Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
40801	Factor	tan(theta)^4+2tan(theta)^2+1	$\tan^{4} (θ) + 2 \tan^{2} (θ) + 1$
40802	Factor	3x^2-18x+29	$3 x^{2} - 18 x + 29$
40803	Factor	4sin(x)^2-9cos(x)^2	$4 \sin^{2} (x) - 9 \cos^{2} (x)$
40804	Factor	x^3+4x^2-19x+14	$x^{3} + 4 x^{2} - 19 x + 14$
40805	Find the Degree	csc(theta)=2	$\csc (θ) = 2$
40806	Find the Roots (Zeros)	x^3-19x-30	$x^{3} - 19 x - 30$
40807	Find the Asymptotes	(x^2-9)/x	$\frac{x^{2} - 9}{x}$
40808	Find the Asymptotes	(x^2+8x-9)/(x^2+3x-4)	$\frac{x^{2} + 8 x - 9}{x^{2} + 3 x - 4}$
40809	Find the Asymptotes	(1-x^2)/x	$\frac{1 - x^{2}}{x}$
40810	Simplify/Condense	cot(x)(tan(x)-sec(x))	$\cot (x (\tan (x) - \sec (x)))$
40811	Simplify/Condense	(sin(y)^2)/(1-cos(y))	$\frac{\sin^{2} (y)}{1 - \cos (y)}$
40812	Simplify/Condense	log of x-1/2 log of x-9	$\log (x) - \frac{1}{2} \log (x - 9)$
40813	Expand the Trigonometric Expression	tan(3x)^2	$\tan^{2} (3 x)$
40814	Use the Rational Roots Test to Find All Possible Roots	3x^3+4x^2-x-2	$3 x^{3} + 4 x^{2} - x - 2$
40815	Convert Degrees, Minutes, Seconds to Decimal Degrees	105 degrees 32'45''	$105 ° 32' 45''$
40816	Convert Degrees, Minutes, Seconds to Decimal Degrees	11 degrees 11'11''	$11 ° 11' 11''$
40817	Find the Roots/Zeros Using the Rational Roots Test	f(x)=7x^3+51x^2+15x+7	$f (x) = 7 x^{3} + 51 x^{2} + 15 x + 7$
40818	Find the Roots (Zeros)	f(x)=x^3-6x^2+21x-26	$f (x) = x^{3} - 6 x^{2} + 21 x - 26$
40819	Find the Roots (Zeros)	f(x)=9x^4-9x^3-58x^2+4x+24	$f (x) = 9 x^{4} - 9 x^{3} - 58 x^{2} + 4 x + 24$
40820	Expand the Logarithmic Expression	log of (b^3)/a	$\log (\frac{b^{3}}{a})$
40821	Expand the Logarithmic Expression	log base 2 of cube root of x^2y^4	$\log_{2} (\sqrt[3]{x^{2} y^{4}})$
40822	Expand the Logarithmic Expression	log of ( square root of y^7)/(xz^3)	$\log (\frac{\sqrt{y^{7}}}{x z^{3}})$
40823	Expand the Logarithmic Expression	log base 4 of x square root of y	$\log_{4} (x \sqrt{y})$
40824	Find the Roots (Zeros)	f(x)=x^5+2x^4-6x^3-25x^2+8x+8	$f (x) = x^{5} + 2 x^{4} - 6 x^{3} - 25 x^{2} + 8 x + 8$
40825	Find the Domain	square root of (2x)/(x+8)-1	$\sqrt{\frac{2 x}{x + 8} - 1}$
40826	Find the Domain	5/(x/(x+5))	$\frac{5}{\frac{x}{x + 5}}$
40827	Convert to Rectangular Coordinates	(-2,(4pi)/3)	$(- 2, \frac{4 π}{3})$
40828	Convert to Rectangular Coordinates	(4,pi/2)	$(4, \frac{π}{2})$
40829	Find the Domain	f(x)=(19x)/(x^2-121)	$f (x) = \frac{19 x}{x^{2} - 121}$
40830	Find the Domain	f(x) = square root of x/(2x-1)-1	$f (x) = \sqrt{\frac{x}{2 x - 1} - 1}$
40831	Find the Domain	h(x)=(x+9)/(x^2-81)	$h (x) = \frac{x + 9}{x^{2} - 81}$
40832	Find the Domain	f(x) = square root of 7+x	$f (x) = \sqrt{7 + x}$
