Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
20401	Evaluate the Integral	integral from 0 to infinity of e^(-x^3) with respect to x	$\int_{0}^{\infty} e^{- x^{3}} d x$
20402	Write in Standard Form	y=(-13x)/9+22/9	$y = \frac{- 13 x}{9} + \frac{22}{9}$
20403	Simplify	((p^2)/(q^3))(p/q)^-2	$(\frac{p^{2}}{q^{3}}) {(\frac{p}{q})}^{- 2}$
20404	Solve the Rational Equation for x	square root of 2x-4 = square root of x	$\sqrt{2 x - 4} = \sqrt{x}$
20405	Evaluate	cube root of 5^5* square root of 5	$\sqrt[3]{5^{5}} \cdot \sqrt{5}$
20406	Find dy/dx	square root of 2x+y=2x	$\sqrt{2 x + y} = 2 x$
20407	Simplify	0^(2/3)	$0^{\frac{2}{3}}$
20408	Write the Fraction in Simplest Form	(-5t^5)/((5t^-5)^2)	$\frac{- 5 t^{5}}{{(5 t^{- 5})}^{2}}$
20409	Find the Turning Points	y=3x^3-x-3	$y = 3 x^{3} - x - 3$
20410	Simplify	(3x)/(4y^2)-y/(6x)	$\frac{3 x}{4 y^{2}} - \frac{y}{6 x}$
20411	Simplify	(5x)/4+3/(x^2)	$\frac{5 x}{4} + \frac{3}{x^{2}}$
20412	Simplify the Radical Expression	(2x)^3	${(2 x)}^{3}$
20413	Write with Rational (Fractional) Exponents	( eighth root of (4a)^3)^8	${(\sqrt[8]{{(4 a)}^{3}})}^{8}$
20414	Evaluate	(-2x^5y^7)^3+7x^15y^21	${(- 2 x^{5} y^{7})}^{3} + 7 x^{15} y^{21}$
20415	Graph	x+2y=6 2x+y=6	$x + 2 y = 6$ $2 x + y = 6$
20416	Solve for x	9+ square root of x^2-5x=12	$9 + \sqrt{x^{2} - 5 x} = 12$
20417	Find the Asymptotes	f(x)=(3x^2+6x)/(x^2+x)	$f (x) = \frac{3 x^{2} + 6 x}{x^{2} + x}$
20418	Graph	-2x+y+4<9	$- 2 x + y + 4 < 9$
20419	Write in Standard Form	2x(3x^2+4)-3x^2	$2 x (3 x^{2} + 4) - 3 x^{2}$
20420	Simplify the Radical Expression	i^22	$i^{22}$
20421	Simplify	x^0y	$x^{0} y$
20422	Solve for x	-15/x=x+8	$\frac{- 15}{x} = x + 8$
20423	Solve the Function Operation	f(x)=2x-6 if x!=4; 6 if x=4 Find f(-1)	$f (x) = {\begin{cases} 2 x - 6 & x \neq 4 \\ 6 & x = 4 \end{cases}$ Find $f (- 1)$
20424	Find f(h(x))	f(x)=3x+5 g(x)=4x^2-2 h(x)=x^2-3x+1	$f (x) = 3 x + 5$ $g (x) = 4 x^{2} - 2$ $h (x) = x^{2} - 3 x + 1$
20425	Simplify	((x^2-10x+9)/(3x))÷((x^2-7x-18)/(x^2+2x))	$\frac{x^{2} - 10 x + 9}{3 x} \div \frac{x^{2} - 7 x - 18}{x^{2} + 2 x}$
20426	Divide Using Synthetic Division	Use synthetic division to find the result when x^3+3x^2+8x+12 is divided by x+2	Use synthetic division to find the result when $x^{3} + 3 x^{2} + 8 x + 12$ is divided by $x + 2$
20427	Evaluate	(2(3+2)^3)/(-1+11)	$\frac{2 {(3 + 2)}^{3}}{- 1 + 11}$
20428	Solve for h	2.4(5h+10)-3=27	$2.4 (5 h + 10) - 3 = 27$
20429	Add	square root of 2+ square root of 6-2 square root of 2+7 square root of 6	$\sqrt{2} + \sqrt{6} - 2 \sqrt{2} + 7 \sqrt{6}$
20430	Simplify	1 3/4+7/3-27/12	$1 \frac{3}{4} + \frac{7}{3} - \frac{27}{12}$
20431	Simplify the Radical Expression	square root of 32x	$\sqrt{32 x}$
20432	Simplify	-2x^2-4x from 2x^2-2x-5	$- 2 x^{2} - 4 x$ from $2 x^{2} - 2 x - 5$
20433	Solve for x	(x+3)/(x+2)-5/(x-9)=5/(x^2-7x-18)	$\frac{x + 3}{x + 2} - \frac{5}{x - 9} = \frac{5}{x^{2} - 7 x - 18}$
