Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
22801	Evaluate the Integral	integral of ((x^2-1)^3)/(x^2) with respect to x	$\int \frac{{(x^{2} - 1)}^{3}}{x^{2}} d x$
22802	Solve for B	cot(theta)=A/B	$\cot (θ) = \frac{A}{B}$
22803	Solve for y	square root of 6y+5 = square root of 2y+10	$\sqrt{6 y + 5} = \sqrt{2 y + 10}$
22804	Graph	y=-x if x<2; x-6 if x>=2	$y = {\begin{cases} - x & x < 2 \\ x - 6 & x \geq 2 \end{cases}$
22805	Solve for x	3x-11+4x-7+44=180	$3 x - 11 + 4 x - 7 + 44 = 180$
22806	Evaluate the Integral	integral from 0 to 5 of pi((20-4x)/5)^2 with respect to x	$\int_{0}^{5} π {(\frac{20 - 4 x}{5})}^{2} d x$
22807	Solve for d	t = square root of d/16	$t = \sqrt{\frac{d}{16}}$
22808	Convert to Interval Notation	x<-9 or x>-6	$x < - 9$ or $x > - 6$
22809	Multiply	(8x+64)/(x-4)*(x^2-49)/(x^2+x-56)	$\frac{8 x + 64}{x - 4} \cdot \frac{x^{2} - 49}{x^{2} + x - 56}$
22810	Graph	table[[x,y],[-1,-4],[0,-3],[1,-2]]	$\begin{array}{c} x & y \\ - 1 & - 4 \\ 0 & - 3 \\ 1 & - 2 \end{array}$
22811	Simplify	((6^4)/(3^2))^3	${(\frac{6^{4}}{3^{2}})}^{3}$
22812	Divide Using Synthetic Division	Use synthetic division to find the result when 4x^3+3x^2-10x-9 is divided by x+1	Use synthetic division to find the result when $4 x^{3} + 3 x^{2} - 10 x - 9$ is divided by $x + 1$
22813	Solve the Function Operation	f(x)=(x+2)^2-6 if x!=-1; -6 if x=-1 Find f(-1)	$f (x) = {\begin{cases} {(x + 2)}^{2} - 6 & x \neq - 1 \\ - 6 & x = - 1 \end{cases}$ Find $f (- 1)$
22814	Solve for x	4(3-x)+6x=x+12-3x	$4 (3 - x) + 6 x = x + 12 - 3 x$
22815	Write the Fraction in Simplest Form	limit as x approaches 0 of (e^(2x)-1)/(e^x-1)	$lim_{x \to 0} \frac{e^{2 x} - 1}{e^{x} - 1}$
22816	Find the Constant of Variation	y=36 when x=3	$y = 36$ when $x = 3$
22817	Find the Roots (Zeros)	y=x^2-2 square root of 2x+2	$y = x^{2} - 2 \sqrt{2} x + 2$
22818	Factor	6a^(2x)-24b^2	$6 a^{2 x} - 24 b^{2}$
22819	Evaluate	((3m^-2n)^-3)/(6mn^-2)	$\frac{{(3 m^{- 2} n)}^{- 3}}{6 m n^{- 2}}$
22820	Convert from Radians to Degrees	16rad	$16$ rad
22821	Find the Product	2m^2*2m^3	$2 m^{2} \cdot 2 m^{3}$
22822	Solve the Inequality for x	3(x-5)+x<13	$3 (x - 5) + x < 13$
22823	Evaluate the Limit	limit as x approaches 8 of 2f(x)-12h(x)	$lim_{x \to 8} 2 f (x) - 12 h (x)$
22824	Rationalize the Denominator	-1/( cube root of 2m^2n)	$- \frac{1}{\sqrt[3]{2 m^{2} n}}$
22825	Solve for x	4x^2-8x+4=1	$4 x^{2} - 8 x + 4 = 1$
22826	Find the Derivative - d/dx	d/(dx)( log base 7 of 1-x)	$\frac{d}{d x} (\log_{7} (1 - x))$
22827	Simplify	(cot(x)^2)/(1+cot(x)^2)	$\frac{\cot^{2} (x)}{1 + \cot^{2} (x)}$
22828	Evaluate the Integral	integral of (5 cube root of x^4)/3 with respect to x	$\int \frac{5 \sqrt[3]{x^{4}}}{3} d x$
22829	Find the Product	-2/3n^2(-9n^2+3n+6)	$- \frac{2}{3} n^{2} (- 9 n^{2} + 3 n + 6)$
22830	Simplify the Radical Expression	((2^4)/(3^4))^(1/8)	${(\frac{2^{4}}{3^{4}})}^{\frac{1}{8}}$
22831	Simplify the Radical Expression	((3q^(5/2)r^(1/4))/(6^(1/2)))^2	${(\frac{3 q^{\frac{5}{2}} r^{\frac{1}{4}}}{6^{\frac{1}{2}}})}^{2}$
22832	Find the Domain and Range	y=4+ square root of x+6	$y = 4 + \sqrt{x + 6}$
22833	Simplify	(3 square root of 20)/( square root of 45)	$\frac{3 \sqrt{20}}{\sqrt{45}}$
22834	Solve for c	c^3+27=0	$c^{3} + 27 = 0$
22835	Simplify	2y*3x^-1y^4	$2 y \cdot 3 x^{- 1} y^{4}$
22836	Find the Midpoint	What is the midpoint of the points (2,4) and (-5,5) ?	What is the midpoint of the points $(2, 4)$ and $(- 5, 5)$ ?
