Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
40701	Convert to Interval Notation	x^2+6x+9<=0	$x^{2} + 6 x + 9 \leq 0$
40702	Convert to Interval Notation	x(1-x^2)^3>7(1-x^2)^3	$x {(1 - x^{2})}^{3} > 7 {(1 - x^{2})}^{3}$
40703	Convert to Interval Notation	(x-4)/(x+5)>=0	$\frac{x - 4}{x + 5} \geq 0$
40704	Find the Range	y=arcsec(x)	$y = arcsec (x)$
40705	Find the Domain	f(x) = square root of (2x)/(x+5)-1	$f (x) = \sqrt{\frac{2 x}{x + 5} - 1}$
40706	Find the Domain	f(x) = square root of x^2-121	$f (x) = \sqrt{x^{2} - 121}$
40707	Find the x and y Intercepts	y=64-x^2	$y = 64 - x^{2}$
40708	Find the x and y Intercepts	y=-5sin(4x+pi/3)	$y = - 5 \sin (4 x + \frac{π}{3})$
40709	Find Amplitude, Period, and Phase Shift	y=sin(x/3)	$y = \sin (\frac{x}{3})$
40710	Find the Asymptotes	T(x)=(x^3)/(x^4-81)	$T (x) = \frac{x^{3}}{x^{4} - 81}$
40711	Find the Domain and Range	(2x+8)/(-8x+4)	$\frac{2 x + 8}{- 8 x + 4}$
40712	Find the Domain and Range	log base 3 of x+1	$\log_{3} (x + 1)$
40713	Evaluate the Function	f( square root of 2)=6x^2+3x-12	$f (\sqrt{2}) = 6 x^{2} + 3 x - 12$
40714	Find the Trig Value	tan(theta)=4/3	$\tan (θ) = \frac{4}{3}$
40715	Find the Domain and Range	f(x)=x^2-6x+18	$f (x) = x^{2} - 6 x + 18$
40716	Find the Equation Given the Roots	1-2i	$1 - 2 i$
40717	Divide	(2pi)/(3pi)	$\frac{2 π}{3 π}$
40718	Divide	32/3	$\frac{32}{3}$
40719	Divide	(1/2)/((- square root of 3)/2)	$\frac{\frac{1}{2}}{\frac{- \sqrt{3}}{2}}$
40720	Divide	720/3	$\frac{720}{3}$
40721	Divide	16/12	$\frac{16}{12}$
40722	Divide	19/2	$\frac{19}{2}$
40723	Divide	(pi/2)÷3	$\frac{π}{2} \div 3$
40724	Divide	((3pi)/2)÷2	$\frac{3 π}{2} \div 2$
40725	Multiply	cot(x)(tan(x)-sec(x))	$\cot (x (\tan (x) - \sec (x)))$
40726	Multiply	64*3	$64 \cdot 3$
40727	Find the Vertex	f(x)=2x^2-12x+10	$f (x) = 2 x^{2} - 12 x + 10$
40728	Find All Complex Solutions	2sin(theta)+ square root of 3=0	$2 \sin (θ) + \sqrt{3} = 0$
40729	Find the x and y Intercepts	f(x)=3cos(x)	$f (x) = 3 \cos (x)$
40730	Find the x and y Intercepts	f(x)=(5x)/(x^2-16)	$f (x) = \frac{5 x}{x^{2} - 16}$
40731	Find the x and y Intercepts	f(x)=-3(x-1)^2(x^2-9)	$f (x) = - 3 {(x - 1)}^{2} (x^{2} - 9)$
40732	Find the Domain and Range	y=cot(1/12x)	$y = \cot (\frac{1}{12} x)$
40733	Convert to Rectangular	theta=(2pi)/3	$θ = \frac{2 π}{3}$
40734	Find the Degree	sin(theta)=-( square root of 3)/2	$\sin (θ) = - \frac{\sqrt{3}}{2}$
40735	Write in Exponential Form	log base 216 of 6=1/3	$\log_{216} (6) = \frac{1}{3}$
