Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
27301	Solve for y	-3/(y-2)=-6/(2y-4)+1	$- \frac{3}{y - 2} = - \frac{6}{2 y - 4} + 1$
27302	Evaluate the Integral	integral of cot(x)^3csc(x)^2 with respect to x	$\int \cot^{3} (x) \csc^{2} (x) d x$
27303	Solve Over the Interval	sin(2x)=( square root of 3)/2 , 0<=x<2pi	$\sin (2 x) = \frac{\sqrt{3}}{2}$ , $0 \leq x < 2 π$
27304	Find the Domain and Range	f(x)=x+1 if -9<=x<3; -x+4 if x>3	$f (x) = {\begin{cases} x + 1 & - 9 \leq x < 3 \\ - x + 4 & x > 3 \end{cases}$
27305	Simplify	(x-1)/(4x^2-9)-(x+3)/(2x-3)	$\frac{x - 1}{4 x^{2} - 9} - \frac{x + 3}{2 x - 3}$
27306	Simplify	(27a^2bc^3)/(18a^2b^2c)	$\frac{27 a^{2} b c^{3}}{18 a^{2} b^{2} c}$
27307	Simplify	-3x+x^3-2x^2-(4x^3-2x^2-4x)	$- 3 x + x^{3} - 2 x^{2} - (4 x^{3} - 2 x^{2} - 4 x)$
27308	Simplify	((x-y)^2)/(2xy+6y)*(4x+12)/(x^2-y^2)	$\frac{{(x - y)}^{2}}{2 x y + 6 y} \cdot \frac{4 x + 12}{x^{2} - y^{2}}$
27309	Evaluate the Integral	integral of cos(2-5x)^2 with respect to x	$\int \cos^{2} (2 - 5 x) d x$
27310	Simplify	4(6^0)+3(3^-1)	$4 (6^{0}) + 3 (3^{- 1})$
27311	Find the LCD	(2a)/(4b) , 3/(4b)	$\frac{2 a}{4 b}$ , $\frac{3}{4 b}$
27312	Solve for x	6(2x-3)-3x=2x-18+x	$6 (2 x - 3) - 3 x = 2 x - 18 + x$
27313	Simplify	(-x^3+3x^2+13x-15)/(-2x^3+7x^2+20x-25)	$\frac{- x^{3} + 3 x^{2} + 13 x - 15}{- 2 x^{3} + 7 x^{2} + 20 x - 25}$
27314	Graph	x+y>22x-y>1	$x + y > 22 x - y > 1$
27315	Simplify	fourth root of (xy^6)/81	$\sqrt[4]{\frac{x y^{6}}{81}}$
27316	Simplify	-9x^2y^2+5x^2y-11xy+1-5x^2y^2-15xy-11	$- 9 x^{2} y^{2} + 5 x^{2} y - 11 x y + 1 - 5 x^{2} y^{2} - 15 x y - 11$
27317	Simplify	28(1/4y+1/7)	$28 (\frac{1}{4} y + \frac{1}{7})$
27318	Write the Fraction in Simplest Form	(2^-2m^-3)/(n^0)	$\frac{2^{- 2} m^{- 3}}{n^{0}}$
27319	Solve for x	x/(3z)=y-2	$\frac{x}{3 z} = y - 2$
27320	Evaluate the Integral	integral of e^((2x)/3) with respect to x	$\int e^{\frac{2 x}{3}} d x$
27321	Solve for x	1/2(20-8x)=-2(-2+x)+2	$\frac{1}{2} (20 - 8 x) = - 2 (- 2 + x) + 2$
27322	Find the Product	(q-3/4)(q+1/4)	$(q - \frac{3}{4}) (q + \frac{1}{4})$
27323	Evaluate	(t-8)-(t+15)	$(t - 8) - (t + 15)$
27324	Find the Derivative - d/dx	y=3 square root of sin(x)	$y = 3 \sqrt{\sin (x)}$
27325	Simplify	3(2)^-1	$3 {(2)}^{- 1}$
27326	Simplify	( fourth root of x^9)/( fourth root of x^2)	$\frac{\sqrt[4]{x^{9}}}{\sqrt[4]{x^{2}}}$
27327	Simplify	( square root of 3)/( square root of 27- square root of 3)	$\frac{\sqrt{3}}{\sqrt{27} - \sqrt{3}}$
27328	Solve the Function Operation	f(x)=(x+6)^2-6 if x!=-5; -1 if x=-5 Find f(-3)	$f (x) = {\begin{cases} {(x + 6)}^{2} - 6 & x \neq - 5 \\ - 1 & x = - 5 \end{cases}$ Find $f (- 3)$
27329	Solve for q	-2(-2q-7)=11q	$- 2 (- 2 q - 7) = 11 q$
27330	Factor	a^2+2ab+b^2=(a+b)^2	$a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$
27331	Find Amplitude, Period, and Phase Shift	y=-2-4sin(pi/2(x-1/3))	$y = - 2 - 4 \sin (\frac{π}{2} (x - \frac{1}{3}))$
27332	Solve the Inequality for x	3x^2+38>24x-7	$3 x^{2} + 38 > 24 x - 7$
