Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
601	Evaluate the Limit	limit as x approaches 1 of (4- square root of x+15)/(1-x^2)	$lim_{x \to 1} \frac{4 - \sqrt{x + 15}}{1 - x^{2}}$
602	Simplify	x(3x+y)	$x (3 x + y)$
603	Simplify	square root of 5x^5* square root of 10a^2	$\sqrt{5 x^{5}} \cdot \sqrt{10 a^{2}}$
604	Simplify	4x^3y^3*(3x^3-7xy^2+2xy-y)	$4 x^{3} y^{3} \cdot (3 x^{3} - 7 x y^{2} + 2 x y - y)$
605	Simplify	(2 4/9-5 2/3)/2 1/3	$\frac{2 \frac{4}{9} - 5 \frac{2}{3}}{2 \frac{1}{3}}$
606	Simplify	cube root of 216/512	$\sqrt[3]{\frac{216}{512}}$
607	Simplify	(1/(4m))^-3	${(\frac{1}{4 m})}^{- 3}$
608	Solve for y	48/y=6/(1/8)	$\frac{48}{y} = \frac{6}{\frac{1}{8}}$
609	Simplify	5 fifth root of 2x^3y^4*3 fifth root of 16x^2y	$5 \sqrt[5]{2 x^{3} y^{4}} \cdot 3 \sqrt[5]{16 x^{2} y}$
610	Solve the System of Equations	-y-10=6x 5x+y=-10	$- y - 10 = 6 x$ $5 x + y = - 10$
611	Solve for x	4(3^(-2x-4))=36	$4 (3^{- 2 x - 4}) = 36$
612	Evaluate the Integral	integral from 0 to a of 6x^2 with respect to x=-2	$\int_{0}^{a} 6 x^{2} d x = - 2$
613	Evaluate	((2x^-2y^3)/(3xy^-4))^4	${(\frac{2 x^{- 2} y^{3}}{3 x y^{- 4}})}^{4}$
614	Solve for D	n=5(m^2+D)	$n = 5 (m^{2} + D)$
615	Evaluate	(3.5*2/7-2/3)÷16	$(3.5 \cdot \frac{2}{7} - \frac{2}{3}) \div 16$
616	Evaluate	((-t)/3)^2	${(\frac{- t}{3})}^{2}$
617	Find the Product	(x^2-3x+9)(x+3)	$(x^{2} - 3 x + 9) (x + 3)$
618	Evaluate the Limit	limit as x approaches infinity of (-x^2-x)/(4x^2+1)	$lim_{x \to \infty} \frac{- x^{2} - x}{4 x^{2} + 1}$
619	Simplify	square root of (5m)/(7n^2)	$\sqrt{\frac{5 m}{7 n^{2}}}$
620	Simplify	(1/2c^3d)^5	${(\frac{1}{2} c^{3} d)}^{5}$
621	Solve for x	-2 cube root of x+4<12	$- 2 \sqrt[3]{x + 4} < 12$
622	Simplify	(-16ab^4)/(4b^3)	$\frac{- 16 a b^{4}}{4 b^{3}}$
623	Divide	(8x^3+5x^2+3x-1)÷2x	$(8 x^{3} + 5 x^{2} + 3 x - 1) \div 2 x$
624	Simplify	(2 1/3x^(2m-1/2))^2*(3/7x^(1/2))^2	${(2 \frac{1}{3} x^{2 m - \frac{1}{2}})}^{2} \cdot {(\frac{3}{7} x^{\frac{1}{2}})}^{2}$
625	Simplify	square root of 5a square root of 3b	$\sqrt{5 a} \sqrt{3 b}$
626	Simplify	( square root of 10)/( square root of 180- square root of 20)	$\frac{\sqrt{10}}{\sqrt{180} - \sqrt{20}}$
627	Simplify	(2t(t+1))/(t-1)-(3+t)/(t-1)	$\frac{2 t (t + 1)}{t - 1} - \frac{3 + t}{t - 1}$
628	Simplify	(2x^3+4x^2+2x)/(6x^3-6x)	$\frac{2 x^{3} + 4 x^{2} + 2 x}{6 x^{3} - 6 x}$
629	Solve for d	1/4d=2 1/8	$\frac{1}{4} d = 2 \frac{1}{8}$
630	Find the Domain	x/(x+1)-(x+1)/(x^2+2x+1)-2/(x^2-1)	$\frac{x}{x + 1} - \frac{x + 1}{x^{2} + 2 x + 1} - \frac{2}{x^{2} - 1}$
631	Simplify	9p^7q^9+10p^4q^8*(-2p^3q)	$9 p^{7} q^{9} + 10 p^{4} q^{8} \cdot (- 2 p^{3} q)$
632	Simplify	(6a^5b^7)/(-2a^3b^7)	$\frac{6 a^{5} b^{7}}{- 2 a^{3} b^{7}}$
633	Graph	y>=-3 square root of x-1+2	$y \geq - 3 \sqrt{x - 1} + 2$
