Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
3601	Evaluate the Integral	integral from 0 to pi of integral from 0 to 2pi of cos(theta)sin(theta)sin(x)^2(sin(x)-sin(theta)) with respect to theta with respect to x	$\int_{0}^{π} \int_{0}^{2 π} \cos (θ) \sin (θ) \sin^{2} (x) (\sin (x) - \sin (θ)) d θ d x$
3602	Solve for v	3(1.4v-1)=0.2v+1	$3 (1.4 v - 1) = 0.2 v + 1$
3603	Solve for n	4x^2+nx=-9	$4 x^{2} + n x = - 9$
3604	Evaluate	-3^-1+3	$- 3^{- 1} + 3$
3605	Simplify	(3x+5)/(2x-1)+(7x+3)/(1-2x)	$\frac{3 x + 5}{2 x - 1} + \frac{7 x + 3}{1 - 2 x}$
3606	Simplify the Radical Expression	square root of 3^3*6^3	$\sqrt{3^{3}} \cdot 6^{3}$
3607	Solve for m₂	(1-2/3m_2)(1)=m_2+2/3	$(1 - \frac{2}{3} m_{2}) (1) = m_{2} + \frac{2}{3}$
3608	Find the Derivative - d/dx	2(sin(x))/(cos(x))+2cot(x)*sin(x)	$2 \frac{\sin (x)}{\cos (x)} + 2 \cot (x) \cdot \sin (x)$
3609	Find the Domain	(3x^2-12)/(x^2-x-6)	$\frac{3 x^{2} - 12}{x^{2} - x - 6}$
3610	Write in Exponential Form	(n root of a)^n	${(\sqrt[n]{a})}^{n}$
3611	Simplify	( square root of 8m^2)/( square root of 6m)	$\frac{\sqrt{8 m^{2}}}{\sqrt{6 m}}$
3612	Find the Antiderivative	27x^2+cos(x)	$27 x^{2} + \cos (x)$
3613	Solve for y	-325/y=13	$- \frac{325}{y} = 13$
3614	Simplify	5 cube root of 9a^2*4 cube root of 3a	$5 \sqrt[3]{9 a^{2}} \cdot 4 \sqrt[3]{3 a}$
3615	Simplify	(4x)/(x+1)*(3x+3)/2	$\frac{4 x}{x + 1} \cdot \frac{3 x + 3}{2}$
3616	Simplify	(2^-1+5^-1)^2	${(2^{- 1} + 5^{- 1})}^{2}$
3617	Evaluate the Summation	sum from i=1 to 11 of 3i^2-8	$\sum_{i = 1}^{11} 3 i^{2} - 8$
3618	Solve for n	fourth root of n+1=2	$\sqrt[4]{n + 1} = 2$
3619	Find the Exact Value	cos(-420 degrees )	$\cos (- 420 °)$
3620	Find the Degree, Leading Term, and Leading Coefficient	f(x)=2x+x^3+4	$f (x) = 2 x + x^{3} + 4$
3621	Evaluate the Integral	integral of ((3x-2)^2)/( square root of x) with respect to x	$\int \frac{{(3 x - 2)}^{2}}{\sqrt{x}} d x$
3622	Evaluate the Limit	limit as x approaches 0 of (sin(x))/(tan(3x))	$lim_{x \to 0} \frac{\sin (x)}{\tan (3 x)}$
3623	Solve the System of Equations	4x-1/3y=8 2/3x+1/3y=11/3	$4 x - \frac{1}{3} y = 8$ $\frac{2}{3} x + \frac{1}{3} y = \frac{11}{3}$
3624	Simplify the Radical Expression	1/( cube root of 5)	$\frac{1}{\sqrt[3]{5}}$
3625	Simplify	(7/9)÷(y/(y-11))	$\frac{7}{9} \div \frac{y}{y - 11}$
3626	Find g(f(x))	f(x)=3x+5 , g(x)=-2x-3	$f (x) = 3 x + 5$ , $g (x) = - 2 x - 3$
3627	Solve for x	3/4(1/6x+16)=3/7(4 3/8x-21)	$\frac{3}{4} (\frac{1}{6} x + 16) = \frac{3}{7} (4 \frac{3}{8} x - 21)$
3628	Find the Derivative - d/dx	y=3^4*x^3	$y = 3^{4} \cdot x^{3}$
3629	Evaluate	log base b of (x)^n	$\log_{b} ({(x)}^{n})$
3630	Add	(3y)/(2y^2-y)+2/(2y)	$\frac{3 y}{2 y^{2} - y} + \frac{2}{2 y}$
3631	Subtract	(9a^3+6a^2-a)-(a^3+6a-3)	$(9 a^{3} + 6 a^{2} - a) - (a^{3} + 6 a - 3)$