27333	Simplify	(1+zi)(1+2i)-(1+zi)(1-2i)	$(1 + z i) (1 + 2 i) - (1 + z i) (1 - 2 i)$
27334	Simplify	(9/6t-9)*2	$(\frac{9}{6} t - 9) \cdot 2$
27335	Solve for x	5=3+4x^(-1/6)	$5 = 3 + 4 x^{- \frac{1}{6}}$
27336	Simplify	fourth root of 9/(2x^2)	$\sqrt[4]{\frac{9}{2 x^{2}}}$
27337	Graph	y<=-(x-1)^2+7	$y \leq - {(x - 1)}^{2} + 7$
27338	Solve for p	12/3=(p-1)/10	$\frac{12}{3} = \frac{p - 1}{10}$
27339	Solve for a	a/3=b/4	$\frac{a}{3} = \frac{b}{4}$
27340	Evaluate	square root of x^2+4=x+2	$\sqrt{x^{2} + 4} = x + 2$
27341	Simplify	(x+2)/(x^2-2x-15)+x/(x+3)	$\frac{x + 2}{x^{2} - 2 x - 15} + \frac{x}{x + 3}$
27342	Solve for x	6 cube root of x-3+2=1/2	$6 \sqrt[3]{x - 3} + 2 = \frac{1}{2}$
27343	Integrate Using u-Substitution	integral of (x^9)/(1+x^20) with respect to x	$\int \frac{x^{9}}{1 + x^{20}} d x$
27344	Simplify the Radical Expression	square root of 100+ square root of -27- square root of 4+ square root of -108	$\sqrt{100} + \sqrt{- 27} - \sqrt{4} + \sqrt{- 108}$
27345	Find the Exact Value	2pi-pi/6	$2 π - \frac{π}{6}$
27346	Solve the Function Operation	f(x)=-(x-1)^2 if x!=-1; 0 if x=-1 Find f(-1)	$f (x) = {\begin{cases} - {(x - 1)}^{2} & x \neq - 1 \\ 0 & x = - 1 \end{cases}$ Find $f (- 1)$
27347	Simplify	9d^-5*((36d^6)÷4d^2)	$9 d^{- 5} \cdot (36 d^{6} \div 4 d^{2})$
27348	Multiply	((x-y)^2)/(x+y)*(3x+3y)/(x^2-y^2)	$\frac{{(x - y)}^{2}}{x + y} \cdot \frac{3 x + 3 y}{x^{2} - y^{2}}$
27349	Find h(g(x))	g(x)=(x-1)^3 and h(x) = cube root of x+1	$g (x) = {(x - 1)}^{3}$ and $h (x) = \sqrt[3]{x} + 1$
27350	Find the Degree, Leading Term, and Leading Coefficient	3xy^3+5x^5y^3+x^3y^7-7x^2y	$3 x y^{3} + 5 x^{5} y^{3} + x^{3} y^{7} - 7 x^{2} y$
27351	Solve for n	n/7-12=5n+5	$\frac{n}{7} - 12 = 5 n + 5$
27352	Solve for x	1/4x+2=\|x-1\|	$\frac{1}{4} x + 2 = \| x - 1 \|$
27353	Solve the Function Operation	If f(x)=-x^3+x^2+x ; find f(-3)	If $f (x) = - x^{3} + x^{2} + x$ ; find $f (- 3)$
27354	Simplify	square root of 12+5 square root of 8-7 square root of 20	$\sqrt{12} + 5 \sqrt{8} - 7 \sqrt{20}$
27355	Convert to a Percentage	20 is what percent of 50	$20$ is what percent of $50$
27356	Factor by Grouping	24x^3-9x^2y^2-12y	$24 x^{3} - 9 x^{2} y^{2} - 12 y$
27357	Find the Derivative - d/dx	-x^2-xy+y^2-1	$- x^{2} - x y + y^{2} - 1$
27358	Solve for y	3y^2+12y+4=y	$3 y^{2} + 12 y + 4 = y$
27359	Evaluate the Integral	integral of x(x^2+7)(1/3) with respect to x	$\int x (x^{2} + 7) (\frac{1}{3}) d x$
27360	Multiply	( square root of 5+ square root of 6+ square root of 7)*( square root of 5+ square root of 6- square root of 7)	$(\sqrt{5} + \sqrt{6} + \sqrt{7}) \cdot (\sqrt{5} + \sqrt{6} - \sqrt{7})$
27361	Find Where Increasing/Decreasing	f'(x)=((x+1)^2)/(x-4)	$f' (x) = \frac{{(x + 1)}^{2}}{x - 4}$
27362	Solve the System of Equations	x=-5 y=-4/5x-5	$x = - 5$ $y = - \frac{4}{5} x - 5$
27363	Find the Exact Value	log base 2 of (2^4)/(2^10)	$\log_{2} (\frac{2^{4}}{2^{10}})$
