Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
13401	Add	(20mn+5n)+(7mn-2n+3n)	$(20 m n + 5 n) + (7 m n - 2 n + 3 n)$
13402	Simplify	1/(x^(-1/2))	$\frac{1}{x^{\frac{- 1}{2}}}$
13403	Solve the Function Operation	f(x)=3x^2+6x+5 g(x)=-x+3 Find: f(g(x))	$f (x) = 3 x^{2} + 6 x + 5$ $g (x) = - x + 3$ Find: $f (g (x))$
13404	Solve the System of Equations	x^2+y^2=16 3x-4y=20	$x^{2} + y^{2} = 16$ $3 x - 4 y = 20$
13405	Simplify the Radical Expression	( square root of 16)^3	${(\sqrt{16})}^{3}$
13406	Graph	y=1/2cos(2x+1/3pi)	$y = \frac{1}{2} \cos (2 x + \frac{1}{3} π)$
13407	Solve for x	4/(9x^2-1)+1/(3x^2-x)=4/(9x^2-6x+1)	$\frac{4}{9 x^{2} - 1} + \frac{1}{3 x^{2} - x} = \frac{4}{9 x^{2} - 6 x + 1}$
13408	Solve the Inequality for a	-2a+3>=6a-1>3a-10	$- 2 a + 3 \geq 6 a - 1 > 3 a - 10$
13409	Simplify	1/2x^3+1/4x^3	$\frac{1}{2} x^{3} + \frac{1}{4} x^{3}$
13410	Find the Absolute Max and Min over the Interval	f(x)=2/(x^4-16) on interval (0,2)	$f (x) = \frac{2}{x^{4} - 16}$ on interval $(0, 2)$
13411	Evaluate the Integral	integral of csch(1/2x)coth(1/2x) with respect to x	$\int csch (\frac{1}{2} x) \coth (\frac{1}{2} x) d x$
13412	Evaluate	1/6+1/18+1/54+1/162+1/486	$\frac{1}{6} + \frac{1}{18} + \frac{1}{54} + \frac{1}{162} + \frac{1}{486}$
13413	Rationalize the Denominator	(3 square root of 2)/(2- square root of 7)	$\frac{3 \sqrt{2}}{2 - \sqrt{7}}$
13414	Evaluate the Integral	integral of 1/(x cube root of natural log of x) with respect to x	$\int \frac{1}{x \sqrt[3]{\ln (x)}} d x$
13415	Solve for x	3(x-4)<=x-5	$3 (x - 4) \leq x - 5$
13416	Simplify	((36a^5b^8)/(4a^4b^5))^2	${(\frac{36 a^{5} b^{8}}{4 a^{4} b^{5}})}^{2}$
13417	Simplify	(8m^2-7n^2)-(n^2-12m^2)	$(8 m^{2} - 7 n^{2}) - (n^{2} - 12 m^{2})$
13418	Solve for x	4(x-2)^(1/2)=(x+13)^(1/2)	$4 {(x - 2)}^{\frac{1}{2}} = {(x + 13)}^{\frac{1}{2}}$
13419	Simplify	x/(y-1)+5/(1-y)	$\frac{x}{y - 1} + \frac{5}{1 - y}$
13420	Simplify	(6x+24)/(5x-35)*(9x-63)/(7x+28)	$\frac{6 x + 24}{5 x - 35} \cdot \frac{9 x - 63}{7 x + 28}$
13421	Solve for x	-54=10-(x-10)^(3/2)	$- 54 = 10 - {(x - 10)}^{\frac{3}{2}}$
13422	Find the Center and Radius	x^2+y^2+9=4x-10y	$x^{2} + y^{2} + 9 = 4 x - 10 y$
13423	Solve for x	4/3x-8/3=3/2x+7/4	$\frac{4}{3} x - \frac{8}{3} = \frac{3}{2} x + \frac{7}{4}$
13424	Find the Asymptotes	f(x)=tan(pi/2x)	$f (x) = \tan (\frac{π}{2} x)$
13425	Simplify	(8-x^3)/(25x^2+100-100x)	$\frac{(8 - x^{3})}{25 x^{2} + 100 - 100 x}$
13426	Evaluate the Function	p(x)=2x^2-5x-3 for x=4	$p (x) = 2 x^{2} - 5 x - 3$ for $x = 4$
13427	Evaluate the Limit	limit as theta approaches pi of (sin(theta))/(tan(theta))	$lim_{θ \to π} \frac{\sin (θ)}{\tan (θ)}$
13428	Find the Derivative - d/dx	(3(x+2))/(2(x+3)^(1/2))	$\frac{3 (x + 2)}{2 {(x + 3)}^{\frac{1}{2}}}$
13429	Solve the Function Operation	Given h(x)=5x+2 ; find h(-6)	Given $h (x) = 5 x + 2$ ; find $h (- 6)$
