Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
45101	Convert Degrees, Minutes, Seconds to Decimal Degrees	39 degrees 6'	$39 ° 6'$
45102	Subtract	(6z)/(6z+1)-(2z^2)/(3z+4)	$\frac{6 z}{6 z + 1} - \frac{2 z^{2}}{3 z + 4}$
45103	Convert Degrees, Minutes, Seconds to Decimal Degrees	64 degrees 30'	$64 ° 30'$
45104	Convert Degrees, Minutes, Seconds to Decimal Degrees	71 degrees 42'31''	$71 ° 42' 31''$
45105	Find the Asymptotes	f(x)=(9x^2-3x-8)/(4x^2-5x+3)	$f (x) = \frac{9 x^{2} - 3 x - 8}{4 x^{2} - 5 x + 3}$
45106	Find the Asymptotes	f(x)=(-5x^2-10x)/(2x^2-8)	$f (x) = \frac{- 5 x^{2} - 10 x}{2 x^{2} - 8}$
45107	Find the Asymptotes	f(x)=(x^2)/(x+3)	$f (x) = \frac{x^{2}}{x + 3}$
45108	Find the Asymptotes	f(x)=(x^2)/(x^2-49)	$f (x) = \frac{x^{2}}{x^{2} - 49}$
45109	Find the Asymptotes	f(x)=4/(x^2-3x)	$f (x) = \frac{4}{x^{2} - 3 x}$
45110	Find the Asymptotes	f(x)=(6x^5-3x^3+7x-3)/(2x^2-3)	$f (x) = \frac{6 x^{5} - 3 x^{3} + 7 x - 3}{2 x^{2} - 3}$
45111	Find the Asymptotes	f(x)=(5x^4-7)/(2x+3)	$f (x) = \frac{5 x^{4} - 7}{2 x + 3}$
45112	Find the Asymptotes	f(x)=-1/(x^2-9)	$f (x) = - \frac{1}{x^{2} - 9}$
45113	Find the Asymptotes	f(x)=3/(x^3-4x)	$f (x) = \frac{3}{x^{3} - 4 x}$
45114	Find the Asymptotes	s(t)=(-7t)/((t-4)(t-8))	$s (t) = \frac{- 7 t}{(t - 4) (t - 8)}$
45115	Find the Asymptotes	r(x)=(20x^2-31x-7)/(4x^2-15x+14)	$r (x) = \frac{20 x^{2} - 31 x - 7}{4 x^{2} - 15 x + 14}$
45116	Find the Asymptotes	g(x)=-1/(x-3)	$g (x) = \frac{- 1}{x - 3}$
45117	Find the Asymptotes	f(x)=(x^5-3x^4-13x^3+18x^2-17x+12)/(x-5)	$f (x) = \frac{x^{5} - 3 x^{4} - 13 x^{3} + 18 x^{2} - 17 x + 12}{x - 5}$
45118	Find the Asymptotes	f(x)=(x^3-7x^2-8x-9)/(x-4)	$f (x) = \frac{x^{3} - 7 x^{2} - 8 x - 9}{x - 4}$
45119	Find the Asymptotes	f(x)=(x^2+x-6)/(x^2-6x+8)	$f (x) = \frac{x^{2} + x - 6}{x^{2} - 6 x + 8}$
45120	Find the Asymptotes	f(x)=(x^2-16)/(x+4)	$f (x) = \frac{x^{2} - 16}{x + 4}$
45121	Find the Asymptotes	f(x)=-3(3/5)^x	$f (x) = - 3 {(\frac{3}{5})}^{x}$
45122	Find the Asymptotes	f(x)=-2cot(3x)	$f (x) = - 2 \cot (3 x)$
45123	Find the Asymptotes	f(x)=(x-2)/(x^2-16)	$f (x) = \frac{x - 2}{x^{2} - 16}$
45124	Find the Asymptotes	f(x)=(x-5)/(3x^2-17x-28)	$f (x) = \frac{x - 5}{3 x^{2} - 17 x - 28}$
45125	Verify the Identity	tan(u(csc(u)-sin(u)))=cos(u)	$\tan (u (\csc (u) - \sin (u))) = \cos (u)$
45126	Verify the Identity	tan(theta)cot(theta)=1	$\tan (θ) \cot (θ) = 1$
45127	Verify the Identity	cos(theta-pi/2)=sin(theta)	$\cos (θ - \frac{π}{2}) = \sin (θ)$
45128	Verify the Identity	(sin(theta)^2)/(cos(theta)^2)+1=sec(theta)^2	$\frac{\sin^{2} (θ)}{\cos^{2} (θ)} + 1 = \sec^{2} (θ)$
45129	Verify the Identity	(1+tan(theta)^2)cos(theta)^2=1	$(1 + \tan^{2} (θ)) \cos^{2} (θ) = 1$
