Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
15101	Factor	3p-2p^2-18p+27	$3 p - 2 p^{2} - 18 p + 27$
15102	Simplify	i^5+i^6+i^7+i^8	$i^{5} + i^{6} + i^{7} + i^{8}$
15103	Simplify	(1/3)^(-2/5)*96^(-2/5)	${(\frac{1}{3})}^{- \frac{2}{5}} \cdot 96^{- \frac{2}{5}}$
15104	Solve for z	1/x=1/y-1/z	$\frac{1}{x} = \frac{1}{y} - \frac{1}{z}$
15105	Find the Antiderivative	x^e+e^x	$x^{e} + e^{x}$
15106	Verify the Identity	cot(theta)+csc(theta)=(sin(theta)+tan(theta))/(sin(theta)tan(theta))	$\cot (θ) + \csc (θ) = \frac{\sin (θ) + \tan (θ)}{\sin (θ) \tan (θ)}$
15107	Evaluate the Integral	integral from 1 to e of (x^2+1)/x with respect to x	$\int_{1}^{e} \frac{x^{2} + 1}{x} d x$
15108	Simplify	3((5-2)*3+4)	$3 ((5 - 2) \cdot 3 + 4)$
15109	Solve for y	9x+18=6y-3x for y	$9 x + 18 = 6 y - 3 x$ for $y$
15110	Subtract	32x square root of 5-18x square root of 20	$32 x \sqrt{5} - 18 x \sqrt{20}$
15111	Simplify	7 1/3t-(10 2/3t-6)	$7 \frac{1}{3} t - (10 \frac{2}{3} t - 6)$
15112	Simplify	-6 cube root of 4-8 square root of 2+7 square root of 2- cube root of 4	$- 6 \sqrt[3]{4} - 8 \sqrt{2} + 7 \sqrt{2} - \sqrt[3]{4}$
15113	Simplify	a^-3b^0c^6	$a^{- 3} b^{0} c^{6}$
15114	Simplify	fourth root of (32w)/81	$\sqrt[4]{\frac{32 w}{81}}$
15115	Evaluate	(11^7* square root of 6)/(11^5*6^(3/2))	$\frac{11^{7} \cdot \sqrt{6}}{11^{5} \cdot 6^{\frac{3}{2}}}$
15116	Simplify	(12p-1)/(3p^2)-(1-3p)/(3p^2)	$\frac{12 p - 1}{3 p^{2}} - \frac{1 - 3 p}{3 p^{2}}$
15117	Simplify	2 1/2+3b-1/3b	$2 \frac{1}{2} + 3 b - \frac{1}{3} b$
15118	Solve for x	x/(x+4)-3/(x-4)=3/(x-4)	$\frac{x}{x + 4} - \frac{3}{x - 4} = \frac{3}{x - 4}$
15119	Evaluate	(x^5*x^3)/(x^4)=(x^8)/(x^4)	$\frac{x^{5} \cdot x^{3}}{x^{4}} = \frac{x^{8}}{x^{4}}$
15120	Solve for u	3(3u+2)+5=2(2u-2)	$3 (3 u + 2) + 5 = 2 (2 u - 2)$
15121	Evaluate	natural log of 6/e	$\ln (\frac{6}{e})$
15122	Solve for x	square root of x^2=-8	$\sqrt{x^{2}} = - 8$
15123	Evaluate the Limit	limit as x approaches infinity of 3x^-5+4x^-2+5	$lim_{x \to \infty} 3 x^{- 5} + 4 x^{- 2} + 5$
15124	Determine the Possible Number of Real Roots	x^3+2x-9=0	$x^{3} + 2 x - 9 = 0$
15125	Factor	3ax+2ay-az+3bx+2by-bz	$3 a x + 2 a y - a z + 3 b x + 2 b y - b z$
15126	Solve for x	3(x-4)=-2+3x-10	$3 (x - 4) = - 2 + 3 x - 10$
15127	Add	-4x^2+3xy-y^2-7x^2-xy+6y^2 x^2+4xy-2y^2	$- 4 x^{2} + 3 x y - y^{2} - 7 x^{2} - x y + 6 y^{2}$ $x^{2} + 4 x y - 2 y^{2}$
15128	Find the Derivative - d/dx	d/(dx)(arctan(x)+2 square root of x)	$\frac{d}{d x} (\arctan (x) + 2 \sqrt{x})$
15129	Simplify	(g^8h^2m)/(hg^7)	$\frac{g^{8} h^{2} m}{h g^{7}}$
15130	Find the Asymptotes	f(x)=(x^2-7x)/(x-7)	$f (x) = \frac{x^{2} - 7 x}{x - 7}$
15131	Solve the Inequality for x	-4(x-2)+5<9	$- 4 (x - 2) + 5 < 9$
15132	Find the Maximum/Minimum Value	y=x^4+2x^2+8x+3	$y = x^{4} + 2 x^{2} + 8 x + 3$
15133	Find the Perpendicular Line	(-3,3) 2y=8x-6	$(- 3, 3)$ $2 y = 8 x - 6$
15134	Combine Like Terms	4x^2-3x-x^2+3x	$4 x^{2} - 3 x - x^{2} + 3 x$