13430	Simplify	(3 square root of 5)( square root of 6)( square root of 12)	$(3 \sqrt{5}) (\sqrt{6}) (\sqrt{12})$
13431	Find All Complex Solutions	cot(theta)=- square root of 3	$\cot (θ) = - \sqrt{3}$
13432	Solve for x	4(6-x)-2(3-x)-5=9(5-2x)	$4 (6 - x) - 2 (3 - x) - 5 = 9 (5 - 2 x)$
13433	Simplify the Radical Expression	square root of z/(z^(1/3))	$\sqrt{\frac{z}{z^{\frac{1}{3}}}}$
13434	Multiply	(x+3y-6z)^2	${(x + 3 y - 6 z)}^{2}$
13435	Solve for y	y-x=16 x=12	$y - x = 16$ $x = 12$
13436	Simplify	(x^2+2x-15)/(4x)*(2x^4)/(x^3+5x^2)	$\frac{x^{2} + 2 x - 15}{4 x} \cdot \frac{2 x^{4}}{x^{3} + 5 x^{2}}$
13437	Solve the Function Operation	g(x)=x-11 ; Find g(25)	$g (x) = x - 11$ ; Find $g (25)$
13438	Convert to Radical Form	(3x^2y^2)1/2	$(3 x^{2} y^{2}) \frac{1}{2}$
13439	Rationalize the Denominator	x/( square root of x)	$\frac{x}{\sqrt{x}}$
13440	Factor	12(4-x^2)-2x(4-x^2)-(4-x^2)^2	$12 (4 - x^{2}) - 2 x (4 - x^{2}) - {(4 - x^{2})}^{2}$
13441	Graph	cos(theta)>0 , tan(theta)>0	$\cos (θ) > 0$ , $\tan (θ) > 0$
13442	Simplify the Radical Expression	square root of 48/3	$\sqrt{\frac{48}{3}}$
13443	Find the x and y Intercepts	f(x) = log base 1/4 of x-1+1	$f (x) = \log_{\frac{1}{4}} (x - 1) + 1$
13444	Solve for x	\|x-2\|<8/x	$\| x - 2 \| < \frac{8}{x}$
13445	Rationalize the Denominator	4/(-3+ square root of 2)	$\frac{4}{- 3 + \sqrt{2}}$
13446	Simplify	(-10a^3b^2+25a^2b^5-5a^2b)/(-5a^2b)	$\frac{- 10 a^{3} b^{2} + 25 a^{2} b^{5} - 5 a^{2} b}{- 5 a^{2} b}$
13447	Simplify	square root of 2( square root of 50+7)	$\sqrt{2} (\sqrt{50} + 7)$
13448	Solve for m	12m^2+11m=15	$12 m^{2} + 11 m = 15$
13449	Solve for b	f=(t^2+4b)/c	$f = \frac{t^{2} + 4 b}{c}$
13450	Find Amplitude, Period, and Phase Shift	f(x)=3cot(4t)-5	$f (x) = 3 \cot (4 t) - 5$
13451	Solve for x	8 cube root of 2x=4x	$8 \sqrt[3]{2 x} = 4 x$
13452	Solve the Function Operation	f(x)=x-7 g(x)=3x^2-7x-10 Find: (fog)(x)	$f (x) = x - 7$ $g (x) = 3 x^{2} - 7 x - 10$ Find: $((f \circ g)) (x)$
13453	Convert to Trigonometric Form	cos(theta)+sin(theta)*tan(theta)	$\cos (θ) + \sin (θ) \cdot \tan (θ)$
13454	Evaluate	y+17=3(x+6)-14	$y + 17 = 3 (x + 6) - 14$
13455	Simplify	(2+ square root of 5)(-2+ square root of 5k)	$(2 + \sqrt{5}) (- 2 + \sqrt{5 k})$
13456	Solve for x	1/2x-1/3(x-9)=3x	$\frac{1}{2} x - \frac{1}{3} (x - 9) = 3 x$
13457	Solve for x	4^x=16 square root of 128	$4^{x} = 16 \sqrt{128}$
13458	Simplify	((6*4^n)/(4^(2n+1)+2^(4n+1)))^(n^-1)	${(\frac{6 \times 4^{n}}{4^{2 n + 1} + 2^{4 n + 1}})}^{n^{- 1}}$
13459	Find the Cotangent of the Angle	270	$270$
13460	Find the Exact Value	sec(570 degrees )	$\sec (570 °)$
13461	Simplify	(m^2+5m+6)/(m^2-4)-2/(m-2)	$\frac{m^{2} + 5 m + 6}{m^{2} - 4} - \frac{2}{m - 2}$
13462	Find dy/dx	x^2+3-5y=xy	$x^{2} + 3 - 5 y = x y$
13463	Simplify	(4i)+(-1+7i)+5	$(4 i) + (- 1 + 7 i) + 5$
13464	Solve for x	square root of 2x+1 = square root of 7x-13	$\sqrt{2 x} + 1 = \sqrt{7 x - 13}$
