Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
201	Find the Other Trig Values in Quadrant III	sin(x)=-4/5	$\sin (x) = - \frac{4}{5}$
202	Find the Asymptotes	y=tan(x)	$y = \tan (x)$
203	Solve for x	12^(x/6)=18	$12^{\frac{x}{6}} = 18$
204	Solve for x	sin(3x)=-1/2	$\sin (3 x) = - \frac{1}{2}$
205	Solve for x	8(3^(6-x))=40	$8 (3^{6 - x}) = 40$
206	Solve for x	natural log of x-8+ natural log of x+9=1	$\ln (x - 8) + \ln (x + 9) = 1$
207	Solve for x	natural log of x-2+ natural log of x+3=1	$\ln (x - 2) + \ln (x + 3) = 1$
208	Solve for x	natural log of x-4+ natural log of x+5=1	$\ln (x - 4) + \ln (x + 5) = 1$
209	Solve for y	1/x=1/y+1/z	$\frac{1}{x} = \frac{1}{y} + \frac{1}{z}$
210	Solve for x	x^(-2/5)-3x^(-1/5)+1=0	$x^{- \frac{2}{5}} - 3 x^{- \frac{1}{5}} + 1 = 0$
211	Simplify	(sec(x)-1)(sec(x)+1)	$(\sec (x) - 1) (\sec (x) + 1)$
212	Simplify	((xy^-2z^-3)/(x^2y^3z^-4))^-3	${(\frac{x y^{- 2} z^{- 3}}{x^{2} y^{3} z^{- 4}})}^{- 3}$
213	Solve for x	\|2x-1\|=\|4x+9\|	$\| 2 x - 1 \| = \| 4 x + 9 \|$
214	Solve for x	(1/2)^x=8	${(\frac{1}{2})}^{x} = 8$
215	Solve for ?	csc(x)=-1	$\csc (x) = - 1$
216	Solve for ?	square root of 3tan(x)-1=0	$\sqrt{3} \tan (x) - 1 = 0$
217	Solve for ?	4cos(x)^2-4cos(x)+1=0	$4 \cos^{2} (x) - 4 \cos (x) + 1 = 0$
218	Solve for x	(x+5)/(x-2)=5/(x+2)+28/(x^2-4)	$\frac{x + 5}{x - 2} = \frac{5}{x + 2} + \frac{28}{x^{2} - 4}$
219	Solve for x	2 log of x = log of 2+ log of 4x-6	$2 \log (x) = \log (2) + \log (4 x - 6)$
220	Solve for x	2 log of x = log of 2+ log of 5x-8	$2 \log (x) = \log (2) + \log (5 x - 8)$
221	Solve for x	2sin(x-1)=0	$2 \sin (x - 1) = 0$
222	Solve for x	3 natural log of 2x+1=9	$3 \ln (2 x + 1) = 9$
223	Solve for x	6(2^(3x-1))-7=9	$6 (2^{3 x - 1}) - 7 = 9$
224	Solve for x	(2x-1)^2=18	${(2 x - 1)}^{2} = 18$
225	Solve for x	log base 9 of x=3	$\log_{9} (x) = 3$
226	Solve for x	x^3-4x+2=0	$x^{3} - 4 x + 2 = 0$
227	Solve for x	7^(x/2)=5^(1-x)	$7^{\frac{x}{2}} = 5^{1 - x}$
228	Simplify	square root of 16x+ square root of x^5	$\sqrt{16 x} + \sqrt{x^{5}}$
229	Simplify	(sin(2x))/(cos(x))	$\frac{\sin (2 x)}{\cos (x)}$
230	Simplify	(sin(x)sec(x))/(tan(x))	$\frac{\sin (x) \sec (x)}{\tan (x)}$
231	Simplify	((xy^-2z^-3)/(2x^-2yz^2))^-3	${(\frac{x y^{- 2} z^{- 3}}{2 x^{- 2} y z^{2}})}^{- 3}$
232	Simplify	(z^(4/3))^(9/2)	${(z^{\frac{4}{3}})}^{\frac{9}{2}}$