40833	Find the Domain	f(x) = log of (x+3)/(x-2)	$f (x) = \log (\frac{x + 3}{x - 2})$
40834	Find the Domain	f(x)=(x^2+7)/(36-x^2)	$f (x) = \frac{x^{2} + 7}{36 - x^{2}}$
40835	Write as a Single Logarithm	log of x* log of 2	$\log (x) \cdot \log (2)$
40836	Convert to Trigonometric Form	9i	$9 i$
40837	Verify the Identity	sin(360 degrees +theta)=sin(theta)	$\sin (360 ° + θ) = \sin (θ)$
40838	Verify the Identity	sin(theta)(tan(theta)+cot(theta))=sec(theta)	$\sin (θ (\tan (θ) + \cot (θ))) = \sec (θ)$
40839	Verify the Identity	cos(pi+theta)=-cos(theta)	$\cos (π + θ) = - \cos (θ)$
40840	Verify the Identity	cos(theta)^2-sin(theta)^2=1-2sin(theta)^2	$\cos^{2} (θ) - \sin^{2} (θ) = 1 - 2 \sin^{2} (θ)$
40841	Convert to Interval Notation	x^3+4x^2>=4x+16	$x^{3} + 4 x^{2} \geq 4 x + 16$
40842	Convert to Interval Notation	x^3-x^2-90x>0	$x^{3} - x^{2} - 90 x > 0$
40843	Convert to Interval Notation	(x-2)/(x+3)>=0	$\frac{x - 2}{x + 3} \geq 0$
40844	Convert to Interval Notation	(x-3)(x+1)^2(x-8)>=0	$(x - 3) {(x + 1)}^{2} (x - 8) \geq 0$
40845	Convert to Interval Notation	(x-1)(x+4)(x-5)>=0	$(x - 1) (x + 4) (x - 5) \geq 0$
40846	Convert to Interval Notation	-1/(x-6)<2/(9-x)	$\frac{- 1}{x - 6} < \frac{2}{9 - x}$
40847	Convert to Interval Notation	(x+1)(x-8)^2(x-3)>=0	$(x + 1) {(x - 8)}^{2} (x - 3) \geq 0$
40848	Convert to Interval Notation	x^3>=4x^2	$x^{3} \geq 4 x^{2}$
40849	Convert to Interval Notation	9x^4-97x^2+144<=0	$9 x^{4} - 97 x^{2} + 144 \leq 0$
40850	Convert to Interval Notation	(x+2)(x-3)(x+8)<0	$(x + 2) (x - 3) (x + 8) < 0$
40851	Multiply	(x-(3-i))(x-(3+i))	$(x - (3 - i)) (x - (3 + i))$
40852	Multiply	(sin(x)+cos(x))^2	${(\sin (x) + \cos (x))}^{2}$
40853	Find the Asymptotes	h(x)=(x+3)/(x(x+5))	$h (x) = \frac{x + 3}{x (x + 5)}$
40854	Find the Asymptotes	f(x)=4/((x-2)^2)	$f (x) = \frac{4}{{(x - 2)}^{2}}$
40855	Find the Asymptotes	f(x)=(x^2+3x-10)/(x-5)	$f (x) = \frac{x^{2} + 3 x - 10}{x - 5}$
40856	Find the Asymptotes	f(x)=(x^2+x-30)/(x-6)	$f (x) = \frac{x^{2} + x - 30}{x - 6}$
40857	Find the Asymptotes	f(x)=(7+x)/(7-x)	$f (x) = \frac{7 + x}{7 - x}$
40858	Find the Asymptotes	f(x)=4sec(2x-pi)	$f (x) = 4 \sec (2 x - π)$
40859	Find the Vertex	f(x)=x^2-14x+48	$f (x) = x^{2} - 14 x + 48$
40860	Find the Maximum/Minimum Value	f(x)=4sin(2x)-3	$f (x) = 4 \sin (2 x) - 3$
40861	Find the x and y Intercepts	9y=x+3	$9 y = x + 3$
40862	Find Amplitude, Period, and Phase Shift	y=5/2cos(x/2)	$y = \frac{5}{2} \cos (\frac{x}{2})$
40863	Find Amplitude, Period, and Phase Shift	y=-6sin(2x+pi/2)	$y = - 6 \sin (2 x + \frac{π}{2})$
40864	Find Amplitude, Period, and Phase Shift	y=1/4cos(x)	$y = \frac{1}{4} \cos (x)$
