Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
41701	Identify the Polar Equation	r^2=9sin(2theta)	$r^{2} = 9 \sin (2 θ)$
41702	Identify the Polar Equation	theta=pi/2	$θ = \frac{π}{2}$
41703	Solve by Substitution	y+x^2=9xy+9x=81	$y + x^{2} = 9 x y + 9 x = 81$
41704	Solve by Substitution	y^2=x^2-643y=x-8	$y^{2} = x^{2} - 643 y = x - 8$
41705	Solve by Substitution	-2x+3y=1.2-3x-6y=1.8	$- 2 x + 3 y = 1.2 - 3 x - 6 y = 1.8$
41706	Split Using Partial Fraction Decomposition	(4x-88)/((x-4)^2(x^2+2))	$\frac{4 x - 88}{{(x - 4)}^{2} (x^{2} + 2)}$
41707	Find the Domain	f(x) = log base 4 of 8-3x	$f (x) = \log_{4} (8 - 3 x)$
41708	Find the Domain	f(x)=(x-5)/(x^2-25)	$f (x) = \frac{x - 5}{x^{2} - 25}$
41709	Find the Roots (Zeros)	4x^3-11x^2-54x+45=0	$4 x^{3} - 11 x^{2} - 54 x + 45 = 0$
41710	Find the Domain	log of x-4	$\log (x - 4)$
41711	Solve for b	(8pi)/3=(2pi)/b	$\frac{8 π}{3} = \frac{2 π}{b}$
41712	Solve for t	0.5*10^(8t)=73	$0.5 \cdot 10^{8 t} = 73$
41713	Solve for r	2r^2-3r-77=0	$2 r^{2} - 3 r - 77 = 0$
41714	Solve for B	cos(B)=0.3125	$\cos (B) = 0.3125$
41715	Solve for b	24^2+b^2=25^2	$24^{2} + b^{2} = 25^{2}$
41716	Solve for y	7y-4=15+3y	$7 y - 4 = 15 + 3 y$
41717	Solve for v	v=-9i+12j	$v = - 9 i + 12 j$
41718	Solve for w	w^3-9w=0	$w^{3} - 9 w = 0$
41719	Solve for z	8z^3-125=0	$8 z^{3} - 125 = 0$
41720	Simplify/Condense	sin(x)^3+sin(x)cos(x)^2	$\sin^{3} (x) + \sin (x) \cos^{2} (x)$
41721	Simplify/Condense	8 natural log of x-1/4 natural log of y	$8 \ln (x) - \frac{1}{4} \ln (y)$
41722	Find the Inverse	y=5^x	$y = 5^{x}$
41723	Find the Inverse	y=pi/2+sin(x)	$y = \frac{π}{2} + \sin (x)$
41724	Find the Center and Radius	(x+4)^2+(y-3)^2=7	${(x + 4)}^{2} + {(y - 3)}^{2} = 7$
41725	Find the Center and Radius	(x+3)^2+(y-5)^2=9	${(x + 3)}^{2} + {(y - 5)}^{2} = 9$
41726	Find the Center and Radius	x^2+y^2-2x-8y+13=0	$x^{2} + y^{2} - 2 x - 8 y + 13 = 0$
41727	Find the Center and Radius	x^2+y^2-6x+14y+33=0	$x^{2} + y^{2} - 6 x + 14 y + 33 = 0$
41728	Find the Center and Radius	x^2+y^2-10x-8y+29=0	$x^{2} + y^{2} - 10 x - 8 y + 29 = 0$
41729	Find the Center and Radius	x^2+y^2+12x+12y=-47	$x^{2} + y^{2} + 12 x + 12 y = - 47$
41730	Determine if Odd, Even, or Neither	g(x)=cos(x)	$g (x) = \cos (x)$
41731	Find the Value Using the Unit Circle	-pi/4	$- \frac{π}{4}$
41732	Find the Value Using the Unit Circle	tan(-105 degrees )	$\tan (- 105 °)$
41733	Expand the Trigonometric Expression	sin(pi-theta)	$\sin (π - θ)$
41734	Find the Vertex	x^2+14x+3y+37=0	$x^{2} + 14 x + 3 y + 37 = 0$
41735	Find the Vertex	x^2+12x+2y+42=0	$x^{2} + 12 x + 2 y + 42 = 0$
