 7-2n	$1 + \sqrt{6 - 2 n} = \sqrt{7 - 2 n}$
43091	Solve for B	sin(B)=53(sin(29.2 degrees ))/27	$\sin (B) = 53 \frac{\sin (29.2 °)}{27}$
43092	Solve for b	2pi=(2pi)/b	$2 π = \frac{2 π}{b}$
43093	Solve for b2	a=1/2h(b_1+b_2)	$a = \frac{1}{2} h (b_{1} + b_{2})$
43094	Solve for C	cos(C)=0.7538	$\cos (C) = 0.7538$
43095	Solve for y	y=f(-2)	$y = f (- 2)$
43096	Solve for y	y1/2-7y1/4+12=0	$y \frac{1}{2} - 7 y \frac{1}{4} + 12 = 0$
43097	Solve for y	y=cos(arcsin(1/5))	$y = \cos (\arcsin (\frac{1}{5}))$
43098	Solve for y	-7/(y+8)+6/(7-y)=((-8)y-9)/(y^2+y-56)	$\frac{- 7}{y + 8} + \frac{6}{7 - y} = \frac{(- 8) y - 9}{y^{2} + y - 56}$
43099	Solve for t	t=6pi	$t = 6 π$
43100	Solve for t	t^2+3t-1=0	$t^{2} + 3 t - 1 = 0$