Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
43501	Simplify the Radical Expression	4/(i square root of 2)	$\frac{4}{i \sqrt{2}}$
43502	Solve the Rational Equation for x	(x-5)^(2/3)=4	${(x - 5)}^{\frac{2}{3}} = 4$
43503	Divide	(-1/6)÷(1/3)	$\frac{- 1}{6} \div \frac{1}{3}$
43504	Find Amplitude, Period, and Phase Shift	y=3cos(x+(5pi)/6)	$y = 3 \cos (x + \frac{5 π}{6})$
43505	Simplify	square root of 32/( square root of 2)	$\sqrt{\frac{32}{\sqrt{2}}}$
43506	Find the Domain and Range	y=(2x)/((x-2)(x+1))	$y = \frac{2 x}{(x - 2) (x + 1)}$
43507	Evaluate the Integral	integral of (sec(x)^2-1) with respect to x	$\int (\sec^{2} (x) - 1) d x$
43508	Write in Standard Form	(x^2-4x+2)(-x^2-4x-4)	$(x^{2} - 4 x + 2) (- x^{2} - 4 x - 4)$
43509	Evaluate	square root of (1+cos(80 degrees ))/2	$\sqrt{\frac{1 + \cos (80 °)}{2}}$
43510	Divide Using Synthetic Division	(x^4+8x^3-3x^2-24x)÷(x-3)	$(x^{4} + 8 x^{3} - 3 x^{2} - 24 x) \div (x - 3)$
43511	Simplify	fifth root of -243/32	$\sqrt[5]{\frac{- 243}{32}}$
43512	Evaluate	-( square root of 3)/4-( square root of 3)/4	$- \frac{\sqrt{3}}{4} - \frac{\sqrt{3}}{4}$
43513	Simplify	(64/x)^(2/3)	${(\frac{64}{x})}^{\frac{2}{3}}$
43514	Evaluate	((3pi)/4)	$(\frac{3 π}{4})$
43515	Subtract	(3x)/5-(2x)/9	$\frac{3 x}{5} - \frac{2 x}{9}$
43516	Simplify	( square root of x^2-1)^2	${(\sqrt{x^{2} - 1})}^{2}$
43517	Find the Slope	(-4,8) and (4,4)	$(- 4, 8)$ and $(4, 4)$
43518	Find dy/dx	y=x^(sin(2x+1))	$y = x^{\sin (2 x + 1)}$
43519	Evaluate	(1-cos(x))^2	${(1 - \cos (x))}^{2}$
43520	Evaluate	1/2(1-0.82)	$\frac{1}{2} (1 - 0.82)$
43521	Simplify	(6*10^5)^2	${(6 \cdot 10^{5})}^{2}$
43522	Solve the System of Equations	2y=x+3 5y=x-7	$2 y = x + 3$ $5 y = x - 7$
43523	Solve the Inequality for x	x^2-2<7/2x	$x^{2} - 2 < \frac{7}{2} x$
43524	Evaluate	15% of 120	$15 %$ of $120$
43525	Solve for b	r=(b-8)m	$r = (b - 8) m$
43526	Solve for x	9/(x^2-3x+2)-1/(x-2)=(x+5)/(3x-3)	$\frac{9}{x^{2} - 3 x + 2} - \frac{1}{x - 2} = \frac{x + 5}{3 x - 3}$
43527	Solve for x	x-1/x=5	$x - \frac{1}{x} = 5$
43528	Simplify	(5-2yi)(1-5i)-(5-2yi)(1-i)	$(5 - 2 y i) (1 - 5 i) - (5 - 2 y i) (1 - i)$
43529	Subtract	3/(x-1)-2/x	$\frac{3}{x - 1} - \frac{2}{x}$
43530	Solve the System of Inequalities	3t-15<-3 and -4t<12	$3 t - 15 < - 3$ and $- 4 t < 12$
43531	Graph	x>y^2	$x > y^{2}$
43532	Find the Inflection Points	( cube root of x)/(e^x)+1	$\frac{\sqrt[3]{x}}{e^{x}} + 1$
43533	Solve for x	9^(3-2x)=(1/3)^x*27^(x+1)	$9^{3 - 2 x} = {(\frac{1}{3})}^{x} \cdot 27^{x + 1}$
43534	Find the Parabola with Vertex (-2,4) and Directrix x=-1	The vertex is (-2,4) ; the directrix is x=-1	The vertex is $(- 2, 4)$ ; the directrix is $x = - 1$
43535	Evaluate the Summation	3 sum from t=2 to 5 of 2t^2-8t	$3 \sum_{t = 2}^{5} 2 t^{2} - 8 t$
43536	Simplify	(2-3/2)/(1/2)	$\frac{2 - \frac{3}{2}}{\frac{1}{2}}$