41736	Find the Vertex	4x^2-20x+24y+61=0	$4 x^{2} - 20 x + 24 y + 61 = 0$
41737	Find the Vertex	y^2+4y-x+1=0	$y^{2} + 4 y - x + 1 = 0$
41738	Find the Vertex	x^2+8y+2x-23=0	$x^{2} + 8 y + 2 x - 23 = 0$
41739	Find the Vertex	x^2=44y	$x^{2} = 44 y$
41740	Find the Vertex	y^2-8x+2y+17=0	$y^{2} - 8 x + 2 y + 17 = 0$
41741	Expand Using Pascal's Triangle	(x-6)^5	${(x - 6)}^{5}$
41742	Find the Center	((x-5)^2)/25+((y+8)^2)/81=1	$\frac{{(x - 5)}^{2}}{25} + \frac{{(y + 8)}^{2}}{81} = 1$
41743	Find the Center	4x^2-y^2+24x+4y+28=0	$4 x^{2} - y^{2} + 24 x + 4 y + 28 = 0$
41744	Find the Center	9y^2-x^2+2x+54y+62=0	$9 y^{2} - x^{2} + 2 x + 54 y + 62 = 0$
41745	Find the Vertex Form	x^2-3x+y+y^2=81	$x^{2} - 3 x + y + y^{2} = 81$
41746	Find the Domain and Range	1/( square root of x+10)	$\frac{1}{\sqrt{x + 10}}$
41747	Convert to a Simplified Fraction	square root of 27	$\sqrt{27}$
41748	Convert to a Simplified Fraction	square root of 40	$\sqrt{40}$
41749	Write in Standard Form	(2-2i)^5	${(2 - 2 i)}^{5}$
41750	Find the x and y Intercepts	4x^2+4y^2-32x+16y-20=0	$4 x^{2} + 4 y^{2} - 32 x + 16 y - 20 = 0$
41751	Find the x and y Intercepts	2x^2+2y^2-12x+4y-30=0	$2 x^{2} + 2 y^{2} - 12 x + 4 y - 30 = 0$
41752	Find the x and y Intercepts	x^2+y^2-2x-6y-6=0	$x^{2} + y^{2} - 2 x - 6 y - 6 = 0$
41753	Find the Derivative - d/d@VAR	f(x)=-3x^10-x	$f (x) = - 3 x^{10} - x$
41754	Find the Asymptotes	(x^2+x-12)/(x^2+2x-15)	$\frac{x^{2} + x - 12}{x^{2} + 2 x - 15}$
41755	Convert to Logarithmic Form	e^(3x)=2	$e^{3 x} = 2$
41756	Convert to Logarithmic Form	natural log of ex	$\ln (e x)$
41757	Find the Difference Quotient	f(x)=x-4	$f (x) = x - 4$
41758	Find the Difference Quotient	f(x)=5-6x	$f (x) = 5 - 6 x$
41759	Write in Standard Form	y^2-5x^2+20x=50	$y^{2} - 5 x^{2} + 20 x = 50$
41760	Write in Standard Form	x^2+y^2-9=0	$x^{2} + y^{2} - 9 = 0$
41761	Write in Standard Form	x^2-4y^2-6x-8y=27	$x^{2} - 4 y^{2} - 6 x - 8 y = 27$
41762	Write in Standard Form	x^2+y^2-4=0	$x^{2} + y^{2} - 4 = 0$
41763	Write in Standard Form	x^2+4x+y^2-2y-49=0	$x^{2} + 4 x + y^{2} - 2 y - 49 = 0$
41764	Write in Standard Form	r=9	$r = 9$
41765	Write in Standard Form	x^2+17y^2=17	$x^{2} + 17 y^{2} = 17$
41766	Write in Standard Form	9y^2-4x^2-18y+24x-63=0	$9 y^{2} - 4 x^{2} - 18 y + 24 x - 63 = 0$
41767	Write in Standard Form	9y^2-x^2+2x+54y+71=0	$9 y^{2} - x^{2} + 2 x + 54 y + 71 = 0$
41768	Write in Standard Form	(y-2)^2=5(x+2)	${(y - 2)}^{2} = 5 (x + 2)$
41769	Write in Standard Form	-12y+10=x^2-4x+14	$- 12 y + 10 = x^{2} - 4 x + 14$
41770	Write in Standard Form	25x^2+36y^2-400x+700=0	$25 x^{2} + 36 y^{2} - 400 x + 700 = 0$