13465	Determine if (2,2) is a Solution	5x+y<=12 , (2,2)	$5 x + y \leq 12$ , $(2, 2)$
13466	Factor	3(2x-3)^2(5x-6)+(2x-3)(5x-6)^2	$3 {(2 x - 3)}^{2} (5 x - 6) + (2 x - 3) {(5 x - 6)}^{2}$
13467	Simplify	(a^(3/4)b^-1*b^(7/4))/(3b^-1)	$\frac{a^{\frac{3}{4}} b^{- 1} \cdot b^{\frac{7}{4}}}{3 b^{- 1}}$
13468	Graph	2y<-4x+8	$2 y < - 4 x + 8$
13469	Simplify	1/( square root of 3/2)	$\frac{1}{\sqrt{\frac{3}{2}}}$
13470	Simplify	4^-2x^3y^-5z^0	$4^{- 2} x^{3} y^{- 5} z^{0}$
13471	Write in Standard Form	y^2-6y+8x=15	$y^{2} - 6 y + 8 x = 15$
13472	Simplify	((3^0)/(3^-1))^2	${(\frac{3^{0}}{3^{- 1}})}^{2}$
13473	Write as a Single Logarithm	1+3 natural log of x-4 natural log of y-1/2 natural log of z	$1 + 3 \ln (x) - 4 \ln (y) - \frac{1}{2} \ln (z)$
13474	Simplify	(3/(3x^2-147)*(3x^2+24x+21)/(6x^3+18x^2+12x))÷((x-2)/(x^2-4))	$\frac{3}{3 x^{2} - 147} \cdot \frac{3 x^{2} + 24 x + 21}{6 x^{3} + 18 x^{2} + 12 x} \div \frac{x - 2}{x^{2} - 4}$
13475	Solve the System of Equations	y=x^2-4x+4 3x+y=10	$y = x^{2} - 4 x + 4$ $3 x + y = 10$
13476	Write in Standard Form	(3x^2-7x)-(4x^2+6x)	$(3 x^{2} - 7 x) - (4 x^{2} + 6 x)$
13477	Graph	2x-y>=0 3x+y<5	$2 x - y \geq 0$ $3 x + y < 5$
13478	Divide	7 1/2÷6	$7 \frac{1}{2} \div 6$
13479	Simplify	(3v)^(2/3)*(3v)	${(3 v)}^{\frac{2}{3}} \cdot (3 v)$
13480	Simplify	(-8m^4n^7)^2-(2m^2n)^3*(5m^2n^11)	${(- 8 m^{4} n^{7})}^{2} - {(2 m^{2} n)}^{3} \cdot (5 m^{2} n^{11})$
13481	Multiply	2pi*2	$2 π \cdot 2$
13482	Simplify	(x+2)/(x+3)-5/(x^2+x-6)+1/(2-x)	$\frac{x + 2}{x + 3} - \frac{5}{x^{2} + x - 6} + \frac{1}{2 - x}$
13483	Solve the Inequality for m	m/-5<-3	$\frac{m}{- 5} < - 3$
13484	Solve for x	2 log base 2 of x- log base 2 of 2x=3	$2 \log_{2} (x) - \log_{2} (2 x) = 3$
13485	Solve for x	-4x+2x+5=-6-5x+8	$- 4 x + 2 x + 5 = - 6 - 5 x + 8$
13486	Solve by Substitution	y=2x-4 and 6x-3y=12	$y = 2 x - 4$ and $6 x - 3 y = 12$
13487	Solve the Inequality for x	x^2+8>=6x	$x^{2} + 8 \geq 6 x$
13488	Simplify the Radical Expression	(x^(5/6))/(x^(1/6))	$\frac{x^{\frac{5}{6}}}{x^{\frac{1}{6}}}$
13489	Find the Directrix	y=(x+3)^2-4	$y = {(x + 3)}^{2} - 4$
13490	Evaluate	18+(36÷9)	$18 + (36 \div 9)$
13491	Solve for A	y=-Ax+8	$y = - A x + 8$
13492	Evaluate Using the Given Value	2x^2-y^1+3x^0 for x=3 and y=5	$2 x^{2} - y^{1} + 3 x^{0}$ for $x = 3$ and $y = 5$
13493	Solve for x	cube root of x+4 = cube root of 3x-6	$\sqrt[3]{x + 4} = \sqrt[3]{3 x - 6}$
13494	Solve for x	x^2-2-3xcos(x)=0	$x^{2} - 2 - 3 x \cos (x) = 0$
13495	Evaluate	x/( square root of 2)	$\frac{x}{\sqrt{2}}$
13496	Find the Inverse	y=e^(3-x)	$y = e^{3 - x}$
13497	Find the Product	b(b^2-12b+1)	$b (b^{2} - 12 b + 1)$
13498	Evaluate the Integral	integral from 1 to 4 of (2- square root of t)/(t^2) with respect to t	$\int_{1}^{4} \frac{2 - \sqrt{t}}{t^{2}} d t$
13499	Simplify	i^3*i^7	$i^{3} \cdot i^{7}$
13500	Find the x and y Intercepts	f(x)=(3/2)^(-x)-7	$f (x) = {(\frac{3}{2})}^{- x} - 7$