43537	Simplify	7x-(2(x^2-z)+4x^2-7z)+6z^2	$7 x - (2 (x^{2} - z) + 4 x^{2} - 7 z) + 6 z^{2}$
43538	Solve the Inequality for x	-3x^4-20x^3+7x^2<=0	$- 3 x^{4} - 20 x^{3} + 7 x^{2} \leq 0$
43539	Simplify	2x-1/2x	$2 x - \frac{1}{2} x$
43540	Simplify	square root of 5x^2* square root of 12x^3	$\sqrt{5 x^{2}} \cdot \sqrt{12 x^{3}}$
43541	Divide Using Long Polynomial Division	Use the long division method to find the result when 8x^3+18x^2+19x-6 is divided by 4x-1	Use the long division method to find the result when $8 x^{3} + 18 x^{2} + 19 x - 6$ is divided by $4 x - 1$
43542	Solve for x in Radians	2sin(x)^2=sin(x)	$2 \sin^{2} (x) = \sin (x)$
43543	Solve the Function Operation	f(x)=9(x+9)^(1/3) ; find f^-1(x)	$f (x) = 9 {(x + 9)}^{\frac{1}{3}}$ ; find $f^{- 1} (x)$
43544	Solve the System of Inequalities	-6x>-18 and 1<=2x+5	$- 6 x > - 18$ and $1 \leq 2 x + 5$
43545	Find dx/dy	f(x)=e^(xy)	$f (x) = e^{x y}$
43546	Evaluate	c(4)^3-15*4-68	$c {(4)}^{3} - 15 \cdot 4 - 68$
43547	Solve for x in Degrees	sin(x)+1=0	$\sin (x) + 1 = 0$
43548	Evaluate	sin(x)+1=0	$\sin (x) + 1 = 0$
43549	Find the Domain	F(x) = log of 3x-2	$F (x) = \log (3 x - 2)$
43550	Find the Excluded Values	1/(x+1)+3=7/(x+1)	$\frac{1}{x + 1} + 3 = \frac{7}{x + 1}$
43551	Determine if Dependent, Independent, or Inconsistent	4x=2y-6 y+4x=3	$4 x = 2 y - 6$ $y + 4 x = 3$
43552	Write the Fraction in Simplest Form	2/3*9/10	$\frac{2}{3} \cdot \frac{9}{10}$
43553	Evaluate the Limit	limit as x approaches infinity of x/(x^2)	$lim_{x \to \infty} \frac{x}{x^{2}}$
43554	Find the Derivative - d/dx	2^x+x^2	$2^{x} + x^{2}$
43555	Graph	\|x-5\|<-1	$\| x - 5 \| < - 1$
43556	Simplify	((5x^13y^5z^2)/(3*5^2))	$(\frac{5 x^{13} y^{5} z^{2}}{3 \cdot 5^{2}})$
43557	Solve the Inequality for x	(3x-4)/3<x	$\frac{3 x - 4}{3} < x$
43558	Simplify	((3e^3)/(6e^2))^2	${(\frac{3 e^{3}}{6 e^{2}})}^{2}$
43559	Simplify the Radical Expression	- square root of 81+ square root of -49+ square root of 25+ square root of -1	$- \sqrt{81} + \sqrt{- 49} + \sqrt{25} + \sqrt{- 1}$
43560	Solve for x in Radians	cos(2x)=-1/2	$\cos (2 x) = - \frac{1}{2}$
43561	Simplify	(21x^5y^12)/((3x^-2y^7)^2)	$\frac{21 x^{5} y^{12}}{{(3 x^{- 2} y^{7})}^{2}}$
43562	Graph	x-4>=4 and 6>=x-4	$x - 4 \geq 4$ and $6 \geq x - 4$
43563	Find the Roots (Zeros)	(x^2-7x-18)/(x+2)=x-9	$\frac{x^{2} - 7 x - 18}{x + 2} = x - 9$
43564	Graph	f(x)=x/x	$f (x) = \frac{x}{x}$
43565	Evaluate	(x^-6y^-1y)/(x^2)	$\frac{x^{- 6} y^{- 1} y}{x^{2}}$
43566	Solve by Substitution	2x+4y=28 -2y=x+28	$2 x + 4 y = 28$ $- 2 y = x + 28$
43567	Graph	f(x)=3 if X<2; X-1 if X>=2	$f (x) = {\begin{cases} 3 & X < 2 \\ X - 1 & X \geq 2 \end{cases}$
43568	Find the Asymptotes	y=8*(1/4)^x-1	$y = 8 \cdot {(\frac{1}{4})}^{x} - 1$
43569	Solve for θ in Radians	theta=(-7pi)/4	$θ = \frac{- 7 π}{4}$
43570	Find the Average Rate of Change	f(x)=cos(x/2)	$f (x) = \cos (\frac{x}{2})$
43571	Simplify	8(7g)+8g	$8 (7 g) + 8 g$
