Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
301	Find the Domain	x/( square root of x-6)	$\frac{x}{\sqrt{x - 6}}$ $\frac{x}{\sqrt{x - 6}}$
302	Solve for x	log base 5 of x-5+ log base 5 of x+15=3	$\log_{5} (x - 5) + \log_{5} (x + 15) = 3$ $\log_{5} (x - 5) + \log_{5} (x + 15) = 3$
303	Simplify	e^(3 natural log of x)	$e^{3 \ln (x)}$ $e^{3 \ln (x)}$
304	Simplify	(-2+i)(3-6i)	$(- 2 + i) (3 - 6 i)$ $(- 2 + i) (3 - 6 i)$
305	Simplify	(u^(3/2))^(4/5)	${(u^{\frac{3}{2}})}^{\frac{4}{5}}$ ${(u^{\frac{3}{2}})}^{\frac{4}{5}}$
306	Simplify	csc(x)sin(x)	$\csc (x) \sin (x)$ $\csc (x) \sin (x)$
307	Simplify	sin(x)tan(x)	$\sin (x) \tan (x)$ $\sin (x) \tan (x)$
308	Simplify	sin(x)cos(x)sec(x)csc(x)	$\sin (x) \cos (x) \sec (x) \csc (x)$ $\sin (x) \cos (x) \sec (x) \csc (x)$
309	Simplify	cube root of 135	$\sqrt[3]{135}$ $\sqrt[3]{135}$
310	Simplify	1+1/(1+1/(1+x))	$1 + \frac{1}{1 + \frac{1}{1 + x}}$ $1 + \frac{1}{1 + \frac{1}{1 + x}}$
311	Simplify	(\|x^2\|)/(x^2)	$\frac{\| x^{2} \|}{x^{2}}$ $\frac{\| x^{2} \|}{x^{2}}$
312	Simplify	(csc(x)sin(x))/(cot(x))	$\frac{\csc (x) \sin (x)}{\cot (x)}$ $\frac{\csc (x) \sin (x)}{\cot (x)}$
313	Simplify	(csc(x))/(tan(x)+cot(x))	$\frac{\csc (x)}{\tan (x) + \cot (x)}$ $\frac{\csc (x)}{\tan (x) + \cot (x)}$
314	Simplify	a^(1/2)(a^(3/2)-2a^(1/2))	$a^{\frac{1}{2}} (a^{\frac{3}{2}} - 2 a^{\frac{1}{2}})$ $a^{\frac{1}{2}} (a^{\frac{3}{2}} - 2 a^{\frac{1}{2}})$
315	Simplify	1/(x^2+3x+2)-1/(x^2-2x-3)	$\frac{1}{x^{2} + 3 x + 2} - \frac{1}{x^{2} - 2 x - 3}$ $\frac{1}{x^{2} + 3 x + 2} - \frac{1}{x^{2} - 2 x - 3}$
316	Simplify	((x+h)^-2-x^-2)/h	$\frac{{(x + h)}^{- 2} - x^{- 2}}{h}$ $\frac{{(x + h)}^{- 2} - x^{- 2}}{h}$
317	Simplify	x/(x^2+x-2)-2/(x^2-5x+4)	$\frac{x}{x^{2} + x - 2} - \frac{2}{x^{2} - 5 x + 4}$ $\frac{x}{x^{2} + x - 2} - \frac{2}{x^{2} - 5 x + 4}$
318	Solve for x	3^x=1/9	$3^{x} = \frac{1}{9}$ $3^{x} = \frac{1}{9}$
319	Solve for x	e^(2x)-e^x-30=0	$e^{2 x} - e^{x} - 30 = 0$ $e^{2 x} - e^{x} - 30 = 0$
320	Solve for x	a^2x^2-b^2=0	$a^{2} x^{2} - b^{2} = 0$ $a^{2} x^{2} - b^{2} = 0$
321	Solve for x	square root of 3csc(x)-2=0	$\sqrt{3} \csc (x) - 2 = 0$ $\sqrt{3} \csc (x) - 2 = 0$
322	Solve for x	log base x of 125=3	$\log_{x} (125) = 3$ $\log_{x} (125) = 3$
323	Solve for x	log base 5 of x=-3	$\log_{5} (x) = - 3$ $\log_{5} (x) = - 3$
324	Solve for x	log base 5 of x+ log base 5 of x+1 = log base 5 of 20	$\log_{5} (x) + \log_{5} (x + 1) = \log_{5} (20)$ $\log_{5} (x) + \log_{5} (x + 1) = \log_{5} (20)$