233	Simplify	2/(1+i)-3/(1-i)	$\frac{2}{1 + i} - \frac{3}{1 - i}$
234	Simplify	(cos(x))/(cot(x))	$\frac{\cos (x)}{\cot (x)}$
235	Simplify	(24a^2b^3c)/(16ab^-1c^2)	$\frac{24 a^{2} b^{3} c}{16 a b^{- 1} c^{2}}$
236	Simplify	((6y^3)^4)/(2y^3)	$\frac{{(6 y^{3})}^{4}}{2 y^{3}}$
237	Simplify	arcsin(0)	$\arcsin (0)$
238	Simplify	sec(arcsin(x-1))	$\sec (\arcsin (x - 1))$
239	Simplify	sec(x)-tan(x)	$\sec (x) - \tan (x)$
240	Simplify	((x^-3y^2)^-4)/((y^6x^-4)^-2)	$\frac{{(x^{- 3} y^{2})}^{- 4}}{{(y^{6} x^{- 4})}^{- 2}}$
241	Simplify	sin(2x)-cos(x)	$\sin (2 x) - \cos (x)$
242	Simplify	csc(x)tan(x)	$\csc (x) \tan (x)$
243	Simplify	((4a^3b)/(a^2b^3))((3b^2)/(2a^2b^4))	$(\frac{4 a^{3} b}{a^{2} b^{3}}) (\frac{3 b^{2}}{2 a^{2} b^{4}})$
244	Simplify	tan(pi/4)-sin(pi/6)	$\tan (\frac{π}{4}) - \sin (\frac{π}{6})$
245	Find the Domain	f(x) = square root of x-2	$f (x) = \sqrt{x - 2}$
246	Find the Domain	y=cot(x)	$y = \cot (x)$
247	Find the Domain	f(x) = log base 7 of x^2-9	$f (x) = \log_{7} (x^{2} - 9)$
248	Find the Domain	natural log of x	$\ln (x)$
249	Simplify	square root of s square root of s^5	$\sqrt{s \sqrt{s^{5}}}$
250	Simplify	square root of 9x^2+9	$\sqrt{9 x^{2} + 9}$
251	Expand the Trigonometric Expression	(x+2)^2	${(x + 2)}^{2}$
252	Expand the Trigonometric Expression	(x-1)^2	${(x - 1)}^{2}$
253	Find the Exact Value	cos(arctan(12/5))	$\cos (\arctan (\frac{12}{5}))$
254	Find the Exact Value	cot(-(11pi)/6)	$\cot (- \frac{11 π}{6})$
255	Find the Exact Value	cos(arctan(2))	$\cos (\arctan (2))$
256	Find the Supplement	6	$6$
257	Find Amplitude, Period, and Phase Shift	y=3cos(2x+pi)	$y = 3 \cos (2 x + π)$
258	Evaluate	log base a of b^2	$\log_{a} (b^{2})$
259	Find the Determinant	[[2,3],[2,5]]	$[\begin{array}{c} 2 & 3 \\ 2 & 5 \end{array}]$
260	Convert from Radians to Degrees	(53pi)/30	$\frac{53 π}{30}$
261	Simplify/Condense	1/2 log base 6 of x^4+2+8 log base 6 of 7-x-2 log base 6 of x	$\frac{1}{2} \log_{6} (x^{4} + 2) + 8 \log_{6} (7 - x) - 2 \log_{6} (x)$
262	Convert to Polar Coordinates	(3,3)	$(3, 3)$
263	Simplify/Condense	log base 3 of 27x	$\log_{3} (27 x)$
264	Graph	(x^2)/64+(y^2)/36=1	$\frac{x^{2}}{64} + \frac{y^{2}}{36} = 1$
265	Determine if Odd, Even, or Neither	f(x)=x^3-x	$f (x) = x^{3} - x$
266	Determine if Odd, Even, or Neither	y=csc(x)	$y = \csc (x)$