43572	Find the Slope	(5/6,-2) and (-1/3,-1/3)	$(\frac{5}{6}, - 2)$ and $(- \frac{1}{3}, - \frac{1}{3})$
43573	Expand the Trigonometric Expression	2sin(10 degrees )cos(10 degrees )	$2 \sin (10 °) \cos (10 °)$
43574	Simplify the Radical Expression	3x square root of 180x^5-10 square root of 180x^7	$3 x \sqrt{180 x^{5}} - 10 \sqrt{180 x^{7}}$
43575	Solve the Inequality for x	-3x^2+3x+4<=-2	$- 3 x^{2} + 3 x + 4 \leq - 2$
43576	Factor	1/(1-x^2)	$\frac{1}{1 - x^{2}}$
43577	Evaluate	( square root of 0.9-1)/(0.9-1)	$\frac{\sqrt{0.9} - 1}{0.9 - 1}$
43578	Evaluate	\|x-5\|>14	$\| x - 5 \| > 14$
43579	Simplify	(x+2)(x^2-3x+2)x^2	$(x + 2) (x^{2} - 3 x + 2) x^{2}$
43580	Combine Like Terms	(-7x^5+14-2x)+(10x^4+7x+5x^5)	$(- 7 x^{5} + 14 - 2 x) + (10 x^{4} + 7 x + 5 x^{5})$
43581	Solve for c	5(8)=3478-3c	$5 (8) = 3478 - 3 c$
43582	Find the Domain of the Composition f(g(x))	f(x)=2/(x-7) , g(x) = square root of x-2	$f (x) = \frac{2}{x - 7}$ , $g (x) = \sqrt{x - 2}$
43583	Simplify	((8v^2w^-3x^2)^2)/((2v^3w^2x^-4)^6)*(-v^2w^3x^-2)^-3	$\frac{{(8 v^{2} w^{- 3} x^{2})}^{2}}{{(2 v^{3} w^{2} x^{- 4})}^{6}} \cdot {(- v^{2} w^{3} x^{- 2})}^{- 3}$
43584	Simplify	(9x^3-4x^2-1)-(7-9x^2+9x^3)	$(9 x^{3} - 4 x^{2} - 1) - (7 - 9 x^{2} + 9 x^{3})$
43585	Find the Asymptotes	F(x)=(3x^2-3x)/(x^2+x-12)	$F (x) = \frac{3 x^{2} - 3 x}{x^{2} + x - 12}$
43586	Divide Using Long Polynomial Division	Use the long division method to find the result when 6x^3+15x^2+17x+12 is divided by 2x+3	Use the long division method to find the result when $6 x^{3} + 15 x^{2} + 17 x + 12$ is divided by $2 x + 3$
43587	Simplify	(2x^2-4x+3y-6)-(4y^2-3x-7y+4)	$(2 x^{2} - 4 x + 3 y - 6) - (4 y^{2} - 3 x - 7 y + 4)$
43588	Solve using Gaussian Elimination	3x_1-2x_2+x_3=-1 -x_1-x_2+6x_3=29 5x_1-3x_2-4x_3=-25	$3 x_{1} - 2 x_{2} + x_{3} = - 1$ $- x_{1} - x_{2} + 6 x_{3} = 29$ $5 x_{1} - 3 x_{2} - 4 x_{3} = - 25$
43589	Divide	(25m^2-20m+4)÷(5m-2)	$(25 m^{2} - 20 m + 4) \div (5 m - 2)$
43590	Graph	2y-x<=2 y-3x>=-4 y>=-1	$2 y - x \leq 2$ $y - 3 x \geq - 4$ $y \geq - 1$
43591	Evaluate	2*2^(1/2)	$2 \cdot 2^{\frac{1}{2}}$
43592	Graph	g(x)=4\|1-x\|	$g (x) = 4 \| 1 - x \|$
43593	Solve for x	natural log of 3x-1- natural log of x+2=0	$\ln (3 x - 1) - \ln (x + 2) = 0$
43594	Evaluate the Limit	limit as x approaches -3 of (4x+36)/(3-x)	$lim_{x \to - 3} \frac{4 x + 36}{3 - x}$
43595	Simplify the Radical Expression	( square root of z)/( square root of z- square root of 3)	$\frac{\sqrt{z}}{\sqrt{z} - \sqrt{3}}$
43596	Solve Using the Square Root Property	2(x+5)^2+37=39	$2 {(x + 5)}^{2} + 37 = 39$
43597	Solve for r	4(2r-17)+5(3r-8)=0	$4 (2 r - 17) + 5 (3 r - 8) = 0$
43598	Simplify	(x^-2)^(-1/2)	${(x^{- 2})}^{- \frac{1}{2}}$
43599	Factor	f(x)=x^4+9x^3+15x^2+9x+14	$f (x) = x^{4} + 9 x^{3} + 15 x^{2} + 9 x + 14$
43600	Write the Fraction in Simplest Form	(x^(2/3))^-3	${(x^{\frac{2}{3}})}^{- 3}$