Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
40401	Evaluate the Integral	integral of (1-x)/(x^2) with respect to x	$\int \frac{1 - x}{x^{2}} d x$
40402	Simplify	(5ab)/(a^2-b^2)+(a+b)/(a-b)	$\frac{5 a b}{a^{2} - b^{2}} + \frac{a + b}{a - b}$
40403	Simplify	1/(5m)-2/(3n)	$\frac{1}{5 m} - \frac{2}{3 n}$
40404	Solve the System of Equations	x=5 x+y=12	$x = 5$ $x + y = 12$
40405	Simplify	((x^2-81)/(x^2-14x+45)*(x^2-12x+35)/(-x-9))÷((7-x)/-4)	$\frac{x^{2} - 81}{x^{2} - 14 x + 45} \cdot \frac{x^{2} - 12 x + 35}{- x - 9} \div \frac{7 - x}{- 4}$
40406	Simplify	2y-3x^2+6x^2-3y	$2 y - 3 x^{2} + 6 x^{2} - 3 y$
40407	Write in Exponential Form	cube root of (4x-7)^24	$\sqrt[3]{{(4 x - 7)}^{24}}$
40408	Rationalize the Denominator	(3r^3)/( square root of 20r)	$\frac{3 r^{3}}{\sqrt{20 r}}$
40409	Solve the System of Inequalities	3m+2<5 OR (m+1)/2>4	$3 m + 2 < 5$ OR $\frac{m + 1}{2} > 4$
40410	Simplify	((x^-2y^-3)/(2^0z^-1))^-2	${(\frac{x^{- 2} y^{- 3}}{2^{0} z^{- 1}})}^{- 2}$
40411	Graph	g(x)=1/3f(x)-2	$g (x) = \frac{1}{3} f (x) - 2$
40412	Divide Using Long Polynomial Division	(2x^3-2)÷(x-5)	$(2 x^{3} - 2) \div (x - 5)$
40413	Add	(4)+(14-4i)	$(4) + (14 - 4 i)$
40414	Solve the Inequality for x	2x^2+5x<=2x+5	$2 x^{2} + 5 x \leq 2 x + 5$
40415	Convert to a Decimal	5 percent	$5$ percent
40416	Solve the System of Inequalities	y<-x-6 y>1/2x-3	$y < - x - 6$ $y > \frac{1}{2} x - 3$
40417	Find the Antiderivative	f(x)=x^(3/4)+8 cube root of x+3x^5	$f (x) = x^{\frac{3}{4}} + 8 \sqrt[3]{x} + 3 x^{5}$
40418	Find the Derivative - d/dx	1/2sec(x)^2	$\frac{1}{2} \sec^{2} (x)$
40419	Solve the System of Inequalities	y>1/2x+1 y+3x<=6	$y > \frac{1}{2} x + 1$ $y + 3 x \leq 6$
40420	Find the Excluded Values	(6x(x+3)(x-2))/(3(x-2)(x+9))	$\frac{6 x (x + 3) (x - 2)}{3 (x - 2) (x + 9)}$
40421	Solve for x	x/( square root of x+11)-1=1/( square root of x+11)	$\frac{x}{\sqrt{x + 11}} - 1 = \frac{1}{\sqrt{x + 11}}$
40422	Convert to a Decimal	21 , 5%	$21$ , $5 %$
40423	Divide Using Long Polynomial Division	4x^3+8x^2+13x+5 divided by 2x+1	$4 x^{3} + 8 x^{2} + 13 x + 5$ divided by $2 x + 1$
40424	Describe the Transformation	f(x-3)+5	$f (x - 3) + 5$
40425	Solve the Absolute Value Inequality for r	\|2r+3\|=\|5r-17\|	$\| 2 r + 3 \| = \| 5 r - 17 \|$
40426	Solve the Rational Equation for y	square root of y=3 square root of 5	$\sqrt{y} = 3 \sqrt{5}$
40427	Solve for x	-9<-1/5x	$- 9 < - \frac{1}{5} x$
40428	Evaluate	3/2+2 1/4-7/8	$\frac{3}{2} + 2 \frac{1}{4} - \frac{7}{8}$
40429	Simplify	-(7i)^2	$- {(7 i)}^{2}$
40430	Find the Derivative - d/dx	-y/(x-1)	$- \frac{y}{x - 1}$
40431	Solve for x	x/5+(x-1)/3=2	$\frac{x}{5} + \frac{x - 1}{3} = 2$
40432	Evaluate	2^( log base 2 of 6-3)	$2^{\log_{2} (6) - 3}$
40433	Evaluate	square root of 9-(-1)^2	$\sqrt{9 - {(- 1)}^{2}}$
