Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
701	Simplify	tan(x-pi/2)	$tan (x - \frac{π}{2})$ $\tan (x - \frac{π}{2})$
702	Simplify	(2x^2-9x+4)/(12+x-x^2)	$\frac{2 x^{2} - 9 x + 4}{12 + x - x^{2}}$ $\frac{2 x^{2} - 9 x + 4}{12 + x - x^{2}}$
703	Solve for x	-5x-12=13	$- 5 x - 12 = 13$ $- 5 x - 12 = 13$
704	Simplify	cos(2u)	$cos (2 u)$ $\cos (2 u)$
705	Simplify	cos(-t)+cos(-t)tan(-t)^2	$cos (- t) + cos (- t) {tan}^{2} (- t)$ $\cos (- t) + \cos (- t) \tan^{2} (- t)$
706	Simplify	cos(arcsin((x-h)/r))	$cos (arcsin (\frac{x - h}{r}))$ $\cos (\arcsin (\frac{x - h}{r}))$
707	Simplify	b^8(2b)^7	$b^{8} {(2 b)}^{7}$ $b^{8} {(2 b)}^{7}$
708	Simplify	cot(pi/2-a)cos(a)	$cot (\frac{π}{2} - a) cos (a)$ $\cot (\frac{π}{2} - a) \cos (a)$
709	Simplify	2(3x)^2+18(3x)-14	$2 {(3 x)}^{2} + 18 (3 x) - 14$ $2 {(3 x)}^{2} + 18 (3 x) - 14$
710	Simplify	cube root of 54- cube root of 16	$\sqrt[3]{54} - \sqrt[3]{16}$ $\sqrt[3]{54} - \sqrt[3]{16}$
711	Simplify	(-5z^2)^3(4z^3)	${(- 5 z^{2})}^{3} (4 z^{3})$ ${(- 5 z^{2})}^{3} (4 z^{3})$
712	Simplify	u^(3/2)u^(1/3)	$u^{\frac{3}{2}} u^{\frac{1}{3}}$ $u^{\frac{3}{2}} u^{\frac{1}{3}}$
713	Simplify	sin(pi/6)+cos(pi/6)	$sin (\frac{π}{6}) + cos (\frac{π}{6})$ $\sin (\frac{π}{6}) + \cos (\frac{π}{6})$
714	Simplify	(u^(3/2))/(u^(1/3))	$\frac{u^{\frac{3}{2}}}{u^{\frac{1}{3}}}$ $\frac{u^{\frac{3}{2}}}{u^{\frac{1}{3}}}$
715	Simplify	cos((13pi)/15)cos(-pi/5)-sin((13pi)/15)sin(-pi/5)	$cos (\frac{13 π}{15}) cos (- \frac{π}{5}) - sin (\frac{13 π}{15}) sin (- \frac{π}{5})$ $\cos (\frac{13 π}{15}) \cos (- \frac{π}{5}) - \sin (\frac{13 π}{15}) \sin (- \frac{π}{5})$
716	Simplify	4sin(90)-3tan(180)	$4 sin (90) - 3 tan (180)$ $4 \sin (90) - 3 \tan (180)$
717	Simplify	i^1002	$i^{1002}$ $i^{1002}$
718	Simplify	(9-x^2)/(x^3-27)	$\frac{9 - x^{2}}{x^{3} - 27}$ $\frac{9 - x^{2}}{x^{3} - 27}$
719	Simplify	((6y^3)^4)/(2y^7)	$\frac{{(6 y^{3})}^{4}}{2 y^{7}}$ $\frac{{(6 y^{3})}^{4}}{2 y^{7}}$
720	Simplify	b^4(1/3b^2)(12b^-8)	$b^{4} (\frac{1}{3} b^{2}) (12 b^{- 8})$ $b^{4} (\frac{1}{3} b^{2}) (12 b^{- 8})$
721	Simplify	3/(x-2)+5/(2-x)	$\frac{3}{x - 2} + \frac{5}{2 - x}$ $\frac{3}{x - 2} + \frac{5}{2 - x}$