40865	Find Amplitude, Period, and Phase Shift	y=9cos(x)	$y = 9 \cos (x)$
40866	Find Amplitude, Period, and Phase Shift	y=5cos(2x-pi)	$y = 5 \cos (2 x - π)$
40867	Identify the Polar Equation	r=5/(1+cos(theta))	$r = \frac{5}{1 + \cos (θ)}$
40868	Find the Equation Given the Roots	1-5i	$1 - 5 i$
40869	Find the Domain and Range	-x^2-8x	$- x^{2} - 8 x$
40870	Evaluate the Function	f(-6)=(x^2-49)/x	$f (- 6) = \frac{x^{2} - 49}{x}$
40871	Find the Trig Value	sin(2theta)=-1/2	$\sin (2 θ) = - \frac{1}{2}$
40872	Find the Trig Value	sin(theta)=-5/13	$\sin (θ) = - \frac{5}{13}$
40873	Find the Trig Value	sec(theta)=(2 square root of 3)/3	$\sec (θ) = \frac{2 \sqrt{3}}{3}$
40874	Find the Domain and Range	f(x)=1/3 log of 4x	$f (x) = \frac{1}{3} \log (4 x)$
40875	Find the Domain and Range	f(x)=8x-x^2-17	$f (x) = 8 x - x^{2} - 17$
40876	Find the Domain and Range	g(x)=tan(x)	$g (x) = \tan (x)$
40877	Find the Asymptotes	y=tan(theta)	$y = \tan (θ)$
40878	Find the Asymptotes	y=-tan(x)	$y = - \tan (x)$
40879	Find the Asymptotes	y=tan(x-pi/4)	$y = \tan (x - \frac{π}{4})$
40880	Find the Asymptotes	y=tan(x+pi/2)	$y = \tan (x + \frac{π}{2})$
40881	Find Trig Functions Using Identities	csc(x)(sin(x)+cos(x))=	$\csc (x (\sin (x) + \cos (x))) =$
40882	Find Trig Functions Using Identities	sin(x-pi/3)	$\sin (x - \frac{π}{3})$
40883	Find the Roots (Zeros)	f(x)=x^3-9x^2+9x-81	$f (x) = x^{3} - 9 x^{2} + 9 x - 81$
40884	Find the Roots (Zeros)	f(x)=x^3+x^2-9x-9	$f (x) = x^{3} + x^{2} - 9 x - 9$
40885	Find the Roots (Zeros)	f(x)=x^4-x^5	$f (x) = x^{4} - x^{5}$
40886	Expand the Logarithmic Expression	log base 7 of ( square root of 7x^5)/y	$\log_{7} (\frac{\sqrt{7 x^{5}}}{y})$
40887	Expand the Logarithmic Expression	log of ( cube root of x^7z)/(y^2)	$\log (\frac{\sqrt[3]{x^{7} z}}{y^{2}})$
40888	Convert from Degrees to Radians	970 degrees	$970 °$
40889	Convert from Degrees to Radians	-145 degrees	$- 145 °$
40890	Convert from Degrees to Radians	114 degrees	$114 °$
40891	Convert from Degrees to Radians	138 degrees	$138 °$
40892	Factor	x^4+12x^3+31x^2-12x-32	$x^{4} + 12 x^{3} + 31 x^{2} - 12 x - 32$
40893	Factor	9(5x-2)^2-7(5x-2)(3x+4)	$9 {(5 x - 2)}^{2} - 7 (5 x - 2) (3 x + 4)$
40894	Factor	2x^6-3x^5-13x^4+29x^3-27x^2+32x-12	$2 x^{6} - 3 x^{5} - 13 x^{4} + 29 x^{3} - 27 x^{2} + 32 x - 12$
40895	Find the Inverse	f(x)=arccsc(x)	$f (x) = arccsc (x)$
40896	Find the Inverse	W(h)=50+2.3(h-60)	$W (h) = 50 + 2.3 (h - 60)$
40897	Expand Using Sum/Difference Formulas	sin(135 degrees )	$\sin (135 °)$
40898	Expand Using Sum/Difference Formulas	tan(285 degrees )	$\tan (285 °)$
40899	Divide	15/20	$\frac{15}{20}$
40900	Divide	(pi/4)÷2	$\frac{π}{4} \div 2$