15135	Solve the Function Operation	f(x)=5x-15 g(x)=2x^2+4x-3 Find: f(g(x))	$f (x) = 5 x - 15$ $g (x) = 2 x^{2} + 4 x - 3$ Find: $f (g (x))$
15136	Evaluate the Limit	limit as x approaches 3 of (x-3)/(\|x^3-3x^2\|)	$lim_{x \to 3} \frac{x - 3}{\| x^{3} - 3 x^{2} \|}$
15137	Solve for x	1/4x^2-7=25	$\frac{1}{4} x^{2} - 7 = 25$
15138	Simplify	(x^2-1)*(1/(x-1)-1/(x+1)+1)	$(x^{2} - 1) \times (\frac{1}{x - 1} - \frac{1}{x + 1} + 1)$
15139	Solve for v	v^2=17v	$v^{2} = 17 v$
15140	Find the Integral	(5/8x^4-3x^2+2x^-1)dx	$(\frac{5}{8} x^{4} - 3 x^{2} + 2 x^{- 1}) d x$
15141	Solve for x	x^3-16x<=0	$x^{3} - 16 x \leq 0$
15142	Simplify	3-16÷2*5+3	$3 - 16 \div 2 \cdot 5 + 3$
15143	Evaluate	( log of 100-2 log base 4 of 64)/( log base 7 of 7)	$\frac{\log (100) - 2 \log_{4} (64)}{\log_{7} (7)}$
15144	Write as a Single Logarithm	3 natural log of 5- natural log of 2	$3 \ln (5) - \ln (2)$
15145	Solve for g	g=-5(3)+13	$g = - 5 (3) + 13$
15146	Graph	f(x)=\|x\|-x	$f (x) = \| x \| - x$
15147	Find the Domain and Range	y=(3x)^3	$y = {(3 x)}^{3}$
15148	Simplify	(x+2)/(2x-2)+(4x-3)/(10x-10)	$\frac{x + 2}{2 x - 2} + \frac{4 x - 3}{10 x - 10}$
15149	Solve the Inequality for x	x^2-4x-24>=0	$x^{2} - 4 x - 24 \geq 0$
15150	Integrate By Parts	integral of e^(-x^2) with respect to x	$\int e^{- x^{2}} d x$
15151	Multiply	square root of 9( square root of 3+ square root of 8)	$\sqrt{9} (\sqrt{3} + \sqrt{8})$
15152	Simplify	(20x^6y)*(1/4x^2y)	$(20 x^{6} y) \cdot (\frac{1}{4} x^{2} y)$
15153	Solve for x	2/(x+5)-5/(5-x)=x/(x-5)	$\frac{2}{x + 5} - \frac{5}{5 - x} = \frac{x}{x - 5}$
15154	Write in Standard Form	y+17=3(x+6)-14	$y + 17 = 3 (x + 6) - 14$
15155	Simplify the Radical Expression	cube root of (64x^9)/343	$\sqrt[3]{\frac{64 x^{9}}{343}}$
15156	Evaluate the Integral	integral from square root of pi/2 to square root of pi of 3theta^3cos(theta^2) with respect to theta	$\int_{\sqrt{\frac{π}{2}}}^{\sqrt{π}} 3 θ^{3} \cos (θ^{2}) d θ$
15157	Verify the Identity	(cot(x))/(tan(x)+cot(x))=cos(x)^2	$\frac{\cot (x)}{\tan (x) + \cot (x)} = \cos^{2} (x)$
15158	Solve the Function Operation	f(x)=-(x+1)^2-3 if x<=0; -6 if x>=4 Find f(-2)	$f (x) = {\begin{cases} - {(x + 1)}^{2} - 3 & x \leq 0 \\ - 6 & x \geq 4 \end{cases}$ Find $f (- 2)$
15159	Simplify	square root of 2^(4x-6)	$\sqrt{2^{4 x - 6}}$
15160	Find the Maximum/Minimum Value	V(w)=(60-4w)w^2	$V (w) = (60 - 4 w) w^{2}$
15161	Solve for x	4(6-3x)-8x=1/3(105x-18)+125x	$4 (6 - 3 x) - 8 x = \frac{1}{3} (105 x - 18) + 125 x$
15162	Solve for x	-x-5=-1/3(3x+5)	$- x - 5 = - \frac{1}{3} (3 x + 5)$
15163	Find All Complex Solutions	sin(theta)*sec(theta)-2sin(theta)=0	$\sin (θ) \cdot \sec (θ) - 2 \sin (θ) = 0$
15164	Write as a Single Logarithm	1/2( log base 2 of 4+ log base 2 of 16)- log base 2 of 2	$\frac{1}{2} (\log_{2} (4) + \log_{2} (16)) - \log_{2} (2)$
15165	Simplify	( square root of 3)/( square root of 6)	$\frac{\sqrt[2]{3}}{\sqrt{6}}$