722	Simplify	(1+sin(y))/(1+csc(y))	$\frac{1 + sin (y)}{1 + csc (y)}$ $\frac{1 + \sin (y)}{1 + \csc (y)}$
723	Simplify	1/(sec(x)-1)-1/(sec(x)+1)	$\frac{1}{sec (x) - 1} - \frac{1}{sec (x) + 1}$ $\frac{1}{\sec (x) - 1} - \frac{1}{\sec (x) + 1}$
724	Simplify	(1-cot(x))/(tan(x)-1)	$\frac{1 - cot (x)}{tan (x) - 1}$ $\frac{1 - \cot (x)}{\tan (x) - 1}$
725	Simplify	sin(x)^2(1+tan(x)^2)	${sin}^{2} (x) (1 + {tan}^{2} (x))$ $\sin^{2} (x) (1 + \tan^{2} (x))$
726	Simplify	square root of 1/3 square root of -27	$\sqrt{\frac{1}{3}} \sqrt{- 27}$ $\sqrt{\frac{1}{3}} \sqrt{- 27}$
727	Simplify	2sin(2x)	$2 sin (2 x)$ $2 \sin (2 x)$
728	Solve for x	5^(7x+1)=7^(x-5)	$5^{7 x + 1} = 7^{x - 5}$ $5^{7 x + 1} = 7^{x - 5}$
729	Solve for x	4^(x+2)=6^(-2x-3)	$4^{x + 2} = 6^{- 2 x - 3}$ $4^{x + 2} = 6^{- 2 x - 3}$
730	Solve for x	1/x+1/(x+1)=2/(3(x+1))	$\frac{1}{x} + \frac{1}{x + 1} = \frac{2}{3 (x + 1)}$ $\frac{1}{x} + \frac{1}{x + 1} = \frac{2}{3 (x + 1)}$
731	Solve for x	(5x^2)/4=2(x-1)	$\frac{5 x^{2}}{4} = 2 (x - 1)$ $\frac{5 x^{2}}{4} = 2 (x - 1)$
732	Solve for x	4^(1-x)=3^(2x+5)	$4^{1 - x} = 3^{2 x + 5}$ $4^{1 - x} = 3^{2 x + 5}$
733	Solve for x	7^(2x)+7^(x+1)-60=0	$7^{2 x} + 7^{x + 1} - 60 = 0$ $7^{2 x} + 7^{x + 1} - 60 = 0$
734	Solve for x	7/(2x+1)-(8x)/(2x-1)=-4	$\frac{7}{2 x + 1} - \frac{8 x}{2 x - 1} = - 4$ $\frac{7}{2 x + 1} - \frac{8 x}{2 x - 1} = - 4$
735	Solve for x	8^(3x)=360	$8^{3 x} = 360$ $8^{3 x} = 360$
736	Solve for x	e^(2x)-4e^x-21=0	$e^{2 x} - 4 e^{x} - 21 = 0$ $e^{2 x} - 4 e^{x} - 21 = 0$
737	Solve for x	e^(-2x)=7	$e^{- 2 x} = 7$ $e^{- 2 x} = 7$
738	Solve for x	e^(3x)=25	$e^{3 x} = 25$ $e^{3 x} = 25$
739	Solve for x	sin(x)^2-2sin(x)+1=0	${sin}^{2} (x) - 2 sin (x) + 1 = 0$ $\sin^{2} (x) - 2 \sin (x) + 1 = 0$
740	Solve for x	square root of 6x-2 = square root of 4x+4	$\sqrt{6 x - 2} = \sqrt{4 x + 4}$ $\sqrt{6 x - 2} = \sqrt{4 x + 4}$
741	Solve for x	log base 6 of x=3	${log}_{6} (x) = 3$ $\log_{6} (x) = 3$
742	Solve for x	x^6-8x^3-9=0	$x^{6} - 8 x^{3} - 9 = 0$ $x^{6} - 8 x^{3} - 9 = 0$
743	Solve for x	log base 6 of 36=x	${log}_{6} (36) = x$ $\log_{6} (36) = x$
744	Solve for x	log base 5 of x-7+ log base 5 of x-4- log base 5 of x=1	${log}_{5} (x - 7) + {log}_{5} (x - 4) - {log}_{5} (x) = 1$ $\log_{5} (x - 7) + \log_{5} (x - 4) - \log_{5} (x) = 1$