3632	Simplify	(m^(3/2)n^(-1/4))/(m^(3/4)n^(3/4))	$\frac{m^{\frac{3}{2}} n^{- \frac{1}{4}}}{m^{\frac{3}{4}} n^{\frac{3}{4}}}$
3633	Solve the System of Equations	2x-y=-15 2(x+3y)=-22	$2 x - y = - 15$ $2 (x + 3 y) = - 22$
3634	Find the Inverse	y=-1/2x^3+6	$y = - \frac{1}{2} x^{3} + 6$
3635	Solve by Substitution	15x+5y=20 y=8-3x	$15 x + 5 y = 20$ $y = 8 - 3 x$
3636	Find the Product	4a^2b^3*(9a^4b^2-4a^2+3)	$4 a^{2} b^{3} \cdot (9 a^{4} b^{2} - 4 a^{2} + 3)$
3637	Simplify	(5(z+4))/(8z+32)	$\frac{5 (z + 4)}{8 z + 32}$
3638	Simplify	(6x^2y^3)/((-4x^4y)(-3x^3y^2))	$\frac{6 x^{2} y^{3}}{(- 4 x^{4} y) (- 3 x^{3} y^{2})}$
3639	Evaluate the Limit	limit as x approaches 0 from the right of x natural log of x+x^2	$lim_{x \to 0^{+}} x \ln (x + x^{2})$
3640	Find the Domain	f(t)=(2t(t+1))/(t-1)-(3+t)/(t-1)	$f (t) = \frac{2 t (t + 1)}{t - 1} - \frac{3 + t}{t - 1}$
3641	Graph	y<=x+3/2	$y \leq x + \frac{3}{2}$
3642	Solve for x	square root of x-5- square root of x=-2	$\sqrt{x - 5} - \sqrt{x} = - 2$
3643	Evaluate the Limit	limit as x approaches 16 of ( fourth root of x^7-128)/(x-16)	$lim_{x \to 16} \frac{\sqrt[4]{x^{7}} - 128}{x - 16}$
3644	Integrate By Parts	integral of e^(2theta)sin(2theta) with respect to theta	$\int e^{2 θ} \sin (2 θ) d θ$
3645	Simplify	((3r^6n^3)/(2r^5n))^4	${(\frac{3 r^{6} n^{3}}{2 r^{5} n})}^{4}$
3646	Factor	c-2cd+8d-4	$c - 2 c d + 8 d - 4$
3647	Find the Roots (Zeros)	-2x^4+4x^3-6x^2+12x	$- 2 x^{4} + 4 x^{3} - 6 x^{2} + 12 x$
3648	Simplify	7x^2y^2+12xy^2-3x^2y+11+4xy-13x^2y+7	$7 x^{2} y^{2} + 12 x y^{2} - 3 x^{2} y + 11 + 4 x y - 13 x^{2} y + 7$
3649	Simplify	(-2n^6y^5)(-6n^3y^2)(ny)^3	$(- 2 n^{6} y^{5}) (- 6 n^{3} y^{2}) {(n y)}^{3}$
3650	Simplify	((9m^4n^10)/(-3m^2n^5))^-1	${(\frac{9 m^{4} n^{10}}{- 3 m^{2} n^{5}})}^{- 1}$
3651	Evaluate Using Summation Formulas	sum from k=1 to n of k/(n^2)	$\sum_{k = 1}^{n} \frac{k}{n^{2}}$
3652	Simplify	( square root of 27- square root of 6)/( square root of 18-3)	$\frac{\sqrt{27} - \sqrt{6}}{\sqrt{18} - 3}$
3653	Evaluate	3!2!	$3! 2!$
3654	Find the Domain and Range	f(x)=tan(2x-pi)	$f (x) = \tan (2 x - π)$
3655	Find the Asymptotes	y=(x^2-3x-4)/(1-3x-4x^2)	$y = \frac{x^{2} - 3 x - 4}{1 - 3 x - 4 x^{2}}$
3656	Solve for x	(1/216)^(10x+16)=(1/6)^(-2x^2+8x)	${(\frac{1}{216})}^{10 x + 16} = {(\frac{1}{6})}^{- 2 x^{2} + 8 x}$
3657	Graph	x-y=7 x-y=-4	$x - y = 7$ $x - y = - 4$
3658	Solve the Inequality for h	h-26<4	$h - 26 < 4$
3659	Find the x and y Intercepts	2x-2/3=3/4y+3	$2 x - \frac{2}{3} = \frac{3}{4} y + 3$
3660	Solve for y	y=x/3+5 , x=6	$y = \frac{x}{3} + 5$ , $x = 6$
3661	Find the Domain	f(x)=1/(\|x\|-3)	$f (x) = \frac{1}{\| x \| - 3}$
3662	Find the Derivative - d/dx	7^( square root of x+2)	$7^{\sqrt{x} + 2}$
3663	Solve for r	8000=4/3pir^3	$8000 = \frac{4}{3} π r^{3}$
3664	Find the Exact Value	2(32-(4-1)^3)	$2 (32 - {(4 - 1)}^{3})$