45130	Verify the Identity	(sec(theta)^2-1)cos(theta)^2=sin(theta)^2	$(\sec^{2} (θ) - 1) \cos^{2} (θ) = \sin^{2} (θ)$
45131	Verify the Identity	(1-sin(theta)^2)sec(theta)^2=1	$(1 - \sin^{2} (θ)) \sec^{2} (θ) = 1$
45132	Find the Inverse	[[8,-3],[5,-3]]	$[\begin{array}{c} 8 & - 3 \\ 5 & - 3 \end{array}]$
45133	Find the Inverse	[[12,-8],[5,-7]]	$[\begin{array}{c} 12 & - 8 \\ 5 & - 7 \end{array}]$
45134	Solve the System of @WORD	x^2-6x+7<0	$x^{2} - 6 x + 7 < 0$
45135	Solve the System of @WORD	x^2-2x-15>0	$x^{2} - 2 x - 15 > 0$
45136	Solve the System of @WORD	9x^4-97x^2+144<=0	$9 x^{4} - 97 x^{2} + 144 \leq 0$
45137	Convert to Interval Notation	\|3x-4\|<=8	$\| 3 x - 4 \| \leq 8$
45138	Convert to Interval Notation	\|5x-2\|<=8	$\| 5 x - 2 \| \leq 8$
45139	Convert to Interval Notation	11x+12<22x-4	$11 x + 12 < 22 x - 4$
45140	Convert to Interval Notation	3x+4<6x-3	$3 x + 4 < 6 x - 3$
45141	Convert to Trigonometric Form	-8+6i	$- 8 + 6 i$
45142	Convert to Trigonometric Form	6-3i	$6 - 3 i$
45143	Verify the Identity	sin(2x)-tan(x)=tan(x)cos(2x)	$\sin (2 x) - \tan (x) = \tan (x) \cos (2 x)$
45144	Verify the Identity	sin(pi/6-x)=1/2(cos(x)+ square root of 3sin(x))	$\sin (\frac{π}{6} - x) = \frac{1}{2} (\cos (x) + \sqrt{3} \sin (x))$
45145	Verify the Identity	sec(theta)+csc(theta)-cos(theta)-sin(theta)=sin(theta)tan(theta)+cos(theta)cot(theta)	$\sec (θ) + \csc (θ) - \cos (θ) - \sin (θ) = \sin (θ) \tan (θ) + \cos (θ) \cot (θ)$
45146	Convert to Trigonometric Form	15-20i	$15 - 20 i$
45147	Convert to Trigonometric Form	16-4i	$16 - 4 i$
45148	Convert to Trigonometric Form	(4+4i)^5	${(4 + 4 i)}^{5}$
45149	Convert to Trigonometric Form	(-5 square root of 3)/2+5/2i	$\frac{- 5 \sqrt{3}}{2} + \frac{5}{2} i$
45150	Convert to Trigonometric Form	-35i	$- 35 i$
45151	Convert to Trigonometric Form	-4+8i	$- 4 + 8 i$
45152	Convert to Trigonometric Form	4-4i square root of 3	$4 - 4 i \sqrt{3}$
45153	Convert to Interval Notation	(x+3)/(x-5)<=0	$\frac{x + 3}{x - 5} \leq 0$
45154	Convert to Interval Notation	(x+4)/(x-8)>=3	$\frac{x + 4}{x - 8} \geq 3$
45155	Convert to Interval Notation	(x-6)/(x+5)<=0	$\frac{x - 6}{x + 5} \leq 0$
45156	Convert to Interval Notation	(x-5)(x-2)^2<0	$(x - 5) {(x - 2)}^{2} < 0$
45157	Convert to Interval Notation	(x-1)/(1-x)<0	$\frac{x - 1}{1 - x} < 0$
45158	Convert to Interval Notation	(x-2)(x+4)<0	$(x - 2) (x + 4) < 0$
45159	Find the Slope and y-intercept	theta=pi/3	$θ = \frac{π}{3}$
45160	Identify the Polar Equation	r=4/(1-6sin(theta))	$r = \frac{4}{1 - 6 \sin (θ)}$
45161	Identify the Polar Equation	r=4/(1-cos(theta))	$r = \frac{4}{1 - \cos (θ)}$
45162	Identify the Polar Equation	r=3/(2-5sin(theta))	$r = \frac{3}{2 - 5 \sin (θ)}$
45163	Identify the Polar Equation	r^2cos(theta)^3=sin(theta)	$r^{2} \cos^{3} (θ) = \sin (θ)$