745	Solve for x	log base 3 of 2-x=3	${log}_{3} (2 - x) = 3$ $\log_{3} (2 - x) = 3$
746	Solve for x	log base 2 of x+ log base 2 of x-6=4	${log}_{2} (x) + {log}_{2} (x - 6) = 4$ $\log_{2} (x) + \log_{2} (x - 6) = 4$
747	Solve for x	x-11 square root of x+30=0	$x - 11 \sqrt{x} + 30 = 0$ $x - 11 \sqrt{x} + 30 = 0$
748	Solve for x	log base 16 of x+ log base 4 of x+ log base 2 of x=7	${log}_{16} (x) + {log}_{4} (x) + {log}_{2} (x) = 7$ $\log_{16} (x) + \log_{4} (x) + \log_{2} (x) = 7$
749	Solve for x	5x^3+7x^2-11x+3=0	$5 x^{3} + 7 x^{2} - 11 x + 3 = 0$ $5 x^{3} + 7 x^{2} - 11 x + 3 = 0$
750	Solve for x	5(2^(3-x))-13=100	$5 (2^{3 - x}) - 13 = 100$ $5 (2^{3 - x}) - 13 = 100$
751	Solve for x	5(3^x)=7	$5 (3^{x}) = 7$ $5 (3^{x}) = 7$
752	Solve for x	5 natural log of 3-x=4	$5 ln (3 - x) = 4$ $5 \ln (3 - x) = 4$
753	Solve for x	3- log of x+2=5	$3 - log (x + 2) = 5$ $3 - \log (x + 2) = 5$
754	Solve for x	4e^(2x)=40	$4 e^{2 x} = 40$ $4 e^{2 x} = 40$
755	Solve for x	2sin(x)cos(x)+sin(x)=0	$2 sin (x) cos (x) + sin (x) = 0$ $2 \sin (x) \cos (x) + \sin (x) = 0$
756	Solve for x	2 log of x = log of 2+ log of 6x-10	$2 log (x) = log (2) + log (6 x - 10)$ $2 \log (x) = \log (2) + \log (6 x - 10)$
757	Solve for x	2000=500e^(4x)	$2000 = 500 e^{4 x}$ $2000 = 500 e^{4 x}$
758	Solve for x	3+2e^(-x)=6	$3 + 2 e^{- x} = 6$ $3 + 2 e^{- x} = 6$
759	Solve for x	3+2 natural log of x=10	$3 + 2 ln (x) = 10$ $3 + 2 \ln (x) = 10$
760	Solve for x	\|x+3\|=\|2x+1\|	$\| x + 3 \| = \| 2 x + 1 \|$ $\| x + 3 \| = \| 2 x + 1 \|$
761	Solve for x	3(5^(x-1))=21	$3 (5^{x - 1}) = 21$ $3 (5^{x - 1}) = 21$
762	Solve for x	(x+1)/3+(x+2)/7=5	$\frac{x + 1}{3} + \frac{x + 2}{7} = 5$ $\frac{x + 1}{3} + \frac{x + 2}{7} = 5$
763	Solve for x	(x-2)/(x+4)=(x-6)/(x-4)	$\frac{x - 2}{x + 4} = \frac{x - 6}{x - 4}$
764	Solve for x	x^4-x^3+4x^2-16x-192=0	$x^{4} - x^{3} + 4 x^{2} - 16 x - 192 = 0$
765	Solve for x	x^(4/3)-5x^(2/3)+6=0	$x^{\frac{4}{3}} - 5 x^{\frac{2}{3}} + 6 = 0$
766	Solve for d	d=(f(x+h)-f(x))/h	$d = \frac{f (x + h) - f (x)}{h}$
767	Solve for B	A=1/2*((B+b)h)	$A = \frac{1}{2} \cdot ((B + b) h)$
