Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
44701	Use the Rational Roots Test to Find All Possible Roots	f(x)=3x^4-x^2+2	$f (x) = 3 x^{4} - x^{2} + 2$
44702	Find the Inverse	y=8^(2x)	$y = 8^{2 x}$
44703	Find the Center and Radius	(x-3/4)^2+(y-9)^2=20	${(x - \frac{3}{4})}^{2} + {(y - 9)}^{2} = 20$
44704	Find the Center and Radius	x^2+y^2-8x+10y+15=0	$x^{2} + y^{2} - 8 x + 10 y + 15 = 0$
44705	Find the Center and Radius	(x-4)^2+(y-2)^2=25	${(x - 4)}^{2} + {(y - 2)}^{2} = 25$
44706	Find the Center and Radius	(x-1)^2+(y-4)^2=25	${(x - 1)}^{2} + {(y - 4)}^{2} = 25$
44707	Find the Center and Radius	x^2+(y-5)^2=9	$x^{2} + {(y - 5)}^{2} = 9$
44708	Find the Center and Radius	x^2+2y^2-4x-16y+32=0	$x^{2} + 2 y^{2} - 4 x - 16 y + 32 = 0$
44709	Find the Center and Radius	(x-8)^2+(y-2)^2=81	${(x - 8)}^{2} + {(y - 2)}^{2} = 81$
44710	Find the Center and Radius	2x^2+2y^2-16x+4y-16=0	$2 x^{2} + 2 y^{2} - 16 x + 4 y - 16 = 0$
44711	Find the Center and Radius	4x^2+4y^2-24x+32y+36=0	$4 x^{2} + 4 y^{2} - 24 x + 32 y + 36 = 0$
44712	Find the Center and Radius	4x^2+4y^2-24x+8y-60=0	$4 x^{2} + 4 y^{2} - 24 x + 8 y - 60 = 0$
44713	Find the Center and Radius	x^2+y^2-36=0	$x^{2} + y^{2} - 36 = 0$
44714	Find the Center and Radius	x^2+y^2-10y=0	$x^{2} + y^{2} - 10 y = 0$
44715	Expand Using the Binomial Theorem	(x+3y)^10	${(x + 3 y)}^{10}$
44716	Expand Using the Binomial Theorem	(x^5+y^2)^9	${(x^{5} + y^{2})}^{9}$
44717	Expand Using the Binomial Theorem	(x+6y)^4	${(x + 6 y)}^{4}$
44718	Expand Using the Binomial Theorem	(x-4y)^7	${(x - 4 y)}^{7}$
44719	Expand Using the Binomial Theorem	(x-4y)^8	${(x - 4 y)}^{8}$
44720	Expand Using the Binomial Theorem	(z+y)^4	${(z + y)}^{4}$
44721	Expand Using the Binomial Theorem	(x-2/( square root of x))^19	${(x - \frac{2}{\sqrt{x}})}^{19}$
44722	Expand Using the Binomial Theorem	(w-x)^3	${(w - x)}^{3}$
44723	Expand Using the Binomial Theorem	(3x+4y)^8	${(3 x + 4 y)}^{8}$
44724	Expand Using the Binomial Theorem	(4x+5y)^7	${(4 x + 5 y)}^{7}$
44725	Expand Using the Binomial Theorem	(2x-4)^4	${(2 x - 4)}^{4}$
44726	Expand Using the Binomial Theorem	(3p-2q)^4	${(3 p - 2 q)}^{4}$
44727	Expand Using the Binomial Theorem	(2p-3q)^6	${(2 p - 3 q)}^{6}$
44728	Expand Using the Binomial Theorem	(2x+ square root of 3)^6	${(2 x + \sqrt{3})}^{6}$
44729	Expand Using the Binomial Theorem	(2x+3y)^7	${(2 x + 3 y)}^{7}$
44730	Expand Using the Binomial Theorem	(2-2i)^5	${(2 - 2 i)}^{5}$
44731	Expand Using the Binomial Theorem	(2c+b)^4	${(2 c + b)}^{4}$
44732	Expand Using the Binomial Theorem	(1+i)^16	${(1 + i)}^{16}$
44733	Find the Asymptotes	f(x)=(2x^2-5x-3)/(x^2-4)	$f (x) = \frac{2 x^{2} - 5 x - 3}{x^{2} - 4}$
44734	Find the Asymptotes	f(x)=(3x)/(x-5)	$f (x) = \frac{3 x}{x - 5}$