325	Solve for x	log base 2 of x+ log base 2 of x+2 = log base 2 of x+6	$\log_{2} (x) + \log_{2} (x + 2) = \log_{2} (x + 6)$ $\log_{2} (x) + \log_{2} (x + 2) = \log_{2} (x + 6)$
326	Solve for x	square root of x^2+8-3=0	$\sqrt{x^{2} + 8} - 3 = 0$ $\sqrt{x^{2} + 8} - 3 = 0$
327	Solve for x	4 log of x-6=11	$4 \log (x - 6) = 11$ $4 \log (x - 6) = 11$
328	Solve for x	x^6-6x^3+9=0	$x^{6} - 6 x^{3} + 9 = 0$ $x^{6} - 6 x^{3} + 9 = 0$
329	Solve for x	1000e^(-4x)=75	$1000 e^{- 4 x} = 75$ $1000 e^{- 4 x} = 75$
330	Solve for x	14e^(3x+2)=560	$14 e^{3 x + 2} = 560$ $14 e^{3 x + 2} = 560$
331	Solve for x	2e^(3x)=1	$2 e^{3 x} = 1$ $2 e^{3 x} = 1$
332	Solve for x	2sec(x)^2+tan(x)^2-3=0	$2 \sec^{2} (x) + \tan^{2} (x) - 3 = 0$ $2 \sec^{2} (x) + \tan^{2} (x) - 3 = 0$
333	Solve for x	square root of x-10-4=0	$\sqrt{x - 10} - 4 = 0$ $\sqrt{x - 10} - 4 = 0$
334	Solve for ?	2cos(x)^2-1=0	$2 \cos^{2} (x) - 1 = 0$ $2 \cos^{2} (x) - 1 = 0$
335	Solve for ?	cos(x)=1/4	$\cos (x) = \frac{1}{4}$ $\cos (x) = \frac{1}{4}$
336	Solve for ?	sin(x)=1/4	$\sin (x) = \frac{1}{4}$ $\sin (x) = \frac{1}{4}$
337	Solve for t	T=gr+gvt	$T = g r + g v t$ $T = g r + g v t$
338	Simplify	(1-sin(t))(1+sin(t))	$(1 - \sin (t)) (1 + \sin (t))$ $(1 - \sin (t)) (1 + \sin (t))$
339	Simplify	(12x^3y^3)(6x^4y^6)	$(12 x^{3} y^{3}) (6 x^{4} y^{6})$ $(12 x^{3} y^{3}) (6 x^{4} y^{6})$
340	Solve for x	log of 8x- log of 1+ square root of x=2	$\log (8 x) - \log (1 + \sqrt{x}) = 2$ $\log (8 x) - \log (1 + \sqrt{x}) = 2$
341	Solve for x	log of 3x = log of 5+ log of x-2	$\log (3 x) = \log (5) + \log (x - 2)$ $\log (3 x) = \log (5) + \log (x - 2)$
342	Solve for x	log of x=-3	$\log (x) = - 3$ $\log (x) = - 3$
343	Solve for x	sec(x)=0	$\sec (x) = 0$ $\sec (x) = 0$
344	Solve for x	natural log of x- natural log of 2=0	$\ln (x) - \ln (2) = 0$ $\ln (x) - \ln (2) = 0$
345	Solve for x	sin(2x)=-( square root of 3)/2	$\sin (2 x) = - \frac{\sqrt{3}}{2}$ $\sin (2 x) = - \frac{\sqrt{3}}{2}$
346	Solve for x	sin(x)=5/13	$\sin (x) = \frac{5}{13}$ $\sin (x) = \frac{5}{13}$
347	Find the Other Trig Values in Quadrant III	cos(theta)=-24/25	$\cos (θ) = - \frac{24}{25}$ $\cos (θ) = - \frac{24}{25}$
348	Find the Other Trig Values in Quadrant IV	cos(x)=24/25	$\cos (x) = \frac{24}{25}$ $\cos (x) = \frac{24}{25}$
349	Find the Other Trig Values in Quadrant III	tan(x)=4/3	$\tan (x) = \frac{4}{3}$ $\tan (x) = \frac{4}{3}$
