Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
43201	Find the Value Using the Unit Circle	cot(225 degrees )	$\cot (225 °)$
43202	Find the Value Using the Unit Circle	tan(330 degrees )	$\tan (330 °)$
43203	Find the Value Using the Unit Circle	tan(300 degrees )	$\tan (300 °)$
43204	Find the x and y Intercepts	f(x)=-4x^2+2x-5	$f (x) = - 4 x^{2} + 2 x - 5$
43205	Find the x and y Intercepts	f(x)=4x^2+8x-1	$f (x) = 4 x^{2} + 8 x - 1$
43206	Find the x and y Intercepts	f(x) = log base 1/3 of x	$f (x) = \log_{\frac{1}{3}} (x)$
43207	Find the x and y Intercepts	f(x)=x^4-x^3-14x^2+2x+24	$f (x) = x^{4} - x^{3} - 14 x^{2} + 2 x + 24$
43208	Find the x and y Intercepts	(x^2-9)/(x-3)	$\frac{x^{2} - 9}{x - 3}$
43209	Find the Axis of Symmetry	(y+4)^2=12(x-5)	${(y + 4)}^{2} = 12 (x - 5)$
43210	Find the Axis of Symmetry	x=10y^2	$x = 10 y^{2}$
43211	Find the Equation of the Circle	r=6cos(theta)	$r = 6 \cos (θ)$
43212	Find the Equation of the Circle	r=10sin(theta)	$r = 10 \sin (θ)$
43213	Find the Equation of the Circle	r=-5	$r = - 5$
43214	Find the Vertex	f(x)=2x^2-12x+19	$f (x) = 2 x^{2} - 12 x + 19$
43215	Find the Vertex	f(x)=-2x^2+4x-5	$f (x) = - 2 x^{2} + 4 x - 5$
43216	Find Amplitude, Period, and Phase Shift	f(x)=3sin(2x-4)	$f (x) = 3 \sin (2 x - 4)$
43217	Find Amplitude, Period, and Phase Shift	f(x)=cot(x+5pi)	$f (x) = \cot (x + 5 π)$
43218	Find the Vertex	f(x)=x^2-3x-4	$f (x) = x^{2} - 3 x - 4$
43219	Find the Vertex	f(x)=3x^2-12x+13	$f (x) = 3 x^{2} - 12 x + 13$
43220	Find the Maximum/Minimum Value	f(x)=x^2-8x+15	$f (x) = x^{2} - 8 x + 15$
43221	Find the Maximum/Minimum Value	H(t)=-16t^2+1000t+15	$H (t) = - 16 t^{2} + 1000 t + 15$
43222	Find the Maximum/Minimum Value	H(t)=-16t^2+1000t+30	$H (t) = - 16 t^{2} + 1000 t + 30$
43223	Find Amplitude, Period, and Phase Shift	f(x)=-1/2cos(3t+3pi)-3	$f (x) = - \frac{1}{2} \cos (3 t + 3 π) - 3$
43224	Find the Vertex	f(x)=x^2+5	$f (x) = x^{2} + 5$
43225	Find the Vertex	f(x)=x^2-6x+9	$f (x) = x^{2} - 6 x + 9$
43226	Find the Vertex	f(x)=x^2-6	$f (x) = x^{2} - 6$
43227	Find the Vertex	f(x)=x^2-6x+10	$f (x) = x^{2} - 6 x + 10$
43228	Find Amplitude, Period, and Phase Shift	f(x)=-3sin(3x)	$f (x) = - 3 \sin (3 x)$
43229	Find the Vertex	f(x)=4x^2	$f (x) = 4 x^{2}$
43230	Find the Vertex	f(x)=3x^2-6x+9	$f (x) = 3 x^{2} - 6 x + 9$
43231	Find the Vertex	f(x)=2x^2-4x-3	$f (x) = 2 x^{2} - 4 x - 3$
43232	Find the Vertex	f(x)=-(x+1)^2+4	$f (x) = - {(x + 1)}^{2} + 4$
43233	Find the Vertex	f(x)=-(x+4)^2+9	$f (x) = - {(x + 4)}^{2} + 9$
43234	Find the Vertex	f(x)=(x-3)^2+1	$f (x) = {(x - 3)}^{2} + 1$
43235	Find the Vertex	f(x)=(x-3)^2+4	$f (x) = {(x - 3)}^{2} + 4$