768	Solve for ?	3tan(x)^3=tan(x)	$3 \tan^{3} (x) = \tan (x)$
769	Solve for ?	cos(x)-1=0	$\cos (x) - 1 = 0$
770	Solve for ?	cos(2x)=( square root of 2)/2	$\cos (2 x) = \frac{\sqrt{2}}{2}$
771	Solve for ?	cos(2x)=1	$\cos (2 x) = 1$
772	Solve for ?	cos(2x-pi/2)=-1	$\cos (2 x - \frac{π}{2}) = - 1$
773	Solve for ?	cos(x)^2-1=0	$\cos^{2} (x) - 1 = 0$
774	Solve for ?	sec(x)=-1	$\sec (x) = - 1$
775	Solve for ?	sin(x)=7/25	$\sin (x) = \frac{7}{25}$
776	Solve for ?	tan(x)+1=0	$\tan (x) + 1 = 0$
777	Solve for ?	tan(x/2+pi/3)=1	$\tan (\frac{x}{2} + \frac{π}{3}) = 1$
778	Solve for x	2^(3x)=34	$2^{3 x} = 34$
779	Solve for x	5 = square root of 4x-3	$5 = \sqrt{4 x - 3}$
780	Solve for x	2^(x-1)=10	$2^{x - 1} = 10$
781	Solve for x	2^(x-3)=16	$2^{x - 3} = 16$
782	Solve for x	1/x+1/(x+2)=1/2	$\frac{1}{x} + \frac{1}{x + 2} = \frac{1}{2}$
783	Solve for x	1025/(8+e^(4x))=5	$\frac{1025}{8 + e^{4 x}} = 5$
784	Solve for x	119/(e^(6x)-14)=7	$\frac{119}{e^{6 x} - 14} = 7$
785	Solve for x	(2x-1)^2=8	${(2 x - 1)}^{2} = 8$
786	Solve for r1	1/r=1/a+1/b	$\frac{1}{r} = \frac{1}{a} + \frac{1}{b}$
787	Solve for s	3-2s=2(3-st)	$3 - 2 s = 2 (3 - s t)$
788	Simplify	(7-i)(3+3i)	$(7 - i) (3 + 3 i)$
789	Simplify	(8-i)-(4-i)	$(8 - i) - (4 - i)$
790	Simplify	(12x-7)-(5x-12)	$(12 x - 7) - (5 x - 12)$
791	Solve for b	b/(b+1)-(b+1)/(b-4)=5/(b^2-3b-4)	$\frac{b}{b + 1} - \frac{b + 1}{b - 4} = \frac{5}{b^{2} - 3 b - 4}$
792	Solve for z	z=2+6i	$z = 2 + 6 i$
793	Solve for x	log of 4x = log of 5+ log of x-3	$\log (4 x) = \log (5) + \log (x - 3)$
794	Solve for x	log of x+4- log of x = log of x+2	$\log (x + 4) - \log (x) = \log (x + 2)$
795	Solve for x	log of x-4=3	$\log (x - 4) = 3$
796	Solve for x	natural log of x-4- natural log of x+1 = natural log of 6	$\ln (x - 4) - \ln (x + 1) = \ln (6)$
797	Solve for x	natural log of x-8- natural log of x+7 = natural log of x-10- natural log of x+8	$\ln (x - 8) - \ln (x + 7) = \ln (x - 10) - \ln (x + 8)$
798	Solve for x	natural log of x+ natural log of x+1=4	$\ln (x) + \ln (x + 1) = 4$
799	Solve for x	natural log of x+ natural log of x+10=3	$\ln (x) + \ln (x + 10) = 3$
800	Solve for x	8(4^(6-2x))+13=41	$8 (4^{6 - 2 x}) + 13 = 41$