45164	Identify the Polar Equation	r=1/(cos(theta)+5sin(theta))	$r = \frac{1}{\cos (θ) + 5 \sin (θ)}$
45165	Identify the Polar Equation	r=1/(1+cos(theta))	$r = \frac{1}{1 + \cos (θ)}$
45166	Identify the Polar Equation	r=2/(1+sin(theta))	$r = \frac{2}{1 + \sin (θ)}$
45167	Identify the Polar Equation	z=3 square root of 3-3i	$z = 3 \sqrt{3} - 3 i$
45168	Identify the Polar Equation	rcos(theta)=4	$r \cos (θ) = 4$
45169	Identify the Polar Equation	r=9sec(theta)	$r = 9 \sec (θ)$
45170	Identify the Polar Equation	r=4cos(2theta)	$r = 4 \cos (2 θ)$
45171	Identify the Polar Equation	r=-10sin(theta)	$r = - 10 \sin (θ)$
45172	Find the Domain and Range	x^3-7	$x^{3} - 7$
45173	Find the Domain and Range	9-x^2	$9 - x^{2}$
45174	Find the Domain and Range	4x^2-10x+3	$4 x^{2} - 10 x + 3$
45175	Find the Domain and Range	x^2+5x+6	$x^{2} + 5 x + 6$
45176	Find the Domain and Range	-x^2-4x-4	$- x^{2} - 4 x - 4$
45177	Find the Trig Value	tan(theta)=8/5	$\tan (θ) = \frac{8}{5}$
45178	Find the Trig Value	tan(x)^2=1/2	$\tan^{2} (x) = \frac{1}{2}$
45179	Find the Domain and Range	(4x-8)/((x-4)(x+1))	$\frac{4 x - 8}{(x - 4) (x + 1)}$
45180	Find the Domain and Range	square root of 2x-6	$\sqrt{2 x - 6}$
45181	Find the Domain and Range	cube root of x+9	$\sqrt[3]{x + 9}$
45182	Find the Trig Value	csc(theta)=13/5	$\csc (θ) = \frac{13}{5}$
45183	Find the Trig Value	(7/25,24/25)	$(\frac{7}{25}, \frac{24}{25})$
45184	Evaluate the Function	f(x)=3x-1	$f (x) = 3 x - 1$
45185	Evaluate the Function	f(2a)=x^2-2x+5	$f (2 a) = x^{2} - 2 x + 5$
45186	Evaluate the Function	g(0)=x/( square root of 9-x^2)	$g (0) = \frac{x}{\sqrt{9 - x^{2}}}$
45187	Evaluate the Function	g(-3)=x/( square root of 9-x^2)	$g (- 3) = \frac{x}{\sqrt{9 - x^{2}}}$
45188	Find the Equation Using Two Points	(0,5) , (3,-1)	$(0, 5)$ , $(3, - 1)$
45189	Plot	theta=pi/4	$θ = \frac{π}{4}$
45190	Determine if True	sin(75 degrees )=sin(30 degrees +45 degrees )	$\sin (75 °) = \sin (30 ° + 45 °)$
45191	Expand Using Sum/Difference Formulas	sin(150 degrees )	$\sin (150 °)$
45192	Identify the Conic	16x^2+4y^2+96x-8y+84=0	$16 x^{2} + 4 y^{2} + 96 x - 8 y + 84 = 0$
45193	Identify the Conic	16x^2-9y^2-64x-18y-89=0	$16 x^{2} - 9 y^{2} - 64 x - 18 y - 89 = 0$
45194	Identify the Conic	4x^2+y^2-8x-4y-28=0	$4 x^{2} + y^{2} - 8 x - 4 y - 28 = 0$
45195	Identify the Conic	5y^2-4x^2=20	$5 y^{2} - 4 x^{2} = 20$
45196	Convert to Degrees, Minutes, and Seconds	197.41 degrees	$197.41 °$
45197	Identify the Conic	x^2-y^2+12y+18x=42	$x^{2} - y^{2} + 12 y + 18 x = 42$
45198	Identify the Conic	y^2-3x+6y+12=0	$y^{2} - 3 x + 6 y + 12 = 0$
45199	Find the Axis of Symmetry	y=-1/2x^2+3x-5/2	$y = - \frac{1}{2} x^{2} + 3 x - \frac{5}{2}$
45200	Find the Range	f(x)=2^(x+0.1)+0.01	$f (x) = 2^{x + 0.1} + 0.01$