43236	Find the Vertex	f(x)=(x+6)^2+3	$f (x) = {(x + 6)}^{2} + 3$
43237	Divide Using Synthetic Division	(x^3+2x^2-5x-6)/(x-2)	$\frac{(x^{3} + 2 x^{2} - 5 x - 6)}{x - 2}$
43238	Determine if Odd, Even, or Neither	f(x)=x^2+4	$f (x) = x^{2} + 4$
43239	Determine if Odd, Even, or Neither	f(x)=8x	$f (x) = 8 x$
43240	Determine if Odd, Even, or Neither	f(x)=8x^3+5	$f (x) = 8 x^{3} + 5$
43241	Determine if Odd, Even, or Neither	f(x)=x^3-2	$f (x) = x^{3} - 2$
43242	Determine if Odd, Even, or Neither	f(x)=2sin(x)	$f (x) = 2 \sin (x)$
43243	Determine if Odd, Even, or Neither	f(x)=-3x^2-5	$f (x) = - 3 x^{2} - 5$
43244	Find the Eccentricity	35x^2+y^2=35	$35 x^{2} + y^{2} = 35$
43245	Find the Eccentricity	49x^2+4y^2=196	$49 x^{2} + 4 y^{2} = 196$
43246	Find the Eccentricity	(x^2)/108+(y^2)/144=1	$\frac{x^{2}}{108} + \frac{y^{2}}{144} = 1$
43247	Find the Eccentricity	(x^2)/36+(y^2)/9=1	$\frac{x^{2}}{36} + \frac{y^{2}}{9} = 1$
43248	Find the Cofactor Matrix	[[12,23,-6],[11,-8,13],[7,21,15]]	$[\begin{array}{c} 12 & 23 & - 6 \\ 11 & - 8 & 13 \\ 7 & 21 & 15 \end{array}]$
43249	Find the Reciprocal	pi/8	$\frac{π}{8}$
43250	Simplify/Condense	(2tan((2pi)/5))/(1-tan((2pi)/5)^2)	$\frac{2 \tan (\frac{2 π}{5})}{1 - \tan^{2} (\frac{2 π}{5})}$
43251	Simplify/Condense	1/2 natural log of y+ natural log of z	$\frac{1}{2} \ln (y) + \ln (z)$
43252	Find the Inverse	y=1/2x+1	$y = \frac{1}{2} x + 1$
43253	Find the Points of Intersection	x^2+y^2=64 , (x^2)/25+(y^2)/16=1	$x^{2} + y^{2} = 64$ , $\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1$
43254	Find the Inverse	y=4e^(x-3)	$y = 4 e^{x - 3}$
43255	Find the Inverse	y=4x-3	$y = 4 x - 3$
43256	Find the Inverse	y=-2x^2-5x-1	$y = - 2 x^{2} - 5 x - 1$
43257	Find the Inverse	y=2x^2-3	$y = 2 x^{2} - 3$
43258	Find the Inverse	y=10^x	$y = 10^{x}$
43259	Find the Inverse	y=tan(x-pi/2)	$y = \tan (x - \frac{π}{2})$
43260	Find the Inverse	y=x^3-7	$y = x^{3} - 7$
43261	Find the Inverse	y=x-3	$y = x - 3$
43262	Simplify/Condense	log of 3z- log of 8	$\log (3 z) - \log (8)$
43263	Simplify/Condense	log base 3 of 8+ log base 3 of x-2 log base 3 of x+4	$\log_{3} (8) + \log_{3} (x) - 2 \log_{3} (x + 4)$
43264	Simplify/Condense	log base 5 of 2y+ log base 5 of 8	$\log_{5} (2 y) + \log_{5} (8)$
43265	Find the Maximum/Minimum Value	y=2sin(x+pi/2)+2	$y = 2 \sin (x + \frac{π}{2}) + 2$
43266	Find the Maximum/Minimum Value	r=-3+5sin(theta)	$r = - 3 + 5 \sin (θ)$
43267	Find the Roots/Zeros Using the Rational Roots Test	8x^3+50x^2-41x+7=0	$8 x^{3} + 50 x^{2} - 41 x + 7 = 0$
43268	Find the Inverse	square root of 2x+6	$\sqrt{2 x + 6}$