40736	Factor	1-2cos(theta)^2+cos(theta)^4	$1 - 2 \cos^{2} (θ) + \cos^{4} (θ)$
40737	Factor	cot(x)^2+csc(x)-11	$\cot^{2} (x) + \csc (x) - 11$
40738	Factor	x^4+6x^3+7x^2-6x-8	$x^{4} + 6 x^{3} + 7 x^{2} - 6 x - 8$
40739	Factor	x^3y-9xy	$x^{3} y - 9 x y$
40740	Expand Using Sum/Difference Formulas	sin(-15 degrees )	$\sin (- 15 °)$
40741	Find the Roots (Zeros)	2x^3-5x^2-5x-1=0	$2 x^{3} - 5 x^{2} - 5 x - 1 = 0$
40742	Expand the Logarithmic Expression	log of (z^3)/(y square root of x^5)	$\log (\frac{z^{3}}{y \sqrt{x^{5}}})$
40743	Expand the Logarithmic Expression	log of cube root of xy^4z^2	$\log (\sqrt[3]{x y^{4} z^{2}})$
40744	Find the Roots/Zeros Using the Rational Roots Test	f(x)=5x^3+28x^2+16x+5	$f (x) = 5 x^{3} + 28 x^{2} + 16 x + 5$
40745	Find the Domain	x/(8x+49)	$\frac{x}{8 x + 49}$
40746	Find the Roots (Zeros)	2x^3-11x^2+12x+9	$2 x^{3} - 11 x^{2} + 12 x + 9$
40747	Find the Roots (Zeros)	x^3-6x^2+9x-54	$x^{3} - 6 x^{2} + 9 x - 54$
40748	Verify the Identity	sin(theta)+cos(theta)cot(theta)=csc(theta)	$\sin (θ) + \cos (θ) \cot (θ) = \csc (θ)$
40749	Verify the Identity	(sec(theta)+1)(sec(theta)-1)=tan(theta)^2	$(\sec (θ) + 1) (\sec (θ) - 1) = \tan^{2} (θ)$
40750	Verify the Identity	(cot(theta)+tan(theta))cos(theta)=csc(theta)	$(\cot (θ) + \tan (θ)) \cos (θ) = \csc (θ)$
40751	Convert to Interval Notation	x^2-6x+9<=0	$x^{2} - 6 x + 9 \leq 0$
40752	Convert to Interval Notation	x^3-100x<=0	$x^{3} - 100 x \leq 0$
40753	Convert to Interval Notation	(x-5)/(x-7)>0	$\frac{x - 5}{x - 7} > 0$
40754	Convert to Interval Notation	x^3+x^2+64x+64>0	$x^{3} + x^{2} + 64 x + 64 > 0$
40755	Convert to Interval Notation	(x-1)/(x+2)>=0	$\frac{x - 1}{x + 2} \geq 0$
40756	Find the x and y Intercepts	x^2+y^2-2x-4y-11=0	$x^{2} + y^{2} - 2 x - 4 y - 11 = 0$
40757	Find Amplitude, Period, and Phase Shift	y=-1/2cot(2x)	$y = - \frac{1}{2} \cot (2 x)$
40758	Find Amplitude, Period, and Phase Shift	y=-4sin(6x+pi/2)	$y = - 4 \sin (6 x + \frac{π}{2})$
40759	Find Amplitude, Period, and Phase Shift	f(x)=2csc(4x-pi)+1	$f (x) = 2 \csc (4 x - π) + 1$
40760	Find Amplitude, Period, and Phase Shift	V(t)=229sin(120pit)	$V (t) = 229 \sin (120 π t)$
40761	Find the Vertex	f(x)=x^2-12x+32	$f (x) = x^{2} - 12 x + 32$
40762	Find the Domain and Range	(2x^2+16x-18)/(x^2+x-6)	$\frac{2 x^{2} + 16 x - 18}{x^{2} + x - 6}$
40763	Find the Domain and Range	2x^2-3x+2	$2 x^{2} - 3 x + 2$
40764	Find the Domain and Range	-1/2x^2-4x+10	$- \frac{1}{2} x^{2} - 4 x + 10$
40765	Find the Trig Value	cos(theta)=4/5	$\cos (θ) = \frac{4}{5}$
