Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
12501	Solve by Substitution	y=-1x-5 4x-8y=4	$y = - 1 x - 5$ $4 x - 8 y = 4$
12502	Simplify	x(3x^2+4)+2(7x-3)	$x (3 x^{2} + 4) + 2 (7 x - 3)$
12503	Evaluate	csc(theta) = square root of 2	$\csc (θ) = \sqrt{2}$
12504	Simplify	((x^2)/9+1/4)/(6x)	$\frac{\frac{x^{2}}{9} + \frac{1}{4}}{6 x}$
12505	Solve the Function Operation	f(x)=-x^3 , (f(a+h)-f(a))/h	$f (x) = - x^{3}$ , $\frac{f (a + h) - f (a)}{h}$
12506	Evaluate the Limit	limit as x approaches 0 of x/( square root of 1+x- square root of 1-x)	$lim_{x \to 0} \frac{x}{\sqrt{1 + x} - \sqrt{1 - x}}$
12507	Find the Average Value of the Function	f(x)=3/x , [1,7]	$f (x) = \frac{3}{x}$ , $[1, 7]$
12508	Determine if a Polynomial	-10x^6-2x^5+4x^4+7x^3-9x^2+5.5x-1	$- 10 x^{6} - 2 x^{5} + 4 x^{4} + 7 x^{3} - 9 x^{2} + 5.5 x - 1$
12509	Evaluate the Limit	limit as x approaches pi/((2)^(-)) of tan(x)	$lim_{x \to \frac{π}{{(2)}^{-}}} \tan (x)$
12510	Simplify	(32ab^4)/(-8a^-2b)-3a^3b^3	$\frac{32 a b^{4}}{- 8 a^{- 2} b} - 3 a^{3} b^{3}$
12511	Solve for x	3/(6x-48)+1=3/(x-8)	$\frac{3}{6 x - 48} + 1 = \frac{3}{x - 8}$
12512	Simplify	5x-3(x-2)-x	$5 x - 3 (x - 2) - x$
12513	Solve by Substitution	y=-3x+7 3x-5=-y	$y = - 3 x + 7$ $3 x - 5 = - y$
12514	Write the Fraction in Simplest Form	( square root of 2+ square root of 5)/( square root of 2- square root of 5)	$\frac{\sqrt{2} + \sqrt{5}}{\sqrt{2} - \sqrt{5}}$
12515	Simplify the Radical Expression	2 square root of 5+5 square root of 5-4 square root of 5	$2 \sqrt{5} + 5 \sqrt{5} - 4 \sqrt{5}$
12516	Find the Inverse	f(x) = square root of x+2+9	$f (x) = \sqrt{x + 2 + 9}$
12517	Solve the Rational Equation for x	fourth root of 8x+12-9=-11	$\sqrt[4]{8 x + 12} - 9 = - 11$
12518	Simplify	(12x^3y^2z)/(16xy^3z^2)	$\frac{12 x^{3} y^{2} z}{16 x y^{3} z^{2}}$
12519	Simplify	x+2+x+2+x	$x + 2 + x + 2 + x$
12520	Solve for b	5/6b=1 7/8	$\frac{5}{6} b = 1 \frac{7}{8}$
12521	Simplify	(3x+5)+(4x^2-2)-(x^2-3x+1)	$(3 x + 5) + (4 x^{2} - 2) - (x^{2} - 3 x + 1)$
12522	Simplify	(x-2)/(10x^2+12x)-5/2	$\frac{x - 2}{10 x^{2} + 12 x} - \frac{5}{2}$
12523	Evaluate	(y^-2y^6)/(x^-7x^6)	$\frac{y^{- 2} y^{6}}{x^{- 7} x^{6}}$
12524	Factor	Factor 4x^2-9	Factor $4 x^{2} - 9$
12525	Find the Asymptotes	f(x)=(x-6)/(x^2-6x)	$f (x) = \frac{x - 6}{x^{2} - 6 x}$
12526	Write as a Single Logarithm	1/3 log of x+3 log of x-3	$\frac{1}{3} \log (x) + 3 \log (x - 3)$
12527	Solve the Inequality for m	m+1/3<-2 1/4	$m + \frac{1}{3} < - 2 \frac{1}{4}$
12528	Find dy/dx	-xy=4-5y^3	$- x y = 4 - 5 y^{3}$
12529	Graph	y=-0.0005x^2+1.2345x+-2.2	$y = - 0.0005 x^{2} + 1.2345 x + - 2.2$
12530	Simplify	-13m+2/5m(25m-10)	$- 13 m + \frac{2}{5} m (25 m - 10)$
12531	Simplify	(csc(theta)*cos(theta))/(tan(theta)+cot(theta))	$\frac{\csc (θ) \cdot \cos (θ)}{\tan (θ) + \cot (θ)}$