44735	Find the Asymptotes	f(x)=(3x^2-5x+1)/(x+1)	$f (x) = \frac{3 x^{2} - 5 x + 1}{x + 1}$
44736	Find the Asymptotes	f(x)=(x^2)/(x+1)	$f (x) = \frac{x^{2}}{x + 1}$
44737	Find the Asymptotes	f(x)=(7x^2-3x-9)/(2x^2-4x+5)	$f (x) = \frac{7 x^{2} - 3 x - 9}{2 x^{2} - 4 x + 5}$
44738	Convert to Interval Notation	(x^2(4+x)(x-9))/((x+2)(x-7))>=0	$\frac{x^{2} (4 + x) (x - 9)}{(x + 2) (x - 7)} \geq 0$
44739	Convert to Interval Notation	(3x-2)/(x+5)<=2	$\frac{3 x - 2}{x + 5} \leq 2$
44740	Convert to Trigonometric Form	3-7i	$3 - 7 i$
44741	Convert to Trigonometric Form	32i	$32 i$
44742	Convert to Trigonometric Form	-100i	$- 100 i$
44743	Convert to Trigonometric Form	cube root of -1+i square root of 3	$\sqrt[3]{- 1 + i \sqrt{3}}$
44744	Convert to Trigonometric Form	-256i	$- 256 i$
44745	Convert to Trigonometric Form	-2-6i	$- 2 - 6 i$
44746	Convert to Trigonometric Form	-1-2i	$- 1 - 2 i$
44747	Convert to Trigonometric Form	-17+32i	$- 17 + 32 i$
44748	Convert to Trigonometric Form	6+6 square root of 3i	$6 + 6 \sqrt{3} i$
44749	Convert to Trigonometric Form	8 square root of 3+8i	$8 \sqrt{3} + 8 i$
44750	Verify the Identity	(tan(theta))/(sec(theta))=sin(theta)	$\frac{\tan (θ)}{\sec (θ)} = \sin (θ)$
44751	Verify the Identity	(1+sec(theta))(1-sec(theta))=-tan(theta)^2	$(1 + \sec (θ)) (1 - \sec (θ)) = - \tan^{2} (θ)$
44752	Verify the Identity	(cos(theta))/(1-sin(theta))=sec(theta)+tan(theta)	$\frac{\cos (θ)}{1 - \sin (θ)} = \sec (θ) + \tan (θ)$
44753	Verify the Identity	cos(theta)^4-sin(theta)^4=cos(2theta)	$\cos^{4} (θ) - \sin^{4} (θ) = \cos (2 θ)$
44754	Verify the Identity	cot(theta)sec(theta)=csc(theta)	$\cot (θ) \sec (θ) = \csc (θ)$
44755	Verify the Identity	tan(theta)*csc(theta)=sec(theta)	$\tan (θ) \cdot \csc (θ) = \sec (θ)$
44756	Convert Degrees, Minutes, Seconds to Decimal Degrees	-128 degrees 41'	$- 128 ° 41'$
44757	Convert to Logarithmic Form	(1/7)^2=1/49	${(\frac{1}{7})}^{2} = \frac{1}{49}$
44758	Convert to Logarithmic Form	1/216=6^-3	$\frac{1}{216} = 6^{- 3}$
44759	Convert to Logarithmic Form	(9/4)^-0.5=2/3	${(\frac{9}{4})}^{- 0.5} = \frac{2}{3}$
44760	Convert to Logarithmic Form	11^x=121	$11^{x} = 121$
44761	Convert to Logarithmic Form	10^x=3.91	$10^{x} = 3.91$
44762	Convert to Logarithmic Form	10^x=4	$10^{x} = 4$
44763	Find the Asymptotes	(x^3-8)/(x^2-7x+10)	$\frac{x^{3} - 8}{x^{2} - 7 x + 10}$
44764	Find the Asymptotes	(x-1)/(3x)	$\frac{x - 1}{3 x}$
44765	Convert to Logarithmic Form	e^k=h	$e^{k} = h$
44766	Convert to Logarithmic Form	3e^(5x)=1977	$3 e^{5 x} = 1977$
44767	Expand the Trigonometric Expression	cos(arctan(u)-arccos(v))	$\cos (\arctan (u) - \arccos (v))$
44768	Evaluate the Function	f(x)=1 , 50	$f (x) = 1$ , $50$
44769	Find the Domain and Range	2(5^x)	$2 (5^{x})$