43269	Find the Inverse	(x-5)/4	$\frac{(x - 5)}{4}$
43270	Expand Using De Moivre's Theorem	(cos((4pi)/7)+isin((4pi)/7))^5	${(\cos (\frac{4 π}{7}) + i \sin (\frac{4 π}{7}))}^{5}$
43271	Expand Using De Moivre's Theorem	(1-i)^28	${(1 - i)}^{28}$
43272	Find the Center	(x^2)/36+(y^2)/9=1	$\frac{x^{2}}{36} + \frac{y^{2}}{9} = 1$
43273	Find the Center	((x-8)^2)/25+((y-2)^2)/16=1	$\frac{{(x - 8)}^{2}}{25} + \frac{{(y - 2)}^{2}}{16} = 1$
43274	Find the Center	16x^2+25y^2-128x+50y-119=0	$16 x^{2} + 25 y^{2} - 128 x + 50 y - 119 = 0$
43275	Find the Center	16x^2-64x+9y^2+72y+64=0	$16 x^{2} - 64 x + 9 y^{2} + 72 y + 64 = 0$
43276	Find the Center	16x^2-9y^2-64x-18y-89=0	$16 x^{2} - 9 y^{2} - 64 x - 18 y - 89 = 0$
43277	Find the Center	25x^2+16y^2-250x+128y+481=0	$25 x^{2} + 16 y^{2} - 250 x + 128 y + 481 = 0$
43278	Find the Center	4x^2-y^2-16x+2y+13=0	$4 x^{2} - y^{2} - 16 x + 2 y + 13 = 0$
43279	Find the Center	9x^2+25y^2-90x+150y+225=0	$9 x^{2} + 25 y^{2} - 90 x + 150 y + 225 = 0$
43280	Find the Center	-2x^2+3y^2-8x+6y-11=0	$- 2 x^{2} + 3 y^{2} - 8 x + 6 y - 11 = 0$
43281	Find the Center	9x^2+25y^2-18x+250y+409=0	$9 x^{2} + 25 y^{2} - 18 x + 250 y + 409 = 0$
43282	Find the Center	x^2-4y^2=4	$x^{2} - 4 y^{2} = 4$
43283	Find the Center	x^2-y^2-8x-4y-4=0	$x^{2} - y^{2} - 8 x - 4 y - 4 = 0$
43284	Add	[[-4,2,3],[0,-1,-4]]+[[-2,3,-1],[1,5,-4]]	$[\begin{array}{c} - 4 & 2 & 3 \\ 0 & - 1 & - 4 \end{array}] + [\begin{array}{c} - 2 & 3 & - 1 \\ 1 & 5 & - 4 \end{array}]$
43285	Add	(3-4i)+(6+7i)	$(3 - 4 i) + (6 + 7 i)$
43286	Add	(4-5i)+(8+2i)	$(4 - 5 i) + (8 + 2 i)$
43287	Solve the System of @WORD	x^2-7x<=-10	$x^{2} - 7 x \leq - 10$
43288	Solve the System of @WORD	3x^2-5x>=2	$3 x^{2} - 5 x \geq 2$
43289	Convert to Interval Notation	x^3-3x^2-54x>0	$x^{3} - 3 x^{2} - 54 x > 0$
43290	Convert to Interval Notation	x^3-x^2-56x<0	$x^{3} - x^{2} - 56 x < 0$
43291	Solve the System of @WORD	1+5/(a-1)<=7/6	$1 + \frac{5}{a - 1} \leq \frac{7}{6}$
43292	Solve the System of @WORD	\|4-7x\|-5<8	$\| 4 - 7 x \| - 5 < 8$
43293	Solve the System of @WORD	(1-x)/(x-2)+1>0	$\frac{1 - x}{x - 2} + 1 > 0$
43294	Convert to Interval Notation	2x^3-32x<x^2-16	$2 x^{3} - 32 x < x^{2} - 16$
43295	Convert to Interval Notation	2x^2<13x+7	$2 x^{2} < 13 x + 7$
43296	Convert to Interval Notation	2x^3-50x<x^2-25	$2 x^{3} - 50 x < x^{2} - 25$
43297	Convert to Interval Notation	-2<=x<=5	$- 2 \leq x \leq 5$
43298	Convert to Interval Notation	4x^3-15x^2<=25x	$4 x^{3} - 15 x^{2} \leq 25 x$
43299	Convert to Interval Notation	x^2+9>6x	$x^{2} + 9 > 6 x$
43300	Convert to Interval Notation	x^3+x^2-17x+15>=0	$x^{3} + x^{2} - 17 x + 15 \geq 0$