20434	Simplify	3(2t^2-4t-15(6t(5t+2)))	$3 (2 t^{2} - 4 t - 15 (6 t (5 t + 2)))$
20435	Solve the Inequality for x	(2\|x-1\|)/5>=2	$\frac{2 \| x - 1 \|}{5} \geq 2$
20436	Simplify	(2/(3x^(1/3)))^2	${(\frac{2}{3 x^{\frac{1}{3}}})}^{2}$
20437	Determine if (3,3) is a Solution	y=3x+6 y=-2x+9 (3,3)	$y = 3 x + 6$ $y = - 2 x + 9$ $(3, 3)$
20438	Solve the Absolute Value Inequality for x	\|x\|>=-2	$\| x \| \geq - 2$
20439	Integrate Using u-Substitution	integral of x/(1+x^2) with respect to x	$\int \frac{x}{1 + x^{2}} d x$
20440	Solve for θ in Degrees	2sin(theta)^2+3sin(theta)=0	$2 \sin^{2} (θ) + 3 \sin (θ) = 0$
20441	Evaluate	(x+3)^2-3=49	${(x + 3)}^{2} - 3 = 49$
20442	Combine Like Terms	1/4x+1+3/4x-2/3-1/2x	$\frac{1}{4} x + 1 + \frac{3}{4} x - \frac{2}{3} - \frac{1}{2} x$
20443	Evaluate the Integral	integral of (2-3e^x) with respect to x	$\int (2 - 3 e^{x}) d x$
20444	Evaluate	(2pi)/3(180/pi)	$\frac{2 π}{3} (\frac{180}{π})$
20445	Solve the Function Operation	Given that f(x)=x^2+10x+21 and g(x)=x+3 ; find f(x)*g(x) and express the result in standard form.	Given that $f (x) = x^{2} + 10 x + 21$ and $g (x) = x + 3$ ; find $f (x) \cdot g (x)$ and express the result in standard form.
20446	Solve using Gaussian Elimination	x+2y=5 2x+3y=6	$x + 2 y = 5$ $2 x + 3 y = 6$
20447	Solve for x	15-3x=5(x+4)-8x	$15 - 3 x = 5 (x + 4) - 8 x$
20448	Evaluate the Integral	integral from 1 to e of (( natural log of x)^2)/x with respect to x	$\int_{1}^{e} \frac{\ln^{2} (x)}{x} d x$
20449	Combine Like Terms	-7m-m^2+4m^2-3m	$- 7 m - m^{2} + 4 m^{2} - 3 m$
20450	Graph	2>x-2 or 4	$2 > x - 2$ or $4$
20451	Solve for x	2^x+2^(-x)=5/2	$2^{x} + 2^{- x} = \frac{5}{2}$
20452	Graph	\|2x-y\|<=x+y	$\| 2 x - y \| \leq x + y$
20453	Evaluate	((-9)^0j^-1k^-4)/(2^0)	$\frac{{(- 9)}^{0} j^{- 1} k^{- 4}}{2^{0}}$
20454	Simplify	(8+i^2)-(2-i^6)	$(8 + i^{2}) - (2 - i^{6})$
20455	Find the Maximum/Minimum Value	y=2sin(x-pi/2)	$y = 2 \sin (x - \frac{π}{2})$
20456	Evaluate the Limit	limit as x approaches 3 of f(x)-2g(x)	$lim_{x \to 3} f (x) - 2 g (x)$
20457	Simplify the Radical Expression	fourth root of (x^3)/8	$\sqrt[4]{\frac{x^{3}}{8}}$
20458	Divide Using Synthetic Division	Use synthetic division to find the result when 4x^4+14x^3+13x^2+x-2 is divided by x+2	Use synthetic division to find the result when $4 x^{4} + 14 x^{3} + 13 x^{2} + x - 2$ is divided by $x + 2$
20459	Solve the Function Operation	f(x)=(x-8)^(1/2) ; find f^-1(x)	$f (x) = {(x - 8)}^{\frac{1}{2}}$ ; find $f^{- 1} (x)$
20460	Find the Asymptotes	(x^2-1)/(3x^2+3x)	$\frac{x^{2} - 1}{3 x^{2} + 3 x}$
20461	Find the Derivative - d/dx	square root of cos(2x)	$\sqrt{\cos (2 x)}$
20462	Graph	y<=1/(x-2)-1	$y \leq \frac{1}{x - 2} - 1$
20463	Simplify	((4at^5)/(a^3t^-1))^2	${(\frac{4 a t^{5}}{a^{3} t^{- 1}})}^{2}$
20464	Find Where Increasing/Decreasing	g(x)=(x^3)/(3x^2+1)	$g (x) = \frac{x^{3}}{3 x^{2} + 1}$
20465	Graph	2x+y=-4 -3y=2x+12	$2 x + y = - 4$ $- 3 y = 2 x + 12$