267	Graph	6x^2+6y^2=144	$6 x^{2} + 6 y^{2} = 144$
268	Graph	y=3cos(1/2x)	$y = 3 \cos (\frac{1}{2} x)$
269	Graph	f(x)=x(x-2)^3(x+2)^2	$f (x) = x {(x - 2)}^{3} {(x + 2)}^{2}$
270	Find the Vertex	y=x^2+2x-8	$y = x^{2} + 2 x - 8$
271	Find the Vertex	y=2x^2+3x-7	$y = 2 x^{2} + 3 x - 7$
272	Find the Vertex	y=2x^2-8x	$y = 2 x^{2} - 8 x$
273	Evaluate	sin((3pi)/8)	$\sin (\frac{3 π}{8})$
274	Evaluate	square root of -7 square root of -28	$\sqrt{- 7} \sqrt{- 28}$
275	Simplify/Condense	3 log of x+4 log of x-2	$3 \log (x) + 4 \log (x - 2)$
276	Find the Properties	(x^2)/25+(y^2)/16=1	$\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1$
277	Find the Properties	x^2=20y	$x^{2} = 20 y$
278	Evaluate	log base 16 of 15	$\log_{16} (15)$
279	Evaluate	log base 2 of 17	$\log_{2} (17)$
280	Evaluate	2/3 natural log of 10	$\frac{2}{3} \ln (10)$
281	Evaluate	log base 2 of ( square root of 2)^5	$\log_{2} ({(\sqrt{2})}^{5})$
282	Evaluate	log base 3 of 20	$\log_{3} (20)$
283	Expand the Logarithmic Expression	log of (a^2)/(b^4 square root of c)	$\log (\frac{a^{2}}{b^{4} \sqrt{c}})$
284	Convert from Radians to Degrees	-3.5	$- 3.5$
285	Evaluate	log base 1/2 of 16	$\log_{\frac{1}{2}} (16)$
286	Find the Reference Angle	150 degrees	$150 °$
287	Find Amplitude, Period, and Phase Shift	y=-3cos(2x)	$y = - 3 \cos (2 x)$
288	Find the Exact Value	cos((29pi)/12)	$\cos (\frac{29 π}{12})$
289	Find the Exact Value	cot(-225)	$\cot (- 225)$
290	Find the Exact Value	sin(arccos(3/7))	$\sin (\arccos (\frac{3}{7}))$
291	Simplify	square root of cube root of 11a^7b	$\sqrt{\sqrt[3]{11 a^{7} b}}$
292	Simplify	square root of square root of 16x^4	$\sqrt{\sqrt{16 x^{4}}}$
293	Divide Using Synthetic Division	(2x^3-3x^2-5x+4)/(x-2)	$\frac{2 x^{3} - 3 x^{2} - 5 x + 4}{x - 2}$
294	Divide Using Synthetic Division	(2x^5-x^4+3x^2-x+5)/(x-1)	$\frac{2 x^{5} - x^{4} + 3 x^{2} - x + 5}{x - 1}$
295	Simplify	( cube root of 54xy^2)/( cube root of 2xy^-1)	$\frac{\sqrt[3]{54 x y^{2}}}{\sqrt[3]{2 x y^{- 1}}}$
296	Find the Domain	x^2+1	$x^{2} + 1$
297	Find the Domain	y=3^x	$y = 3^{x}$
298	Find the Domain	f(x)=5x^2+2x-1	$f (x) = 5 x^{2} + 2 x - 1$
299	Find the Domain	f(x) = square root of 25-x^2	$f (x) = \sqrt{25 - x^{2}}$
300	Find the Domain	f(x) = square root of x^4-16x^2	$f (x) = \sqrt{x^{4} - 16 x^{2}}$