350	Find the Other Trig Values in Quadrant II	sin(x)=24/25	$\sin (x) = \frac{24}{25}$ $\sin (x) = \frac{24}{25}$
351	Find the Other Trig Values in Quadrant II	tan(x)=-15/8	$\tan (x) = - \frac{15}{8}$ $\tan (x) = - \frac{15}{8}$
352	Find the Degree	x	$x$ $x$
353	Find the Asymptotes	f(x)=1/(x-5)	$f (x) = \frac{1}{x - 5}$ $f (x) = \frac{1}{x - 5}$
354	Find the Asymptotes	f(x)=3^x	$f (x) = 3^{x}$ $f (x) = 3^{x}$
355	Find the Asymptotes	f(x)=1/(x^2)	$f (x) = \frac{1}{x^{2}}$ $f (x) = \frac{1}{x^{2}}$
356	Find the Asymptotes	f(x)=5^x	$f (x) = 5^{x}$ $f (x) = 5^{x}$
357	Find the Asymptotes	f(x)=x/(x-5)	$f (x) = \frac{x}{x - 5}$ $f (x) = \frac{x}{x - 5}$
358	Find the Range	f(x)=e^x	$f (x) = e^{x}$ $f (x) = e^{x}$
359	Write in Standard Form	(4-i)/(2-i)	$\frac{4 - i}{2 - i}$ $\frac{4 - i}{2 - i}$
360	Divide	(x^5+1)/(x+1)	$\frac{x^{5} + 1}{x + 1}$ $\frac{x^{5} + 1}{x + 1}$
361	Find the Roots (Zeros)	cos(2x)-cos(x)=0	$\cos (2 x) - \cos (x) = 0$ $\cos (2 x) - \cos (x) = 0$
362	Find the Roots (Zeros)	f(x)=x^4-3x^3-2x^2+3x-5	$f (x) = x^{4} - 3 x^{3} - 2 x^{2} + 3 x - 5$ $f (x) = x^{4} - 3 x^{3} - 2 x^{2} + 3 x - 5$
363	Find the x and y Intercepts	y=cos(x)	$y = \cos (x)$ $y = \cos (x)$
364	Find the x and y Intercepts	y=-\|x+10\|	$y = - \| x + 10 \|$ $y = - \| x + 10 \|$
365	Solve Using the Quadratic Formula	x^2-2x-15=0	$x^{2} - 2 x - 15 = 0$ $x^{2} - 2 x - 15 = 0$
366	Find the Roots/Zeros Using the Rational Roots Test	x^3-3x^2-4x+12	$x^{3} - 3 x^{2} - 4 x + 12$ $x^{3} - 3 x^{2} - 4 x + 12$
367	Find the Roots/Zeros Using the Rational Roots Test	x^3-4x^2-7x+10	$x^{3} - 4 x^{2} - 7 x + 10$ $x^{3} - 4 x^{2} - 7 x + 10$
368	Find the Inverse	f(x)=3x-6	$f (x) = 3 x - 6$ $f (x) = 3 x - 6$
369	Find the Inverse	f(x)=6x^3-3	$f (x) = 6 x^{3} - 3$ $f (x) = 6 x^{3} - 3$
370	Find the Inverse	f(x)=x-5	$f (x) = x - 5$ $f (x) = x - 5$
371	Find the Vertex	f(x)=x^2-6x+5	$f (x) = x^{2} - 6 x + 5$ $f (x) = x^{2} - 6 x + 5$
372	Find the Vertex	f(x)=x^2+4x-5	$f (x) = x^{2} + 4 x - 5$ $f (x) = x^{2} + 4 x - 5$
373	Find the Vertex	f(x)=x^2-8x+16	$f (x) = x^{2} - 8 x + 16$ $f (x) = x^{2} - 8 x + 16$
374	Find the Vertex	f(x)=2x^2+x-6	$f (x) = 2 x^{2} + x - 6$ $f (x) = 2 x^{2} + x - 6$
375	Solve by Substitution	3x-y=7 , -3x+y=5	$3 x - y = 7$ $3 x - y = 7$ , $- 3 x + y = 5$ $- 3 x + y = 5$
376	Evaluate	(3^-2+4^-2)^(-1/2)	${(3^{- 2} + 4^{- 2})}^{- \frac{1}{2}}$ ${(3^{- 2} + 4^{- 2})}^{- \frac{1}{2}}$