22837	Factor	5ax-2ay-3bz+2by+3az-5bx	$5 a x - 2 a y - 3 b z + 2 b y + 3 a z - 5 b x$
22838	Graph	P(x)=x^4-3x^2+x-8	$P (x) = x^{4} - 3 x^{2} + x - 8$
22839	Find the Antiderivative	((x-1)^3)/(2x^2)	$\frac{{(x - 1)}^{3}}{2 x^{2}}$
22840	Solve for x	log base 9 of x+6+ log base 9 of x+4=1/2	$\log_{9} (x + 6) + \log_{9} (x + 4) = \frac{1}{2}$
22841	Factor	xz(x+z)+xy(x-y)-yz(y+z)	$x z (x + z) + x y (x - y) - y z (y + z)$
22842	Solve for h	h^2+7h+10=0	$h^{2} + 7 h + 10 = 0$
22843	Simplify	e^x*6e^(3x-1)	$e^{x} \cdot 6 e^{3 x - 1}$
22844	Simplify	10/( square root of 3x^5)	$\frac{10}{\sqrt{3 x^{5}}}$
22845	Evaluate	1/3*5/6-2/9	$\frac{1}{3} \cdot \frac{5}{6} - \frac{2}{9}$
22846	Find the Maximum/Minimum Value	y=-2cos(x)+5	$y = - 2 \cos (x) + 5$
22847	Solve for b	10+5b^2=200	$10 + 5 b^{2} = 200$
22848	Solve the Inequality for x	(x-\|5x+2\|)/(2x+\|5x+2\|)>x	$\frac{x - \| 5 x + 2 \|}{2 x + \| 5 x + 2 \|} > x$
22849	Solve for x	x^2+2x-8<=0	$x^{2} + 2 x - 8 \leq 0$
22850	Simplify	( square root of 15)/(2 square root of 4)	$\frac{\sqrt{15}}{2 \sqrt{4}}$
22851	Simplify	-36114/9	$- 36 \cdot 11 \cdot \frac{4}{9}$
22852	Solve for x	2/5=x/3+1/3	$\frac{2}{5} = \frac{x}{3} + \frac{1}{3}$
22853	Convert to Radical Form	(64n^12)^(-1/6)	${(64 n^{12})}^{- \frac{1}{6}}$
22854	Solve the System of Inequalities	k-3<-7 or k+5>=8	$k - 3 < - 7$ or $k + 5 \geq 8$
22855	Simplify	-z^3 square root of 16z^3+3 square root of 36z^7	$- z^{3} \sqrt{16 z^{3}} + 3 \sqrt{36 z^{7}}$
22856	Simplify	(x^2)/(2 square root of x)	$\frac{x^{2}}{2 \sqrt{x}}$
22857	Solve the Function Operation	f(x)=3x-2 ; find f(-6)	$f (x) = 3 x - 2$ ; find $f (- 6)$
22858	Simplify	-1/3 square root of -90	$- \frac{1}{3} \sqrt{- 90}$
22859	Find dy/dx	y=x^2-xcos(x)	$y = x^{2} - x \cos (x)$
22860	Find the Antiderivative	x*e^(-x^2)	$x \cdot e^{- x^{2}}$
22861	Divide Using Synthetic Division	Use synthetic division to find the result when 4x^4+9x^3-3x^2+2x+10 is divided by x+1	Use synthetic division to find the result when $4 x^{4} + 9 x^{3} - 3 x^{2} + 2 x + 10$ is divided by $x + 1$
22862	Simplify the Radical Expression	20x^6 cube root of -1/1000x^36	$20 x^{6} \sqrt[3]{\frac{- 1}{1000} x^{36}}$
22863	Simplify the Radical Expression	fourth root of (3a^2)/(8b^7)	$\sqrt[4]{\frac{3 a^{2}}{8 b^{7}}}$
22864	Simplify	(3a^-1b^-4)/(3ab)	$\frac{3 a^{- 1} b^{- 4}}{3 a b}$
22865	Find the Roots (Zeros)	f(x)=x^4-4x^3+2x^2+x+4	$f (x) = x^{4} - 4 x^{3} + 2 x^{2} + x + 4$
22866	Solve the Rational Equation for x	8/(3x-2)=2/(x-1)	$\frac{8}{3 x - 2} = \frac{2}{x - 1}$
22867	Graph	f(x)=-x(x+2)(x-2)(x+1)	$f (x) = - x (x + 2) (x - 2) (x + 1)$
22868	Find dy/dx	5+3xy+4y^3=0	$5 + 3 x y + 4 y^{3} = 0$