15166	Find the Antiderivative	(x+1)/(x-1)	$\frac{x + 1}{x - 1}$
15167	Solve the Inequality for x	2^(x-5)<5	$2^{x - 5} < 5$
15168	Solve for b	b^2+5=8b-10	$b^{2} + 5 = 8 b - 10$
15169	Simplify	7/(b^2+5b+4)*(b^2+8b+7)/(b+7)	$\frac{7}{b^{2} + 5 b + 4} \cdot \frac{b^{2} + 8 b + 7}{b + 7}$
15170	Divide	((7x^3)/3)÷((14x^2)/6)	$\frac{7 x^{3}}{3} \div \frac{14 x^{2}}{6}$
15171	Simplify	4*7-(6^2)÷3	$4 \cdot 7 - 6^{2} \div 3$
15172	Find the Maximum/Minimum Value	y=x^3+x^2-5	$y = x^{3} + x^{2} - 5$
15173	Write as a Single Logarithm	( log of 3- log of 6)+ log of 2	$(\log (3) - \log (6)) + \log (2)$
15174	Simplify	((7x^2)/(12x))÷((14x^3)/(48y^3))	$\frac{7 x^{2}}{12 x} \div \frac{14 x^{3}}{48 y^{3}}$
15175	Solve for x	log base 2 of 3(2x-1) = log base 2 of 3x-2	$\log_{2} (3) (2 x - 1) = \log_{2} (3 x - 2)$
15176	Divide Using Long Polynomial Division	(2x^3+x^2-24x+8)/(x-3)	$\frac{2 x^{3} + x^{2} - 24 x + 8}{x - 3}$
15177	Simplify	3z-7z^2-5z+5z^2+2z^2	$3 z - 7 z^{2} - 5 z + 5 z^{2} + 2 z^{2}$
15178	Simplify	((x^2y^3)/(y^2z))^m	${(\frac{x^{2} y^{3}}{y^{2} z})}^{m}$
15179	Simplify	(10x^8y^5)(x^3yz)	$(10 x^{8} y^{5}) (x^{3} y z)$
15180	Evaluate Using Summation Formulas	sum from k=1 to n of k	$\sum_{k = 1}^{n} k$
15181	Simplify	(2/3)/( square root of 9-(2/3)^2)	$\frac{\frac{2}{3}}{\sqrt{9 - {(\frac{2}{3})}^{2}}}$
15182	Factor	(5x-4)^2+3x(5x-4)	${(5 x - 4)}^{2} + 3 x (5 x - 4)$
15183	Solve the Inequality for d	-1<=(d+2)/5<=6/5	$- 1 \leq \frac{d + 2}{5} \leq \frac{6}{5}$
15184	Multiply	1 1/21 1/31 1/4*1 1/5	$1 \frac{1}{2} \cdot 1 \frac{1}{3} \cdot 1 \frac{1}{4} \cdot 1 \frac{1}{5}$
15185	Simplify	(-3r^3w^4)^3(2rw)^2(-3r^2)^3(4rw^2)^3(2r^2w^3)	${(- 3 r^{3} w^{4})}^{3} {(2 r w)}^{2} {(- 3 r^{2})}^{3} {(4 r w^{2})}^{3} (2 r^{2} w^{3})$
15186	Find Trig Functions Using Identities	sin(theta)=-3/4 , cos(theta)>0	$\sin (θ) = - \frac{3}{4}$ , $\cos (θ) > 0$
15187	Simplify	sec(x)-tan(x)sin(x)-1/(sec(x))	$\sec (x) - \tan (x) \sin (x) - \frac{1}{\sec (x)}$
15188	Evaluate the Limit	limit as x approaches 2 of (4-x^2)tan(x)(pix)/4	$lim_{x \to 2} (4 - x^{2}) \tan (x) \frac{π x}{4}$
15189	Graph	3x+y=0 , x>=0	$3 x + y = 0$ , $x \geq 0$
15190	Evaluate Using the Given Value	-x^3-3x^2+4 for x=-2	$- x^{3} - 3 x^{2} + 4$ for $x = - 2$
15191	Write in Standard Form	(2x+1)(4-9x)-2x(3x+11)	$(2 x + 1) (4 - 9 x) - 2 x (3 x + 11)$
15192	Graph	2x+3y<=12 3x-5y>=15	$2 x + 3 y \leq 12$ $3 x - 5 y \geq 15$
15193	Simplify	(2x+1)(4-9x)-2x(3x+11)	$(2 x + 1) (4 - 9 x) - 2 x (3 x + 11)$
15194	Graph	8/5>s+12/5	$\frac{8}{5} > s + \frac{12}{5}$
15195	Simplify	(5x^2+4)-(5+5x^3)	$(5 x^{2} + 4) - (5 + 5 x^{3})$
15196	Find the Domain and Range	y=3csc(2x)	$y = 3 \csc (2 x)$
15197	Simplify	square root of square root of 4	$\sqrt{\sqrt{4}}$
15198	Solve for h	15 = square root of h/16	$15 = \sqrt{\frac{h}{16}}$
15199	Evaluate	(3pi)/4(180/pi)	$\frac{3 π}{4} (\frac{180}{π})$
15200	Evaluate	2x-528=x/4+x+270	$2 x - 528 = \frac{x}{4} + x + 270$