377	Find the Value Using the Unit Circle	cos(120)	$\cos (120)$ $\cos (120)$
378	Evaluate	(tan(pi/18)+tan(pi/9))/(1-tan(pi/18)tan(pi/9))	$\frac{\tan (\frac{π}{18}) + \tan (\frac{π}{9})}{1 - \tan (\frac{π}{18}) \tan (\frac{π}{9})}$ $\frac{\tan (\frac{π}{18}) + \tan (\frac{π}{9})}{1 - \tan (\frac{π}{18}) \tan (\frac{π}{9})}$
379	Evaluate	cos(pi/12)	$\cos (\frac{π}{12})$ $\cos (\frac{π}{12})$
380	Find the Domain and Range	f(x)=sin(x)	$f (x) = \sin (x)$ $f (x) = \sin (x)$
381	Graph	y=tan(4x)	$y = \tan (4 x)$ $y = \tan (4 x)$
382	Graph	y=cot(4x)	$y = \cot (4 x)$ $y = \cot (4 x)$
383	Graph	x=-2	$x = - 2$ $x = - 2$
384	Graph	y=2.4^x	$y = {2.4}^{x}$ $y = {2.4}^{x}$
385	Add	1/x+2	$\frac{1}{x} + 2$ $\frac{1}{x} + 2$
386	Determine if Odd, Even, or Neither	f(x)=x^3-5x	$f (x) = x^{3} - 5 x$ $f (x) = x^{3} - 5 x$
387	Graph	(x^2)/64-(y^2)/36=1	$\frac{x^{2}}{64} - \frac{y^{2}}{36} = 1$ $\frac{x^{2}}{64} - \frac{y^{2}}{36} = 1$
388	Find the Domain and Range	y=cos(x)	$y = \cos (x)$ $y = \cos (x)$
389	Solve by Substitution	2x+2y-z=2 , x-3y+z=-28 , -x+y=4	$2 x + 2 y - z = 2$ $2 x + 2 y - z = 2$ , $x - 3 y + z = - 28$ $x - 3 y + z = - 28$ , $- x + y = 4$ $- x + y = 4$
390	Solve by Substitution	x-2y+3z=7 , 2x+y+z=4 , -3x+2y-2z=-10	$x - 2 y + 3 z = 7$ $x - 2 y + 3 z = 7$ , $2 x + y + z = 4$ $2 x + y + z = 4$ , $- 3 x + 2 y - 2 z = - 10$ $- 3 x + 2 y - 2 z = - 10$
391	Solve by Addition/Elimination	3x-4y=4 , x+3y=-3	$3 x - 4 y = 4$ $3 x - 4 y = 4$ , $x + 3 y = - 3$ $x + 3 y = - 3$
392	Find the Vertex	f(x)=4x^2-8x+3	$f (x) = 4 x^{2} - 8 x + 3$ $f (x) = 4 x^{2} - 8 x + 3$
393	Find the Vertex	f(x)=2x^2-8x+9	$f (x) = 2 x^{2} - 8 x + 9$ $f (x) = 2 x^{2} - 8 x + 9$
394	Find the Vertex	f(x)=3x^2-12x+1	$f (x) = 3 x^{2} - 12 x + 1$ $f (x) = 3 x^{2} - 12 x + 1$
395	Find the Vertex	f(x)=x^2-4x-5	$f (x) = x^{2} - 4 x - 5$ $f (x) = x^{2} - 4 x - 5$
396	Find the Inverse	f(x)=(3-x)/7	$f (x) = \frac{3 - x}{7}$ $f (x) = \frac{3 - x}{7}$
397	Find the Domain and Range	f(x)=(x^2+x-2)/(x^2-3x-4)	$f (x) = \frac{x^{2} + x - 2}{x^{2} - 3 x - 4}$ $f (x) = \frac{x^{2} + x - 2}{x^{2} - 3 x - 4}$
398	Find the Domain	f(x) = square root of 9-x^2	$f (x) = \sqrt{9 - x^{2}}$ $f (x) = \sqrt{9 - x^{2}}$
399	Find the Domain and Range	f(x)=x^4-8x^3+17x^2-8x+16	$f (x) = x^{4} - 8 x^{3} + 17 x^{2} - 8 x + 16$ $f (x) = x^{4} - 8 x^{3} + 17 x^{2} - 8 x + 16$
400	Factor	cos(x)	$\cos (x)$ $\cos (x)$