40766	Find the Trig Value	cos(theta)=2/3	$\cos (θ) = \frac{2}{3}$
40767	Find the Trig Value	sec(theta) = square root of 2	$\sec (θ) = \sqrt{2}$
40768	Find the Asymptotes	f(x)=sec(2x)	$f (x) = \sec (2 x)$
40769	Find the Asymptotes	f(x)=(x^2+2x-63)/(x^2-9)	$f (x) = \frac{x^{2} + 2 x - 63}{x^{2} - 9}$
40770	Find the Asymptotes	f(x)=(x^2+5x-14)/(x-7)	$f (x) = \frac{x^{2} + 5 x - 14}{x - 7}$
40771	Find the Asymptotes	f(x)=(5x)/(x-4)	$f (x) = \frac{5 x}{x - 4}$
40772	Find the Asymptotes	f(x)=1/(3x^2+3x-18)	$f (x) = \frac{1}{3 x^{2} + 3 x - 18}$
40773	Find the Domain and Range	f(x)=1/2 log of 4x	$f (x) = \frac{1}{2} \log (4 x)$
40774	Find the Domain and Range	f(x)=(2x-4)/(x^2+x-2)	$f (x) = \frac{2 x - 4}{x^{2} + x - 2}$
40775	Find the Asymptotes	y=tan(x+pi/4)	$y = \tan (x + \frac{π}{4})$
40776	Multiply	cos(x)sin(x)(csc(x)+tan(x))	$\cos (x) \sin (x (\csc (x) + \tan (x)))$
40777	Multiply	sin(x)cos(x)(cot(x)+sec(x))	$\sin (x) \cos (x (\cot (x) + \sec (x)))$
40778	Multiply	cos(x)sin(x)(sec(x)+csc(x))	$\cos (x) \sin (x (\sec (x) + \csc (x)))$
40779	Divide	1.5/2	$\frac{1.5}{2}$
40780	Divide	49/2	$\frac{49}{2}$
40781	Divide	15/12	$\frac{15}{12}$
40782	Divide	1/(1/4)	$\frac{1}{\frac{1}{4}}$
40783	Divide	(2pi)/(pi/5)	$\frac{2 π}{\frac{π}{5}}$
40784	Divide	120/4	$\frac{120}{4}$
40785	Divide	(5/13)/(12/13)	$\frac{\frac{5}{13}}{\frac{12}{13}}$
40786	Divide	(pi/2)/(2pi)	$\frac{\frac{π}{2}}{2 π}$
40787	Divide	58/2	$\frac{58}{2}$
40788	Find the Inverse	f(x)=7-5x	$f (x) = 7 - 5 x$
40789	Expand Using Sum/Difference Formulas	sin(165 degrees )	$\sin (165 °)$
40790	Find the x and y Intercepts	f(x)=x^4-4x^3+4x^2	$f (x) = x^{4} - 4 x^{3} + 4 x^{2}$
40791	Find All Complex Solutions	sin(theta)^2-cos(theta)^2=1+cos(theta)	$\sin^{2} (θ) - \cos^{2} (θ) = 1 + \cos (θ)$
40792	Find All Complex Solutions	cos(theta)=( square root of 2)/2	$\cos (θ) = \frac{\sqrt{2}}{2}$
40793	Find All Complex Solutions	cos(theta)=1/2	$\cos (θ) = \frac{1}{2}$
40794	Find All Complex Solutions	4sin(x)=-2 square root of 2	$4 \sin (x) = - 2 \sqrt{2}$
40795	Combine	10sin(x)^2+12cos(x)^2-2	$10 \sin^{2} (x) + 12 \cos^{2} (x) - 2$
40796	Find the Vertex	y=-x^2-12x-36	$y = - x^{2} - 12 x - 36$
40797	Find the Domain and Range	y=tan(pi/12x)	$y = \tan (\frac{π}{12} x)$
40798	Find the Domain and Range	y=6cos(x)	$y = 6 \cos (x)$
40799	Use the Rational Roots Test to Find All Possible Roots	f(x)=7x^3+51x^2+15x+7	$f (x) = 7 x^{3} + 51 x^{2} + 15 x + 7$
40800	Factor	4x^3-7x+3	$4 x^{3} - 7 x + 3$