Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
11701	Graph	x+y=4 3x+3y=12	$x + y = 4$ $3 x + 3 y = 12$
11702	Evaluate	cos(45)^2	$\cos^{2} (45)$
11703	Plot	sin(theta)>0 , cos(theta)>0	$\sin (θ) > 0$ , $\cos (θ) > 0$
11704	Solve for x	(2^(x/5))(2^(x/2))=2^14	$(2^{\frac{x}{5}}) (2^{\frac{x}{2}}) = 2^{14}$
11705	Solve for y	ay+b=cx	$a y + b = c x$
11706	Evaluate the Integral	integral from 0 to 1 of 5^((3x)/2) with respect to x	$\int_{0}^{1} 5^{\frac{3 x}{2}} d x$
11707	Simplify the Radical Expression	cube root of (9x^6)/(y^3z^9)	$\sqrt[3]{\frac{9 x^{6}}{y^{3} z^{9}}}$
11708	Evaluate Using L'Hospital's Rule	limit as x approaches infinity of ((3x)/(3x+1))^x	$lim_{x \to \infty} {(\frac{3 x}{3 x + 1})}^{x}$
11709	Write the Fraction in Simplest Form	((-4y)^3)/(4y^-8)	$\frac{{(- 4 y)}^{3}}{4 y^{- 8}}$
11710	Simplify	fourth root of 9/12	$\sqrt[4]{\frac{9}{12}}$
11711	Simplify	(x^2-1)/(x^2+5x+4)*(x^2)/(x^2-x)	$\frac{x^{2} - 1}{x^{2} + 5 x + 4} \cdot \frac{x^{2}}{x^{2} - x}$
11712	Convert to a Decimal	-2pirad	$- 2 π$ radians
11713	Write in Standard Form	(5x^2+8x)+(x^2-5x+1)	$(5 x^{2} + 8 x) + (x^{2} - 5 x + 1)$
11714	Solve for x	(3x+4)/(7x)+5=6/x	$\frac{3 x + 4}{7 x} + 5 = \frac{6}{x}$
11715	Evaluate the Integral	integral of (x^(3/4)-1/(x^(3/4))) with respect to x	$\int (x^{\frac{3}{4}} - \frac{1}{x^{\frac{3}{4}}}) d x$
11716	Write in Standard Form	7xy+x^3-3y^3-5x^2y^2	$7 x y + x^{3} - 3 y^{3} - 5 x^{2} y^{2}$
11717	Solve for k	13-19k=-10+9(-k-13)	$13 - 19 k = - 10 + 9 (- k - 13)$
11718	Simplify	((t^2)^5(t^4)^2)/((t^3)^7)	$\frac{{(t^{2})}^{5} {(t^{4})}^{2}}{{(t^{3})}^{7}}$
11719	Evaluate	3/2(3^-4)	$\frac{3}{2} (3^{- 4})$
11720	Solve the Inequality for c	2/5c>18	$\frac{2}{5} c > 18$
11721	Simplify	((6ax)/(m^2-2m))÷((8ax)/(3m-6))	$\frac{6 a x}{m^{2} - 2 m} \div \frac{8 a x}{3 m - 6}$
11722	Find the Asymptotes	(x^2-1)/(9x^2-30x)	$\frac{x^{2} - 1}{9 x^{2} - 30 x}$
11723	Evaluate the Limit	limit as x approaches 4 of (x^3 square root of x-128)/(x-4)	$lim_{x \to 4} \frac{x^{3} \sqrt{x} - 128}{x - 4}$
11724	Simplify the Radical Expression	( square root of 25)/( square root of 100)	$\frac{\sqrt{25}}{\sqrt{100}}$
11725	Solve for x	( cube root of 5x-5)/( cube root of 2x)=-1	$\frac{\sqrt[3]{5 x - 5}}{\sqrt[3]{2 x}} = - 1$
11726	Find the Derivative - d/dx	y=((3x^2+2)/(x+1))^7	$y = {(\frac{3 x^{2} + 2}{x + 1})}^{7}$
11727	Convert to Radical Form	(2x-5)^(-2/5)	${(2 x - 5)}^{- \frac{2}{5}}$
11728	Solve for x	square root of 27^x=81	$\sqrt{27^{x}} = 81$
11729	Graph	y=-3 y=x-3	$y = - 3$ $y = x - 3$
11730	Solve the Rational Equation for x	8-6/x=5+12/x	$8 - \frac{6}{x} = 5 + \frac{12}{x}$
11731	Solve the Function Operation	f(x)=x^2-x+12 g(x)=3x+8 Find: (fog)(x)	$f (x) = x^{2} - x + 12$ $g (x) = 3 x + 8$ Find: $((f \circ g)) (x)$
11732	Find the Derivative - d/dx	natural log of ((x+1)/(2x-1))^2	$\ln ({(\frac{x + 1}{2 x - 1})}^{2})$