27364	Simplify	(27^(-1/3))/(27^(-4/3))	$\frac{27^{- \frac{1}{3}}}{27^{- \frac{4}{3}}}$
27365	Simplify	fourth root of x^(2a)n^8	$\sqrt[4]{x^{2 a} n^{8}}$
27366	Simplify the Radical Expression	6/( square root of 3- square root of 2)	$\frac{6}{\sqrt{3} - \sqrt{2}}$
27367	Simplify the Radical Expression	square root of 16u^4v^3	$\sqrt{16 u^{4}} v^{3}$
27368	Find g(f(x))	f(x)=x-8 g(x)=x^2+x-15	$f (x) = x - 8$ $g (x) = x^{2} + x - 15$
27369	Simplify	4^0*1^(1/2)	$4^{0} \cdot 1^{\frac{1}{2}}$
27370	Evaluate the Function	f(x)=x^2+4x+3 at x=-1	$f (x) = x^{2} + 4 x + 3$ at $x = - 1$
27371	Solve for x	5-(x-4)=3(x+2)	$5 - (x - 4) = 3 (x + 2)$
27372	Evaluate	3x^3(2x+y)	$3 x^{3} (2 x + y)$
27373	Simplify	square root of a^3b^5*5 square root of 4ab	$\sqrt{a^{3} b^{5}} \cdot 5 \sqrt{4 a b}$
27374	Solve Using the Quadratic Formula	25^x-12*5^x+27=0	$25^{x} - 12 \cdot 5^{x} + 27 = 0$
27375	Find the Holes in the Graph	f(x)=(x(x+2))/(x^2-2x)	$f (x) = \frac{x (x + 2)}{x^{2} - 2 x}$
27376	Simplify	(9 square root of 2)/( square root of 10+ square root of 18)	$\frac{9 \sqrt{2}}{\sqrt{10 + \sqrt{18}}}$
27377	Solve for a	2* log of 2a-1=0	$2 \cdot \log (2 a - 1) = 0$
27378	Find the x and y Intercepts	f(x)=-2x^(1/4)	$f (x) = - 2 x^{\frac{1}{4}}$
27379	Divide	(3x^2+6x)/(2x)	$\frac{3 x^{2} + 6 x}{2 x}$
27380	Simplify	square root of x( square root of x+ square root of 2)	$\sqrt{x} (\sqrt{x} + \sqrt{2})$
27381	Solve for x	x^x=1/( fourth root of 2)	$x^{x} = \frac{1}{\sqrt[4]{2}}$
27382	Simplify	52x-52x-6-6	$52 x - 52 x - 6 - 6$
27383	Evaluate	10% of 40	$10 %$ of $40$
27384	Find the Roots (Zeros)	x^4+2x^3=7	$x^{4} + 2 x^{3} = 7$
27385	Graph	y\|y\|>=0	$y \| y \| \geq 0$
27386	Graph	f(x)=-1/4e^(x-3)	$f (x) = - \frac{1}{4} e^{x - 3}$
27387	Find the Asymptotes	(x^2+x-90)/(2x-18)	$\frac{x^{2} + x - 90}{2 x - 18}$
27388	Solve the Inequality for x	x^2+22<=12x+2	$x^{2} + 22 \leq 12 x + 2$
27389	Find All Complex Solutions	log of x(x+6)=2	$\log (x) (x + 6) = 2$
27390	Evaluate the Integral	integral of (x^7 square root of x)/(x^5)-3 cube root of x+5x^4-1/(2x)+e^x+2021 with respect to x	$\int \frac{x^{7} \sqrt{x}}{x^{5}} - 3 \sqrt[3]{x} + 5 x^{4} - \frac{1}{2 x} + e^{x} + 2021 d x$
27391	Solve the Inequality for x	y<=2x+5	$y \leq 2 x + 5$
27392	Solve for x	42 square root of 6=x square root of 14	$42 \sqrt{6} = x \sqrt{14}$
27393	Simplify	((2v^2+16v)/(2v^2-5v-7))/((4v^2+28v-32)/(10v^2-10))	$\frac{\frac{2 v^{2} + 16 v}{2 v^{2} - 5 v - 7}}{\frac{4 v^{2} + 28 v - 32}{10 v^{2} - 10}}$
27394	Evaluate	(4a+b)-3(2a+b)	$(4 a + b) - 3 (2 a + b)$
27395	Solve for x in Radians	cos(x)-sin(x)=0	$\cos (x) - \sin (x) = 0$
27396	Simplify	1÷(-( square root of 3)/2)	$1 \div (- \frac{\sqrt{3}}{2})$
27397	Graph	6>2/3x+5	$6 > \frac{2}{3} x + 5$
27398	Solve the System of Inequalities	7-4/3x<-5 and 1/2x-7<-6	$7 - \frac{4}{3} x < - 5$ and $\frac{1}{2} x - 7 < - 6$
27399	Graph	f(x)=x g(x)=x+6	$f (x) = x$ $g (x) = x + 6$
27400	Simplify	(-2x^2)^3(-y)^5	${(- 2 x^{2})}^{3} {(- y)}^{5}$