40434	Graph	x+2y<=3 x+y>=4 3x-2y>=4	$x + 2 y \leq 3$ $x + y \geq 4$ $3 x - 2 y \geq 4$
40435	Write the Fraction in Simplest Form	((36y)/(y^2-2y+1))÷((12y^2)/(y^2-1))	$\frac{36 y}{y^{2} - 2 y + 1} \div \frac{12 y^{2}}{y^{2} - 1}$
40436	Simplify the Radical Expression	square root of 3(4+5 square root of 3)	$\sqrt{3} (4 + 5 \sqrt{3})$
40437	Find the Derivative - d/dx	e^(1/2x^2)	$e^{\frac{1}{2} x^{2}}$
40438	Simplify	(x+4)/(2x+10)-5/(x^2-25)	$\frac{x + 4}{2 x + 10} - \frac{5}{x^{2} - 25}$
40439	Graph	F(x)=(q(x))/(x^2+12x+36)	$F (x) = \frac{q (x)}{x^{2} + 12 x + 36}$
40440	Find the Parallel Line	through: (-4,0) ; parallel to y=3/4x-2	through: $(- 4, 0)$ ; parallel to $y = \frac{3}{4} x - 2$
40441	Evaluate	(4.9(4.1)^2-4.9(4)^2)/0.1	$\frac{4.9 {(4.1)}^{2} - 4.9 {(4)}^{2}}{0.1}$
40442	Simplify	Simplify fourth root of x^12	Simplify $\sqrt[4]{x^{12}}$
40443	Multiply	2 square root of 3-x*4 cube root of 3-x	$2 \sqrt{3 - x} \cdot 4 \sqrt[3]{3 - x}$
40444	Multiply	(x^2+6y)(x^2-6y)	$(x^{2} + 6 y) (x^{2} - 6 y)$
40445	Find the Reference Angle	cot(150 degrees )	$\cot (150 °)$
40446	Find the Roots (Zeros)	f(x)=((3x+4)(x+2))/((x-4)(x+2))	$f (x) = \frac{(3 x + 4) (x + 2)}{(x - 4) (x + 2)}$
40447	Graph	table[[x,y],[0,0],[1,1],[2,4],[3,9]]	$\begin{array}{c} x & y \\ 0 & 0 \\ 1 & 1 \\ 2 & 4 \\ 3 & 9 \end{array}$
40448	Evaluate	((1/64)^(1/3))^-4	${({(\frac{1}{64})}^{\frac{1}{3}})}^{- 4}$
40449	Find the Domain	((m^2-3m)/(8x^2))÷((3m)/(8x))	$\frac{m^{2} - 3 m}{8 x^{2}} \div \frac{3 m}{8 x}$
40450	Find the Antiderivative	(x^3)/( square root of x^2+1)	$\frac{x^{3}}{\sqrt{x^{2} + 1}}$
40451	Multiply	(a+b-c)(a-b+C)	$(a + b - c) (a - b + C)$
40452	Divide	((x^2-4)/(x-3))÷((x^2+7x-18)/(x+9))	$\frac{x^{2} - 4}{x - 3} \div \frac{x^{2} + 7 x - 18}{x + 9}$
40453	Solve the Inequality for y	-4(2y+3)<=20-4y	$- 4 (2 y + 3) \leq 20 - 4 y$
40454	Solve for θ	2-sin(2theta)=4sin(2theta)	$2 - \sin (2 θ) = 4 \sin (2 θ)$
40455	Find the Derivative of the Integral	h(x) = integral from 1 to square root of x of (5z^2)/(z^4+1) with respect to z	$h (x) = \int_{1}^{\sqrt{x}} \frac{5 z^{2}}{z^{4} + 1} d z$
40456	Simplify	1/4x-4/3+7/2x+5/6	$\frac{1}{4} x - \frac{4}{3} + \frac{7}{2} x + \frac{5}{6}$
40457	Solve for x	16^(2x-3)*4^(-2x)=2^4	$16^{2 x - 3} \cdot 4^{- 2 x} = 2^{4}$
40458	Add	(7x^4+4-x+3x^3)+(5x^3+3x-9)	$(7 x^{4} + 4 - x + 3 x^{3}) + (5 x^{3} + 3 x - 9)$
40459	Simplify	(a^2bc^3)(3a^3bc^4)^2	$(a^{2} b c^{3}) {(3 a^{3} b c^{4})}^{2}$
40460	Graph	f(x)=-2x g(x)=-2x-3	$f (x) = - 2 x$ $g (x) = - 2 x - 3$
40461	Solve the Inequality for x	x^2*5^x-5^(2+x)<0	$x^{2} \cdot 5^{x} - 5^{2 + x} < 0$
40462	Simplify	4x+7+3y-(1+3y+2x)	$4 x + 7 + 3 y - (1 + 3 y + 2 x)$
40463	Solve for k	1/2(10k-16)+11=-2	$\frac{1}{2} (10 k - 16) + 11 = - 2$
40464	Solve for n	4n^2=81	$4 n^{2} = 81$