11733	Solve for x	9-4(3x+1)=3(6-3x)-9	$9 - 4 (3 x + 1) = 3 (6 - 3 x) - 9$
11734	Find the Degree	8b^2+9c^4b^5-b	$8 b^{2} + 9 c^{4} b^{5} - b$
11735	Divide	(-1/2)÷(-( square root of 3)/2)	$- \frac{1}{2} \div (- \frac{\sqrt{3}}{2})$
11736	Write in Standard Form	(x-4y)^2	${(x - 4 y)}^{2}$
11737	Solve the Function Operation	Given g(x)=-4x-2 ; find g(-2)	Given $g (x) = - 4 x - 2$ ; find $g (- 2)$
11738	Solve the Function Operation	f(x)=(x+7)^2-2 if x<-4; -x+3 if -4<=x<=1; x+1 if x>1 Find f(-4)	$f (x) = {\begin{cases} {(x + 7)}^{2} - 2 & x < - 4 \\ - x + 3 & - 4 \leq x \leq 1 \\ x + 1 & x > 1 \end{cases}$ Find $f (- 4)$
11739	Multiply	-8mn*(2m-3mp+p^2)	$- 8 m n \cdot (2 m - 3 m p + p^{2})$
11740	Convert to Radical Form	(2x^2+6)^(-1/4)	${(2 x^{2} + 6)}^{- \frac{1}{4}}$
11741	Solve the Inequality for X	3+X<7	$3 + X < 7$
11742	Solve for k	1/3(x-k)=kx	$\frac{1}{3} (x - k) = k x$
11743	Factor by Grouping	2xy+x^2y-6-3x	$2 x y + x^{2} y - 6 - 3 x$
11744	Evaluate	9^x*3^(x+2)=3^(f(x))	$9^{x} \cdot 3^{x + 2} = 3^{f (x)}$
11745	Graph	-2(x-3y)=12	$- 2 (x - 3 y) = 12$
11746	Add	(10x^4+3x^2-5x+4)+(7x^5-5x^4+2x-9)	$(10 x^{4} + 3 x^{2} - 5 x + 4) + (7 x^{5} - 5 x^{4} + 2 x - 9)$
11747	Solve the System of Equations	x+7y-8z=-7 -x+y+z=-9 x+8y+6z=-9	$x + 7 y - 8 z = - 7$ $- x + y + z = - 9$ $x + 8 y + 6 z = - 9$
11748	Find the Antiderivative	x/(x^2)	$\frac{x}{x^{2}}$
11749	Evaluate the Function	f(3)=1/3(6)^3	$f (3) = \frac{1}{3} {(6)}^{3}$
11750	Graph	F(x) = cube root of x-2+3	$F (x) = \sqrt[3]{x - 2} + 3$
11751	Graph	Graph -14x+21y=84	Graph $- 14 x + 21 y = 84$
11752	Evaluate the Limit	limit as x approaches 0 of (x/(x+1))^x	$lim_{x \to 0} {(\frac{x}{x + 1})}^{x}$
11753	Solve for c	square root of 29+4w=23-cw	$\sqrt{29 + 4 w} = 23 - c w$
11754	Solve for x	5/(x^3+5x^2)=4/(x+5)+1/(x^2)	$\frac{5}{x^{3} + 5 x^{2}} = \frac{4}{x + 5} + \frac{1}{x^{2}}$
11755	Solve the Inequality for x	2^x>=32	$2^{x} \geq 32$
11756	Simplify	2x^3y^3+3xy-3x^3y^3+x^2y-xy+2x^2y	$2 x^{3} y^{3} + 3 x y - 3 x^{3} y^{3} + x^{2} y - x y + 2 x^{2} y$
11757	Multiply	(48x^5y^3)/(y^4)*(x^2y)/(6x^3y^2)	$\frac{48 x^{5} y^{3}}{y^{4}} \cdot \frac{x^{2} y}{6 x^{3} y^{2}}$
11758	Evaluate	54\|8-12\|+2\|-6-2\|+4	$54 \| 8 - 12 \| + 2 \| - 6 - 2 \| + 4$
11759	Solve the Function Operation	f(n)=n^2+4n g(n)=-n-5 Find f(n)+g(n)	$f (n) = n^{2} + 4 n$ $g (n) = - n - 5$ Find $f (n) + g (n)$
11760	Find the Asymptotes	(x^2-5x)/(-2x^2)	$\frac{x^{2} - 5 x}{- 2 x^{2}}$
11761	Simplify	(a^2-b^2)/(a^2-3a)*(2a-6)/((a+b)^2)	$\frac{a^{2} - b^{2}}{a^{2} - 3 a} \cdot \frac{2 a - 6}{{(a + b)}^{2}}$
11762	Solve for x	square root of 9x+1 = square root of 5x+11	$\sqrt{9 x} + 1 = \sqrt{5 x + 11}$
11763	Factor	m(m+n)-3m(m+n)^2	$m \cdot (m + n) - 3 m \cdot {(m + n)}^{2}$
11764	Simplify	(3/(x^2))/( square root of 10-x)	$\frac{\frac{3}{x^{2}}}{\sqrt{10 - x}}$
11765	Simplify	(27^(4/3))/(27^(2/3))	$\frac{27^{\frac{4}{3}}}{27^{\frac{2}{3}}}$