12532	Solve for x	log base 7 of 2x^2-2- log base 7 of x+1=1	$\log_{7} (2 x^{2} - 2) - \log_{7} (x + 1) = 1$
12533	Solve for b	4b^(-3/4)+10=21/2	$4 b^{- \frac{3}{4}} + 10 = \frac{21}{2}$
12534	Simplify	((-4)^-2)÷(4^-4)	${(- 4)}^{- 2} \div 4^{- 4}$
12535	Simplify the Radical Expression	3 square root of 2(4 square root of 2- square root of 3)	$3 \sqrt{2} (4 \sqrt{2} - \sqrt{3})$
12536	Solve for x	sin(x)+xcos(x)=0	$\sin (x) + x \cos (x) = 0$
12537	Find f(g(x))	f(x)=2x^3+2x-3 g(x)=-0.5\|x-4\|	$f (x) = 2 x^{3} + 2 x - 3$ $g (x) = - 0.5 \| x - 4 \|$
12538	Simplify	(y+4)^3-2y(y-1)	${(y + 4)}^{3} - 2 y (y - 1)$
12539	Divide	(5/8)÷4 1/6	$\frac{5}{8} \div 4 \frac{1}{6}$
12540	Simplify	(8x^2)/3*(8x^2)/9	$\frac{8 x^{2}}{3} \cdot \frac{8 x^{2}}{9}$
12541	Solve the Function Operation	f(x)=2x^2-5x+10 g(x)=-2x-3 Find: f(g(x))	$f (x) = 2 x^{2} - 5 x + 10$ $g (x) = - 2 x - 3$ Find: $f (g (x))$
12542	Find Amplitude, Period, and Phase Shift	y=3csc(x-(3pi)/2)	$y = 3 \csc (x - \frac{3 π}{2})$
12543	Find the Axis of Symmetry	f(x)=2+4x-x^2	$f (x) = 2 + 4 x - x^{2}$
12544	Find the Asymptotes	f(x)=(x^3-2x^2-8x)/(3x^2-27)	$f (x) = \frac{x^{3} - 2 x^{2} - 8 x}{3 x^{2} - 27}$
12545	Write in Standard Form	8a^3b^3	$8 a^{3} b^{3}$
12546	Simplify	cube root of (32x^12y^3)/(4x^3)	$\sqrt[3]{\frac{32 x^{12} y^{3}}{4 x^{3}}}$
12547	Find the Perfect Square Trinomial	(2x+3)(2x-4)	$(2 x + 3) (2 x - 4)$
12548	Simplify	( eighth root of 4)/( fourth root of 4)	$\frac{\sqrt[8]{4}}{\sqrt[4]{4}}$
12549	Simplify	(-4a^3b^2)^2*1/2a^3b	${(- 4 a^{3} b^{2})}^{2} \cdot \frac{1}{2} a^{3} b$
12550	Simplify	(3xy^-2)^2(2x^3yz)(6yz^2)^-1	${(3 x y^{- 2})}^{2} (2 x^{3} y z) {(6 y z^{2})}^{- 1}$
12551	Divide	(30x^4+12x^3+30x^2)÷6	$(30 x^{4} + 12 x^{3} + 30 x^{2}) \div 6$
12552	Simplify	((-9c^3d)/(c^2d^2))^2	${(\frac{- 9 c^{3} d}{c^{2} d^{2}})}^{2}$
12553	Find dy/dx	-4+2y^2+2x^2+5y^3=0	$- 4 + 2 y^{2} + 2 x^{2} + 5 y^{3} = 0$
12554	Write in Standard Form	(x^2)/3	$\frac{x^{2}}{3}$
12555	Solve by Substitution	y=8x-9 y=7	$y = 8 x - 9$ $y = 7$
12556	Solve the Inequality for x	((x-4)(x+1))/(x-3)<0	$\frac{(x - 4) (x + 1)}{x - 3} < 0$
12557	Evaluate	(7)(-4)+(3(11-15))/-2	$(7) (- 4) + \frac{3 (11 - 15)}{- 2}$
12558	Solve for x	\|x-5\|+\|x+2\|<8	$\| x - 5 \| + \| x + 2 \| < 8$
12559	Simplify	tan(x)^2sec(x)^2-tan(x)^2	$\tan^{2} (x) \sec^{2} (x) - \tan^{2} (x)$
12560	Graph	1/4y^2=x	$\frac{1}{4} y^{2} = x$
12561	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (2-e^(x/2))^(4/x)	$lim_{x \to 0} {(2 - e^{\frac{x}{2}})}^{\frac{4}{x}}$
12562	Simplify the Radical Expression	(4+ square root of 2)/(5 square root of 2-2)	$\frac{4 + \sqrt{2}}{5 \sqrt{2} - 2}$
12563	Find the Exact Value	cos(arccsc((2)^-1))	$\cos (arccsc ({(2)}^{- 1}))$
12564	Simplify	(-4x^2y)(3xy^2-4xy)	$(- 4 x^{2} y) (3 x y^{2} - 4 x y)$
12565	Solve for x	-2/5(x+3)=8	$- \frac{2}{5} (x + 3) = 8$
12566	Find the Axis of Symmetry	f(x)=3x^2+x	$f (x) = 3 x^{2} + x$