22869	Solve for x	105=(x-2)(x)(x+2)	$105 = (x - 2) (x) (x + 2)$
22870	Find the Possible Factors	factors of 6	factors of $6$
22871	Evaluate the Limit	limit as x approaches infinity of 3-7/x+4/(x^2)	$lim_{x \to \infty} 3 - \frac{7}{x} + \frac{4}{x^{2}}$
22872	Graph the Intersection (and)	y<=-3x+1 y>=-1/4x+6	$y \leq - 3 x + 1$ $y \geq - \frac{1}{4} x + 6$
22873	Solve for x	3^x+3^(1+x)=36	$3^{x} + 3^{1 + x} = 36$
22874	Solve for x	12/(7-x)=x	$\frac{12}{7 - x} = x$
22875	Solve the Function Operation	k(a)=-4^(3a+2) ; Find k(a-2)	$k (a) = - 4^{3 a + 2}$ ; Find $k (a - 2)$
22876	Solve for x	(-3cos(x)-5sin(x))^2-16sin(x)^2=(18+15 square root of 3)/2	${(- 3 \cos (x) - 5 \sin (x))}^{2} - 16 \sin^{2} (x) = \frac{18 + 15 \sqrt{3}}{2}$
22877	Find the Equation with a Point and Slope	What is the equation of the line that passes through the point (8,-8) and has a slope of -1/4 ?	What is the equation of the line that passes through the point $(8, - 8)$ and has a slope of $- \frac{1}{4}$ ?
22878	Simplify	csc(theta)^2+cot(theta)^2-1	$\csc^{2} (θ) + \cot^{2} (θ) - 1$
22879	Simplify the Radical Expression	(b^-2)/(b^4)	$\frac{b^{- 2}}{b^{4}}$
22880	Solve the Function Operation	Given that f(x)=x^2-6x+8 and g(x)=x-2 ; find f(x)+g(x) and express the result in standard form.	Given that $f (x) = x^{2} - 6 x + 8$ and $g (x) = x - 2$ ; find $f (x) + g (x)$ and express the result in standard form.
22881	Simplify	(12x^3y^5)1/2	$(12 x^{3} y^{5}) \frac{1}{2}$
22882	Find dy/dx	3y^2=x^2+2x^3-y^3	$3 y^{2} = x^{2} + 2 x^{3} - y^{3}$
22883	Find dy/dx	-3+xy-y^2=2x^2	$- 3 + x y - y^{2} = 2 x^{2}$
22884	Multiply	-4(rs^2)(-5r^4s)	$- 4 (r s^{2}) (- 5 r^{4} s)$
22885	Factor	(3x^2-12)/(8x^2-18x+4)	$\frac{3 x^{2} - 12}{8 x^{2} - 18 x + 4}$
22886	Find the Domain and Range	f(x)=5-3(x-1)	$f (x) = 5 - 3 (x - 1)$
22887	Solve for x	x2/3=4	$x \frac{2}{3} = 4$
22888	Find the Value Using the Unit Circle	45	$45$
22889	Find the Vertex	x^2+(y-2)^2=4	$x^{2} + {(y - 2)}^{2} = 4$
22890	Solve by Completing the Square	x^2+bx+c=0	$x^{2} + b x + c = 0$
22891	Add	(-3+71i)+(9)	$(- 3 + 71 i) + (9)$
22892	Write in Exponential Form	2 square root of x^2	$2 \sqrt{x^{2}}$
22893	Evaluate	x^2+(y-2)^2=4	$x^{2} + {(y - 2)}^{2} = 4$
22894	Simplify	1/( square root of -5)	$\frac{1}{\sqrt{- 5}}$
22895	Solve for x	7 1/4x+x-2 11/12x+1 2/3x=5 3/5	$7 \frac{1}{4} x + x - 2 \frac{11}{12} x + 1 \frac{2}{3} x = 5 \frac{3}{5}$
22896	Solve by Substitution	x-2y=3 and 4x-8y=12	$x - 2 y = 3$ and $4 x - 8 y = 12$
22897	Solve for m	(2m-1)/19=m/10	$\frac{2 m - 1}{19} = \frac{m}{10}$
22898	Simplify	(-4^-2y)^2	${(- 4^{- 2} y)}^{2}$
22899	Find dy/dx	-y^2-xy-2x=0	$- y^{2} - x y - 2 x = 0$
22900	Simplify	square root of -2x^2	$\sqrt{- 2 x^{2}}$