634	Solve for M	M-(4ab-3b^2)=a^2-7ab+8b^2	$M - (4 a b - 3 b^{2}) = a^{2} - 7 a b + 8 b^{2}$
635	Evaluate	9(3^-2)-(3^4)/(3^2)- square root of 2^6	$9 (3^{- 2}) - \frac{3^{4}}{3^{2}} - \sqrt{2^{6}}$
636	Solve the Inequality for y	2.25y^2-3y+1<0	$2.25 y^{2} - 3 y + 1 < 0$
637	Factor	5ac-5bc-a+b	$5 a c - 5 b c - a + b$
638	Solve for x	4(3-5x)=15-(8x-25)	$4 (3 - 5 x) = 15 - (8 x - 25)$
639	Solve for y	27y^3-27y^2+9y-1=0	$27 y^{3} - 27 y^{2} + 9 y - 1 = 0$
640	Multiply	(2a)(3x^2+2xy-4y^3)	$(2 a) (3 x^{2} + 2 x y - 4 y^{3})$
641	Rationalize the Denominator	4/(3 square root of 2x)	$\frac{4}{3 \sqrt{2 x}}$
642	Find the Domain	((2ab)/(a^2-b^2))÷((4ab)/((a-b)^2))	$\frac{2 a b}{a^{2} - b^{2}} \div \frac{4 a b}{{(a - b)}^{2}}$
643	Solve for y	y^2-1/16=0	$y^{2} - \frac{1}{16} = 0$
644	Solve for x	3x^3-x^2=x^2	$3 x^{3} - x^{2} = x^{2}$
645	Simplify	(27-x^3)/((3-x)^2)	$\frac{27 - x^{3}}{{(3 - x)}^{2}}$
646	Simplify	( square root of 72)/( square root of 36x^8y^2)	$\frac{\sqrt{72}}{\sqrt{36 x^{8} y^{2}}}$
647	Simplify	(3+i square root of 3)/((i- square root of 3)^2)	$\frac{3 + i \sqrt{3}}{{(i - \sqrt{3})}^{2}}$
648	Solve for x	8x^3+12x^2+6x+1=0	$8 x^{3} + 12 x^{2} + 6 x + 1 = 0$
649	Evaluate the Integral	integral of (7x^3)^2 with respect to x	$\int {(7 x^{3})}^{2} d x$
650	Simplify	square root of 49(x^3+4)^6	$\sqrt{49 {(x^{3} + 4)}^{6}}$
651	Evaluate	14-(-11)-(-7-(-17))	$14 - (- 11) - (- 7 - (- 17))$
652	Simplify	(4 square root of 3a^3)^2	${(4 \sqrt{3 a^{3}})}^{2}$
653	Simplify	-2yz^2*(-5y^2z-4z)	$- 2 y z^{2} \cdot (- 5 y^{2} z - 4 z)$
654	Solve for s	8-7s+7=9s-1	$8 - 7 s + 7 = 9 s - 1$
655	Find the Exact Value	(9 square root of 2)/( square root of 10+ square root of 18)	$\frac{9 \sqrt{2}}{\sqrt{10} + \sqrt{18}}$
656	Solve for x	8 square root of x+6-7=-79	$8 \sqrt{x + 6} - 7 = - 79$
657	Solve the Inequality for y	(4-y)/5-5y>=0	$\frac{4 - y}{5} - 5 y \geq 0$
658	Solve for r	f/(r^2)+a=n+k	$\frac{f}{r^{2}} + a = n + k$
659	Simplify	2x+4y-6+x+2-2y+5	$2 x + 4 y - 6 + x + 2 - 2 y + 5$
660	Simplify	-7m-m^2+4m^2-3m	$- 7 m - m^{2} + 4 m^{2} - 3 m$
661	Find the Domain	((a+b)/b-a/(a+b))÷((a+b)/a-b/(a+b))	$(\frac{a + b}{b} - \frac{a}{a + b}) \div (\frac{a + b}{a} - \frac{b}{a + b})$
662	Simplify	(3b-2)(5-2b)+6b^2	$(3 b - 2) (5 - 2 b) + 6 b^{2}$
663	Simplify	((x-y)^2)/(2xy+6y)*(4x+12)/(x^2-y^2)	$\frac{{(x - y)}^{2}}{2 x y + 6 y} \cdot \frac{4 x + 12}{x^{2} - y^{2}}$
664	Simplify	x-5+2x-7+8x+2	$x - 5 + 2 x - 7 + 8 x + 2$
665	Simplify	(16a^3b^2c^5-24a^5bc^4+44a^7b^6c^6)/(4a^2bc^3)	$\frac{16 a^{3} b^{2} c^{5} - 24 a^{5} b c^{4} + 44 a^{7} b^{6} c^{6}}{4 a^{2} b c^{3}}$
666	Solve for x	7/(x+1)=(2x-1)/36	$\frac{7}{x + 1} = \frac{2 x - 1}{36}$
667	Simplify	((x^2-9)/(y^2-25))÷((2x^2-6x)/(3y^2-15y))+(3-1.5y)/(y+5)	$\frac{x^{2} - 9}{y^{2} - 25} \div \frac{2 x^{2} - 6 x}{3 y^{2} - 15 y} + \frac{3 - 1.5 y}{y + 5}$