40465	Evaluate the Limit	limit as x approaches 2 of ( square root of x+7+3)/x	$lim_{x \to 2} \frac{\sqrt{x + 7} + 3}{x}$
40466	Graph	x^2+(y-4 square root of x^2)^2=1	$x^{2} + {(y - 4 \sqrt{x^{2}})}^{2} = 1$
40467	Simplify	((3x+6y)^2)/(5x+10y)	$\frac{{(3 x + 6 y)}^{2}}{5 x + 10 y}$
40468	Evaluate	(3/2x^-7)(2x^-1)^5	$(\frac{3}{2} x^{- 7}) {(2 x^{- 1})}^{5}$
40469	Solve the Absolute Value Inequality for x	2-2\|7+2x\|=0	$2 - 2 \| 7 + 2 x \| = 0$
40470	Simplify	(6+yi)(5+i)-(6+yi)(5-4i)	$(6 + y i) (5 + i) - (6 + y i) (5 - 4 i)$
40471	Simplify	(1/(25^-1))^2	${(\frac{1}{25^{- 1}})}^{2}$
40472	Evaluate the Limit	limit as x approaches infinity of (x^4)/(3x^2-7x)	$lim_{x \to \infty} \frac{x^{4}}{3 x^{2} - 7 x}$
40473	Simplify	4s+1/6s+2 3/5s	$4 s + \frac{1}{6} s + 2 \frac{3}{5} s$
40474	Find the Geometric Mean	3 and 48	$3$ and $48$
40475	Evaluate	e-1/2	$e - \frac{1}{2}$
40476	Find the Derivative - d/dx	4x^4-1/(4x^4)	$4 x^{4} - \frac{1}{4 x^{4}}$
40477	Evaluate	f(-2)+f(3)	$f (- 2) + f (3)$
40478	Solve for b	b = square root of 182.8* square root of 182.8	$b = \sqrt{182.8} \cdot \sqrt{182.8}$
40479	Simplify the Radical Expression	(xy^-6)^2	${(x y^{- 6})}^{2}$
40480	Simplify	(x^2+7x+12)/(x^2-4)*(x+2)/(x^2-16)	$\frac{x^{2} + 7 x + 12}{x^{2} - 4} \cdot \frac{x + 2}{x^{2} - 16}$
40481	Find the Exact Value	(2(3+5)+6)4	$(2 \cdot (3 + 5) + 6) \cdot 4$
40482	Simplify	z^12*6^6	$z^{12} \cdot 6^{6}$
40483	Simplify	square root of 64+(3^2+(9-4(6-1))+5)	$\sqrt{64} + (3^{2} + (9 - 4 (6 - 1)) + 5)$
40484	Simplify	(2+- square root of 36)/6	$\frac{2 + - \sqrt{36}}{6}$
40485	Find the Domain	(4x)/(9x^(1/2))	$\frac{4 x}{9 x^{\frac{1}{2}}}$
40486	Convert from Degrees to Radians	130deg	$130$ degrees
40487	Evaluate	(2x^2y)/(6xy^-1)	$\frac{2 x^{2} y}{6 x y^{- 1}}$
40488	Solve for V	V=10.35 square root of 32	$V = 10.35 \sqrt{32}$
40489	Simplify the Radical Expression	fourth root of 12* fourth root of 8	$\sqrt[4]{12} \cdot \sqrt[4]{8}$
40490	Convert to a Decimal	-160deg	$- 160$ degrees
40491	Simplify	(x^-3y^5z^-4)*(x^6y^-7z^-2)	$(x^{- 3} y^{5} z^{- 4}) \cdot (x^{6} y^{- 7} z^{- 2})$
40492	Multiply	(t^2-2t-3)/(t+1)*(3t-3)/(t^2+2t-3)	$\frac{t^{2} - 2 t - 3}{t + 1} \cdot \frac{3 t - 3}{t^{2} + 2 t - 3}$
40493	Find the Domain and Range	f(x)=sin(arcsin(x))	$f (x) = \sin (\arcsin (x))$
40494	Find the Quotient	(3x^3+9x^2-6x)/(-3x)	$\frac{3 x^{3} + 9 x^{2} - 6 x}{- 3 x}$
40495	Find the Third Derivative	S(t)=1/3t^3-3.5t^2+10t	$S (t) = \frac{1}{3} t^{3} - 3.5 t^{2} + 10 t$
40496	Find the Points of Intersection	y=3x+8 and y=3x-2	$y = 3 x + 8$ and $y = 3 x - 2$
40497	Find dy/dx	y=(x^3-4)^4sin(3x^3)	$y = {(x^{3} - 4)}^{4} \sin (3 x^{3})$
40498	Solve by Substitution	y=x-1 2x-y=0	$y = x - 1$ $2 x - y = 0$
40499	Simplify	natural log of 6/(e^2)	$\ln (\frac{6}{e^{2}})$
40500	Add	(-4x+4x^3+7)+(3x^3-9-3x)	$(- 4 x + 4 x^{3} + 7) + (3 x^{3} - 9 - 3 x)$