44770	Find the Domain and Range	-1/7x^2+200x	$- \frac{1}{7} x^{2} + 200 x$
44771	Find the Domain and Range	2x+1	$2 x + 1$
44772	Expand Using Sum/Difference Formulas	sin(2B)sin(9B)	$\sin (2 B) \sin (9 B)$
44773	Expand Using Sum/Difference Formulas	sin(5x)sin(8x)	$\sin (5 x) \sin (8 x)$
44774	Find the Range	f(x) = square root of x-6	$f (x) = \sqrt{x - 6}$
44775	Convert to Radical Form	a^8+7a^(-3/5)	$a^{8} + 7 a^{- \frac{3}{5}}$
44776	Determine if Odd, Even, or Neither	y=x^5+3x^3	$y = x^{5} + 3 x^{3}$
44777	Expand the Logarithmic Expression	log of x^2+1z	$\log (x^{2} + 1) z$
44778	Expand the Logarithmic Expression	log of (x^2)/4	$\log (\frac{x^{2}}{4})$
44779	Expand the Logarithmic Expression	log of (7^3*8)^3	$\log ({(7^{3} \cdot 8)}^{3})$
44780	Expand the Logarithmic Expression	log of u/v	$\log (\frac{u}{v})$
44781	Expand the Logarithmic Expression	natural log of (xy)^2	$\ln ({(x y)}^{2})$
44782	Expand the Logarithmic Expression	natural log of (e^4)/7	$\ln (\frac{e^{4}}{7})$
44783	Expand the Logarithmic Expression	natural log of 49y	$\ln (49 y)$
44784	Expand the Logarithmic Expression	log base 5 of 10x+5y	$\log_{5} (10 x + 5 y)$
44785	Expand the Logarithmic Expression	log base 5 of 20x+15y	$\log_{5} (20 x + 15 y)$
44786	Expand the Logarithmic Expression	log base 3 of 27x+45y	$\log_{3} (27 x + 45 y)$
44787	Expand the Logarithmic Expression	log base 3 of 6xy^2	$\log_{3} (6 x y^{2})$
44788	Expand the Logarithmic Expression	log base 2 of 2x+6y	$\log_{2} (2 x + 6 y)$
44789	Expand the Logarithmic Expression	log base 2 of (x^6y^7)/8	$\log_{2} (\frac{x^{6} y^{7}}{8})$
44790	Expand the Logarithmic Expression	log base 2 of (8x^3)/(2y)	$\log_{2} (\frac{8 x^{3}}{2 y})$
44791	Expand the Logarithmic Expression	log base 2 of 4x^2+48x+144	$\log_{2} (4 x^{2} + 48 x + 144)$
44792	Expand the Logarithmic Expression	log of z^8y	$\log (z^{8} y)$
44793	Expand the Logarithmic Expression	log base 8 of 16/x	$\log_{8} (\frac{16}{x})$
44794	Expand the Logarithmic Expression	log base 9 of square root of xyz	$\log_{9} (\sqrt{x \cdot y \cdot z})$
44795	Expand the Logarithmic Expression	log base 9 of x^6 square root of y/(z^5)	$\log_{9} (x^{6} \sqrt{\frac{y}{z^{5}}})$
44796	Expand the Logarithmic Expression	log base a of ( square root of a)^k	$\log_{a} ({(\sqrt{a})}^{k})$
44797	Expand the Logarithmic Expression	log base a of MN	$\log_{a} (M N)$
44798	Expand the Logarithmic Expression	log base b of seventh root of (x^2)/(y^7z^5)	$\log_{b} (\sqrt[7]{\frac{x^{2}}{y^{7} z^{5}}})$
44799	Expand the Logarithmic Expression	log base b of square root of (x^3y^2)/(z^4)	$\log_{b} (\sqrt{\frac{x^{3} y^{2}}{z^{4}}})$
44800	Expand the Logarithmic Expression	log base b of x^4y^2	$\log_{b} (x^{4} y^{2})$