11766	Solve for y	(5y+13)/(5y+4)-(4-6y)/(3y-1)=3	$\frac{5 y + 13}{5 y + 4} - \frac{4 - 6 y}{3 y - 1} = 3$
11767	Find g(f(x))	f(x)=x^3+12x^2+25x-70 g(x)=x+7	$f (x) = x^{3} + 12 x^{2} + 25 x - 70$ $g (x) = x + 7$
11768	Subtract	(x-4)/(x^2+4x+3)-(x-1)/(x^2-9)	$\frac{x - 4}{x^{2} + 4 x + 3} - \frac{x - 1}{x^{2} - 9}$
11769	Graph	4x+4y<16 x>y+16	$4 x + 4 y < 16$ $x > y + 16$
11770	Find the Integral	natural log of x+1	$\ln (x + 1)$
11771	Find the Degree, Leading Term, and Leading Coefficient	10+(x^2)/6	$10 + \frac{x^{2}}{6}$
11772	Solve for x	6x(x-1)=2-5x	$6 x (x - 1) = 2 - 5 x$
11773	Solve the Inequality for p	-13<=3+8p<=11	$- 13 \leq 3 + 8 p \leq 11$
11774	Evaluate the Limit	limit as x approaches 0 of (x+1)^(cot(x))	$lim_{x \to 0} {(x + 1)}^{\cot (x)}$
11775	Evaluate	(t^-2)^6	${(t^{- 2})}^{6}$
11776	Solve for p	3^(p-7)*3^(2p+1)=3^(8p-36)	$3^{p - 7} \cdot 3^{2 p + 1} = 3^{8 p - 36}$
11777	Find the Difference Quotient	x^3	$x^{3}$
11778	Simplify	1/(sin(x)cot(x))	$\frac{1}{\sin (x) \cot (x)}$
11779	Solve for d	8d=5-2d	$8 d = 5 - 2 d$
11780	Find Amplitude, Period, and Phase Shift	h(x)=4tan((4pi)/3x)	$h (x) = 4 \tan (\frac{4 π}{3} x)$
11781	Solve by Graphing	y=-1/2x-4 x=-4	$y = - \frac{1}{2} x - 4$ $x = - 4$
11782	Find the Asymptotes	f(x)=(3x^2)/(x-x^2)	$f (x) = \frac{3 x^{2}}{x - x^{2}}$
11783	Solve for x	(1/4)^(x+2)=6	${(\frac{1}{4})}^{x + 2} = 6$
11784	Solve for x	square root of x+4 = square root of x+20	$\sqrt{x + 4} = \sqrt{x + 20}$
11785	Convert to Rectangular Coordinates	(5 square root of 3,pi)	$(5 \sqrt{3}, π)$
11786	Simplify	square root of (20x^3y^2)/(9xz^3)	$\sqrt{\frac{20 x^{3} y^{2}}{9 x z^{3}}}$
11787	Find the Secant Given the Point	(-1,0)	$(- 1, 0)$
11788	Find All Complex Solutions	81x^4-16=0	$81 x^{4} - 16 = 0$
11789	Add	(28a^2-10)+(5a^2-2b+6)	$(28 a^{2} - 10) + (5 a^{2} - 2 b + 6)$
11790	Factor	(x^2-5x+6)/(x^2-3x)	$\frac{x^{2} - 5 x + 6}{x^{2} - 3 x}$
11791	Write in Standard Form	(3y^2-4y+1)+(-y^2+y-2)	$(3 y^{2} - 4 y + 1) + (- y^{2} + y - 2)$
11792	Write in Standard Form	f(x)=-2/3x^3-8x^4-2x+7	$f (x) = - \frac{2}{3} x^{3} - 8 x^{4} - 2 x + 7$
11793	Find the Degree, Leading Term, and Leading Coefficient	f(x)=x-2x^3-4	$f (x) = x - 2 x^{3} - 4$
11794	Simplify	(cos(arcsec(3)+arctan(2)))/(cos(arctan(2)))	$\frac{\cos (arcsec (3) + \arctan (2))}{\cos (\arctan (2))}$
11795	Solve for x	(3x+8)/x-(3x+3)/(2x)=1	$\frac{3 x + 8}{x} - \frac{3 x + 3}{2 x} = 1$
11796	Find the Maximum/Minimum Value	y=cos(x+pi/4)	$y = \cos (x + \frac{π}{4})$
11797	Solve the Rational Equation for x	1+1/(x+1)=-x/(x+1)	$1 + \frac{1}{x + 1} = - \frac{x}{x + 1}$
11798	Solve the Inequality for x	4/(x+5)<3/(x-3)	$\frac{4}{x + 5} < \frac{3}{x - 3}$
11799	Find the Other Trig Values in Quadrant IV	cot(theta)=-( square root of 5)/6	$\cot (θ) = - \frac{\sqrt{5}}{6}$
11800	Simplify	(-3x^4)/(-6x^2+(-3x))	$\frac{- 3 x^{4}}{- 6 x^{2} + (- 3 x)}$