3665	Multiply	4/33.1410^3	$\frac{4}{3} \cdot 3.14 \cdot 10^{3}$
3666	Find the Domain	(8a^3-b^3)/(4a^2-b^2)	$\frac{8 a^{3} - b^{3}}{4 a^{2} - b^{2}}$
3667	Evaluate	log base 4 of x-4=( log base 4 of x)/( log base 4 of 4)	$\log_{4} (x - 4) = \frac{\log_{4} (x)}{\log_{4} (4)}$
3668	Solve for x	1/(16^(3x-4))<=64^(x-1)	$\frac{1}{16^{3 x - 4}} \leq 64^{x - 1}$
3669	Simplify	fourth root of (81x^2y^4)/(z^8)	$\sqrt[4]{\frac{81 x^{2} y^{4}}{z^{8}}}$
3670	Simplify	(15x)÷5xy	$15 x \div 5 x y$
3671	Evaluate	(4+9)-(3(6))/2+8	$(4 + 9) - \frac{3 (6)}{2} + 8$
3672	Simplify	3 square root of x4 square root of 3x square root of 6x	$3 \sqrt{x} \cdot 4 \sqrt{3 x} \cdot \sqrt{6 x}$
3673	Solve the Inequality for b	b+2>=4	$b + 2 \geq 4$
3674	Solve for y	square root of y+(y+2)=6	$\sqrt{y + (y + 2)} = 6$
3675	Solve for x	5^(2x-7)=5^(2x+4)	$5^{2 x - 7} = 5^{2 x + 4}$
3676	Find the Cotangent Given the Point	(-1, square root of 3)	$(- 1, \sqrt{3})$
3677	Evaluate the Function	y=1/4(4)^x for x=3/2	$y = \frac{1}{4} {(4)}^{x}$ for $x = \frac{3}{2}$
3678	Evaluate	log base -1/2 of x=-7	$\log_{- \frac{1}{2}} (x) = - 7$
3679	Solve for x	2^x+2^(5-x)=12	$2^{x} + 2^{5 - x} = 12$
3680	Write as a Single Logarithm	2 log of x+ log of y-2 log of z	$2 \log (x) + \log (y) - 2 \log (z)$
3681	Graph	f(x)=4*(2/3)^x+1	$f (x) = 4 \cdot {(\frac{2}{3})}^{x} + 1$
3682	Simplify the Radical Expression	square root of 75- square root of 27	$\sqrt{75} - \sqrt{27}$
3683	Convert to Rectangular	theta=-pi/4	$θ = - \frac{π}{4}$
3684	Simplify	( cube root of 108)÷( cube root of 2)	$\sqrt[3]{108} \div \sqrt[3]{2}$
3685	Simplify	((-9)^0J^-1k^-4)/(2^0)	$\frac{{(- 9)}^{0} J^{- 1} k^{- 4}}{2^{0}}$
3686	Solve for x	(x+2)+(x-1)=0	$(x + 2) + (x - 1) = 0$
3687	Evaluate the Limit	limit as x approaches -8 of -(4(x+5)^2+1)/(1/(3x+2)+2)	$lim_{x \to - 8} - \frac{4 {(x + 5)}^{2} + 1}{\frac{1}{3 x + 2} + 2}$
3688	Find the Domain	((c+2)^2)/(7c^2+14c)	$\frac{{(c + 2)}^{2}}{7 c^{2} + 14 c}$
3689	Find the Roots (Zeros)	y=x(x-1)^3	$y = x {(x - 1)}^{3}$
3690	Solve for x	(15(x-3))/5=3(2x-3)	$\frac{15 (x - 3)}{5} = 3 (2 x - 3)$
3691	Multiply	(5a-3a^3)(4a-1)	$(5 a - 3 a^{3}) (4 a - 1)$
3692	Solve for a	(2a+1)(6a-2)=3a(4a-1)+4	$(2 a + 1) \cdot (6 a - 2) = 3 a \cdot (4 a - 1) + 4$
3693	Graph Using a Table of Values	f(x) = square root of x+4	$f (x) = \sqrt{x + 4}$
3694	Add	4(m+2)+3(6m-4)	$4 (m + 2) + 3 (6 m - 4)$
3695	Simplify	((-x^-1y)^0)/(4w^-1y^2)	$\frac{{(- x^{- 1} y)}^{0}}{4 w^{- 1} y^{2}}$
3696	Combine Like Terms	(10x^2+3x+9)+(5x^2+x+4)	$(10 x^{2} + 3 x + 9) + (5 x^{2} + x + 4)$
3697	Convert from Radians to Degrees	pi/9rad	$\frac{π}{9}$ radians
3698	Solve for x	(cos(x)+1)(tan(x)+1)=0	$(\cos (x) + 1) (\tan (x) + 1) = 0$
3699	Simplify the Radical Expression	cube root of 216/512	$\sqrt[3]{\frac{216}{512}}$
3700	Simplify	(3(y+8))/(9y+72)	$\frac{3 (y + 8)}{9 y + 72}$