668	Simplify	7p+16-2d+6+5p-7+3d	$7 p + 16 - 2 d + 6 + 5 p - 7 + 3 d$
669	Solve for x	4^x-14*2^x-32=0	$4^{x} - 14 \cdot 2^{x} - 32 = 0$
670	Solve for x	12e^(2x)-5=17e^x	$12 e^{2 x} - 5 = 17 e^{x}$
671	Simplify	(4x^2y+3xy-x^2)(-x^3y^2)	$(4 x^{2} y + 3 x y - x^{2}) (- x^{3} y^{2})$
672	Solve for x	2 cube root of x-3+15=10	$2 \sqrt[3]{x - 3} + 15 = 10$
673	Solve for x	square root of 2x-1-x+2=0	$\sqrt{2 x - 1} - x + 2 = 0$
674	Multiply	square root of 24x* square root of 18y* square root of 15y	$\sqrt{24 x} \cdot \sqrt{18 y} \cdot \sqrt{15 y}$
675	Convert to Rectangular	3(cos(pi/3)+isin(pi/3))*5(cos(pi/4)+isin(pi/4))	$3 (\cos (\frac{π}{3}) + i \sin (\frac{π}{3})) \cdot 5 (\cos (\frac{π}{4}) + i \sin (\frac{π}{4}))$
676	Find the Roots (Zeros)	-3x^2e^(-2x)+3xe^(-2x)	$- 3 x^{2} e^{- 2 x} + 3 x e^{- 2 x}$
677	Solve for x	square root of x- square root of x-5=-1	$\sqrt{x} - \sqrt{x - 5} = - 1$
678	Find the Domain	log base 1-x of x	$\log_{1 - x} (x)$
679	Evaluate	3 square root of 12+1/2 square root of 96- square root of 54	$3 \sqrt{12} + \frac{1}{2} \sqrt{96} - \sqrt{54}$
680	Graph	y<=2 square root of x-2-3	$y \leq 2 \sqrt{x - 2} - 3$
681	Find the Domain	F(x) = square root of x^2+4	$F (x) = \sqrt{x^{2} + 4}$
682	Simplify the Radical Expression	fourth root of 8* fourth root of 8	$\sqrt[4]{8} \cdot \sqrt[4]{8}$
683	Find the Product	2(3a^2)^3	$2 {(3 a^{2})}^{3}$
684	Simplify	square root of (28x^3y^2z)/(7xy^2)	$\sqrt{\frac{28 x^{3} y^{2} z}{7 x y^{2}}}$
685	Simplify	(11y+13)/(3y-3)+(15y+17)/(4-4y)	$\frac{11 y + 13}{3 y - 3} + \frac{15 y + 17}{4 - 4 y}$
686	Simplify	a fourth root of 6ab^4	$a \sqrt[4]{6 a b^{4}}$
687	Solve for t	10^(2t)=9	$10^{2 t} = 9$
688	Simplify	-9k+8k+4+2k+3	$- 9 k + 8 k + 4 + 2 k + 3$
689	Simplify	( cube root of 135)/( cube root of 40)	$\frac{\sqrt[3]{135}}{\sqrt[3]{40}}$
690	Find the Antiderivative	f(x)=1/(2x^3)	$f (x) = \frac{1}{2 x^{3}}$
691	Solve for D	-15y^4=(D)(3y^2)	$- 15 y^{4} = (D) (3 y^{2})$
692	Rationalize the Denominator	(4 square root of 2)/( square root of 20p)	$\frac{4 \sqrt{2}}{\sqrt{20 p}}$
693	Solve for x	2x+7-5x+8=3(5+6x)-12x	$2 x + 7 - 5 x + 8 = 3 (5 + 6 x) - 12 x$
694	Rationalize the Denominator	(3 square root of 3)/( square root of 6m)	$\frac{3 \sqrt{3}}{\sqrt{6 m}}$
695	Simplify	cot(x)(1/(sec(x))+1/(csc(x)))	$\cot (x) (\frac{1}{\sec (x)} + \frac{1}{\csc (x)})$
696	Graph	3x>=12-6y	$3 x \geq 12 - 6 y$
697	Solve the Inequality for x	(x^2-4)/(x^2+36)>=0	$\frac{x^{2} - 4}{x^{2} + 36} \geq 0$
698	Simplify	(5c^2d^3)/(-4c^2d)	$\frac{5 c^{2} d^{3}}{- 4 c^{2} d}$
699	Simplify	8 square root of 3x* square root of 15x	$8 \sqrt{3 x} \cdot \sqrt{15 x}$
700	Multiply	square root of 6x* square root of 15xy* square root of 20	$\sqrt{6 x} \cdot \sqrt{15 x y} \cdot \sqrt{20}$