41771	Write in Standard Form	36x^2+100y^2-144x+200y-3356=0	$36 x^{2} + 100 y^{2} - 144 x + 200 y - 3356 = 0$
41772	Write in Standard Form	4x^2+y^2=16	$4 x^{2} + y^{2} = 16$
41773	Write in Standard Form	4x^2+y^2-16x+2y+13=0	$4 x^{2} + y^{2} - 16 x + 2 y + 13 = 0$
41774	Write in Standard Form	4x^2+7y^2+32x-56y+148=0	$4 x^{2} + 7 y^{2} + 32 x - 56 y + 148 = 0$
41775	Write in Standard Form	4x^2+16y^2-16x-96y+96=0	$4 x^{2} + 16 y^{2} - 16 x - 96 y + 96 = 0$
41776	Find Amplitude, Period, and Phase Shift	-1/3cos(pi/2-3x)	$\frac{- 1}{3} \cos (\frac{π}{2} - 3 x)$
41777	Find the Inverse	[[16,-4],[8,-2]]	$[\begin{array}{c} 16 & - 4 \\ 8 & - 2 \end{array}]$
41778	Solve the System of @WORD	square root of y+2<=3	$\sqrt{y + 2} \leq 3$
41779	Convert to Interval Notation	2x^3-72x<x^2-36	$2 x^{3} - 72 x < x^{2} - 36$
41780	Factor over the Complex Numbers	6-6i	$6 - 6 i$
41781	Find the Asymptotes	f(x) = log base 1/2 of x	$f (x) = \log_{\frac{1}{2}} (x)$
41782	Find the Asymptotes	f(x)=3/(x+2)	$f (x) = \frac{3}{x + 2}$
41783	Find the Asymptotes	f(x)=14/((x-5)(x+1))	$f (x) = \frac{14}{(x - 5) (x + 1)}$
41784	Find the Asymptotes	f(x)=(9x^3+8x-9)/(4x^2-36)	$f (x) = \frac{9 x^{3} + 8 x - 9}{4 x^{2} - 36}$
41785	Find the Asymptotes	f(x)=((x-7)(x+4))/(x^2-4)	$f (x) = \frac{(x - 7) (x + 4)}{x^{2} - 4}$
41786	Find the Dimensions	[[9],[8],[7]]	$[\begin{array}{c} 9 \\ 8 \\ 7 \end{array}]$
41787	Expand Using De Moivre's Theorem	(2(cos(240 degrees )+isin(240 degrees )))^4	${(2 (\cos (240 °) + i \sin (240 °)))}^{4}$
41788	Expand Using De Moivre's Theorem	(2-2i)^7	${(2 - 2 i)}^{7}$
41789	Find the Roots (Zeros)	f(x)=x^3+7x^2-49x-55	$f (x) = x^{3} + 7 x^{2} - 49 x - 55$
41790	Find the Roots (Zeros)	f(x)=x^4+10x^3-20x^2-90x+99	$f (x) = x^{4} + 10 x^{3} - 20 x^{2} - 90 x + 99$
41791	Find the Roots (Zeros)	f(x)=x^4-1	$f (x) = x^{4} - 1$
41792	Find the Roots (Zeros)	f(x)=x^4-14x^3+34x^2+114x+65	$f (x) = x^{4} - 14 x^{3} + 34 x^{2} + 114 x + 65$
41793	Find the Roots (Zeros)	f(x)=\|x^2-64\|	$f (x) = \| x^{2} - 64 \|$
41794	Find the Roots (Zeros)	f(x)=e^(9x-5)-5^(x-9)	$f (x) = e^{9 x - 5} - 5^{x - 9}$
41795	Find the Roots (Zeros)	f(x)=-4x^3+23x^2-14x-5	$f (x) = - 4 x^{3} + 23 x^{2} - 14 x - 5$
41796	Find the Roots (Zeros)	f(x)=-4x^3+31x^2-20x-7	$f (x) = - 4 x^{3} + 31 x^{2} - 20 x - 7$
41797	Find the Vertex	-4x^2+16	$- 4 x^{2} + 16$
41798	Find Trig Functions Using Triangle Sides	t=(5pi)/3	$t = \frac{5 π}{3}$
41799	Find All Complex Solutions	x^3-512=0	$x^{3} - 512 = 0$
41800	Find All Complex Solutions	x^4-6x^3+10x^2+2x-15=0	$x^{4} - 6 x^{3} + 10 x^{2} + 2 x - 15 = 0$