12567	Find the x and y Intercepts	y=2/3	$y = \frac{2}{3}$
12568	Add	Find the sum of -10x^2-x+6 and 10x^2-5	Find the sum of $- 10 x^{2} - x + 6$ and $10 x^{2} - 5$
12569	Solve for x	\|x-2\|-3<=0	$\| x - 2 \| - 3 \leq 0$
12570	Simplify	(3x)/(x^2-2x-3)-(6x)/(x-3)	$\frac{3 x}{x^{2} - 2 x - 3} - \frac{6 x}{x - 3}$
12571	Solve for x	2/(x+1)=(x-6)/(x^2-1)	$\frac{2}{x + 1} = \frac{x - 6}{x^{2} - 1}$
12572	Find the Domain	2tan(x)^2=2cot(x)+1	$2 \tan^{2} (x) = 2 \cot (x) + 1$
12573	Simplify	(x/(x^2+1))((x^2+4)/3)	$(\frac{x}{x^{2} + 1}) (\frac{x^{2} + 4}{3})$
12574	Solve for c	18/c=3/5	$\frac{18}{c} = \frac{3}{5}$
12575	Solve for y	-4y-3=1/3(12y-9)-8y	$- 4 y - 3 = \frac{1}{3} (12 y - 9) - 8 y$
12576	Evaluate the Limit	limit as x approaches 3 of x^4+x^3-4x^2-2x+1	$lim_{x \to 3} x^{4} + x^{3} - 4 x^{2} - 2 x + 1$
12577	Simplify	-2p^4q^-2*3p^-3q^-4	$- 2 p^{4} q^{- 2} \cdot 3 p^{- 3} q^{- 4}$
12578	Simplify	24 root of s*s^8	$\sqrt[24]{s \cdot s^{8}}$
12579	Find the Antiderivative	cos(x)sin(x)	$\cos (x) \sin (x)$
12580	Evaluate the Function	f(1)=(2t(t+1))/(t-1)-(3+t)/(t-1)	$f (1) = \frac{2 t (t + 1)}{t - 1} - \frac{3 + t}{t - 1}$
12581	Solve the Inequality for f	26<f+32	$26 < f + 32$
12582	Convert to Radical Form	(x^3y^7z^4)^(1/2)	${(x^{3} y^{7} z^{4})}^{\frac{1}{2}}$
12583	Simplify	((x^2-6x+8)/(3x-12))÷((x^2-4)/(x^2+5x+6))	$\frac{x^{2} - 6 x + 8}{3 x - 12} \div \frac{x^{2} - 4}{x^{2} + 5 x + 6}$
12584	Divide	(-x)÷(-2)	$- x \div (- 2)$
12585	Write in Standard Form	square root of 3-12x+13x^2	$\sqrt{3} - 12 x + 13 x^{2}$
12586	Convert to Trigonometric Form	(sin(theta))/(1+cos(theta))	$\frac{\sin (θ)}{1 + \cos (θ)}$
12587	Evaluate the Integral	integral of (2x^2e^(5x^3+1))/(3-e^(5x^3+1)) with respect to x	$\int \frac{2 x^{2} e^{5 x^{3} + 1}}{3 - e^{5 x^{3} + 1}} d x$
12588	Solve for x	32/60=(2x+6)/52.5	$\frac{32}{60} = \frac{2 x + 6}{52.5}$
12589	Convert from Degrees to Radians	285deg	$285$ degrees
12590	Write the Fraction in Simplest Form	(20v^9)/((4v)^2)	$\frac{20 v^{9}}{{(4 v)}^{2}}$
12591	Solve the Function Operation	f(x)=-3x-14 g(x)=3x^2-x+15 Find: (fog)(x)	$f (x) = - 3 x - 14$ $g (x) = 3 x^{2} - x + 15$ Find: $((f \circ g)) (x)$
12592	Graph	x+0y=-2	$x + 0 y = - 2$
12593	Simplify	(2m+15a-5)+(5a+10)	$(2 m + 15 a - 5) + (5 a + 10)$
12594	Write in Standard Form	(4h^3+6h^2+1)-(5h^2-8h^4+6)	$(4 h^{3} + 6 h^{2} + 1) - (5 h^{2} - 8 h^{4} + 6)$
12595	Simplify	(5n+15)/(4n+8)*(2n+4)/(3n+9)	$\frac{5 n + 15}{4 n + 8} \cdot \frac{2 n + 4}{3 n + 9}$
12596	Solve for x	fifth root of 32^x=1/8	$\sqrt[5]{32^{x}} = \frac{1}{8}$
12597	Simplify	6m+4-3mn+m+5-8mn+6	$6 m + 4 - 3 m n + m + 5 - 8 m n + 6$
12598	Find the Roots (Zeros)	(x+5)/(y-3)=0	$\frac{(x + 5)}{(y - 3)} = 0$
12599	Solve the Inequality for x	x^2+3x+4<8x	$x^{2} + 3 x + 4 < 8 x$
12600	Solve for y	x=3( cube root of 15+y)	$x = 3 (\sqrt[3]{15 + y})$