20466	Solve the System of Equations	9x^2+25y^2=225 10y+6x=6	$9 x^{2} + 25 y^{2} = 225$ $10 y + 6 x = 6$
20467	Simplify	(9x^3-2x^2+x-6)-(6-9x-4x^2)	$(9 x^{3} - 2 x^{2} + x - 6) - (6 - 9 x - 4 x^{2})$
20468	Solve for x	-20=4 cube root of 11x-15	$- 20 = 4 \sqrt[3]{11 x - 15}$
20469	Evaluate the Integral	integral of x3/5 with respect to x	$\int x \frac{3}{5} d x$
20470	Simplify the Radical Expression	(-64)^(1/2)	${(- 64)}^{\frac{1}{2}}$
20471	Find the Antiderivative	6/(x^3)-4e^(2x)+7	$\frac{6}{x^{3}} - 4 e^{2 x} + 7$
20472	Graph	y=(2x-1)(2x-3)(2x+5)	$y = (2 x - 1) (2 x - 3) (2 x + 5)$
20473	Find Amplitude, Period, and Phase Shift	y=3sin((pix)/3-(2pi)/3)	$y = 3 \sin (\frac{π x}{3} - \frac{2 π}{3})$
20474	Evaluate the Limit	limit as x approaches 0 of (-2x)/(4-(2+x)^2)	$lim_{x \to 0} \frac{- 2 x}{4 - {(2 + x)}^{2}}$
20475	Solve for x in Radians	sin(2x)-sin(x)=0	$\sin (2 x) - \sin (x) = 0$
20476	Simplify	-3/(2 square root of 3)	$- \frac{3}{2 \sqrt{3}}$
20477	Solve for x	2+sin(x)=2	$2 + \sin (x) = 2$
20478	Find dy/dx	5x^3+2y^3-y^2+3=-5x^2	$5 x^{3} + 2 y^{3} - y^{2} + 3 = - 5 x^{2}$
20479	Evaluate	log base 6 of cube root of 1/6	$\log_{6} (\sqrt[3]{\frac{1}{6}})$
20480	Solve the Rational Equation for x	(x-3)/(x+1)=(4x-6)/((x+1)(x+2))	$\frac{x - 3}{x + 1} = \frac{4 x - 6}{(x + 1) (x + 2)}$
20481	Simplify	2a^(1/3)(ab^(1/2))^(2/3)	$2 a^{\frac{1}{3}} {(a b^{\frac{1}{2}})}^{\frac{2}{3}}$
20482	Evaluate the Integral	integral of e^( natural log of x) with respect to x	$\int e^{\ln (x)} d x$
20483	Solve for θ in Degrees	8tan(theta)-12=5tan(theta)-9	$8 \tan (θ) - 12 = 5 \tan (θ) - 9$
20484	Solve the System of Inequalities	2y<-12x+4 y<-6x+4	$2 y < - 12 x + 4$ $y < - 6 x + 4$
20485	Solve for y	4^(y+2)=16^(y-3)	$4^{y + 2} = 16^{y - 3}$
20486	Divide	(4/44)÷(8/-20)	$\frac{4}{44} \div \frac{8}{- 20}$
20487	Solve for d	a=bc+d	$a = b c + d$
20488	Solve for x	x-2/3=6 1/3	$x - \frac{2}{3} = 6 \frac{1}{3}$
20489	Solve the System of Equations	Solve the system of equations 3x+2y=9 and 3x-y=0	Solve the system of equations $3 x + 2 y = 9$ and $3 x - y = 0$
20490	Find the Domain and Range	h(x) = log base 8 of \|x\|	$h (x) = \log_{8} (\| x \|)$
20491	Evaluate	sec(theta)=(2 square root of 3)/3	$\sec (θ) = \frac{2 \sqrt{3}}{3}$
20492	Factor	a(b-c)+d(c-b)	$a (b - c) + d (c - b)$
20493	Write in Exponential Form	( cube root of 10y)^3	${(\sqrt[3]{10 y})}^{3}$
20494	Write in Standard Form	(2i)(1-4i)(1+i)	$(2 i) (1 - 4 i) (1 + i)$
20495	Evaluate	4sec(pi/3)	$4 \sec (\frac{π}{3})$
20496	Combine Like Terms	7/2x-8.62-3/2x-2.38	$\frac{7}{2} x - 8.62 - \frac{3}{2} x - 2.38$
20497	Write as a Single Logarithm	3* log base 2 of 4- log base 2 of 32	$3 \cdot \log_{2} (4) - \log_{2} (32)$
20498	Evaluate	1/(tan(2.5))	$\frac{1}{\tan (2.5)}$
20499	Simplify	(6^5*6)/(6^5)	$\frac{6^{5} \cdot 6}{6^{5}}$
20500	Simplify	(3x-6)/(24x)+(3x+6)/(24x)	$\frac{3 x - 6}{24 x} + \frac{3 x + 6}{24 x}$