Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
48301	Find the Parabola with Focus (0,5) and Directrix y=-5	(0,5) , y=-5	$(0, 5)$ , $y = - 5$
48302	Evaluate the Integral	integral of (2 square root of x^3+7 cube root of x^2) with respect to x	$\int (2 \sqrt{x^{3}} + 7 \sqrt[3]{x^{2}}) d x$
48303	Evaluate	log of (1/9)/k	$\log (\frac{\frac{1}{9}}{k})$
48304	Find the Equation Using Point-Slope Formula	(-2,3) and slope m=9	$(- 2, 3)$ and slope $m = 9$
48305	Simplify	(24m^3n)*(1/4n)	$(24 m^{3} n) \cdot (\frac{1}{4} n)$
48306	Solve for x	f(x)=1/2x-3	$f (x) = \frac{1}{2} x - 3$
48307	Simplify	square root of x^7y^7*4 square root of 2x^11y^2	$\sqrt{x^{7} y^{7}} \cdot 4 \sqrt{2 x^{11} y^{2}}$
48308	Simplify	((3x^-2y)^3)/(9x^5)	$\frac{{(3 x^{- 2} y)}^{3}}{9 x^{5}}$
48309	Split Using Partial Fraction Decomposition	(2x^3-4x^2-15x+5)/(x^2-2x-8)	$\frac{2 x^{3} - 4 x^{2} - 15 x + 5}{x^{2} - 2 x - 8}$
48310	Factor	(x^2-9)/(x^2+5x+6)	$\frac{x^{2} - 9}{x^{2} + 5 x + 6}$
48311	Find the Degree, Leading Term, and Leading Coefficient	f(x)=5x-x^3+3x^5-2	$f (x) = 5 x - x^{3} + 3 x^{5} - 2$
48312	Find the Slope	What is the slope of the line through (-9,6) and (-3,9) ?	What is the slope of the line through $(- 9, 6)$ and $(- 3, 9)$ ?
48313	Solve for x	22=5x-4(x+7)	$22 = 5 x - 4 (x + 7)$
48314	Simplify	(x+4)/5+(x+5)/5	$\frac{x + 4}{5} + \frac{x + 5}{5}$
48315	Solve the Rational Equation for x	1/(x-1)-1=x/(x-1)	$\frac{1}{x - 1} - 1 = \frac{x}{x - 1}$
48316	Find All Complex Solutions	cos(theta)^2=1/2	$\cos^{2} (θ) = \frac{1}{2}$
48317	Find the Roots (Zeros)	16x^2=-72x-83	$16 x^{2} = - 72 x - 83$
48318	Find the Derivative - d/dt	17/2-3/2cos((pit)/6)	$\frac{17}{2} - \frac{3}{2} \cos (\frac{π t}{6})$
48319	Divide Using Long Polynomial Division	2x^3+7x^2+9x+10 divided by 2x+5	$2 x^{3} + 7 x^{2} + 9 x + 10$ divided by $2 x + 5$
48320	Solve the Function Operation	f(x)=x^2-x-6 , (f(-5))/(f(2))	$f (x) = x^{2} - x - 6$ , $\frac{f (- 5)}{f (2)}$
48321	Find the Center and Radius	x^2-10x=-y^2+16y-40	$x^{2} - 10 x = - y^{2} + 16 y - 40$
48322	Evaluate	(10(-1)^2+12(-1)+5)/((5(-1)+3)^2)	$\frac{10 {(- 1)}^{2} + 12 (- 1) + 5}{{(5 (- 1) + 3)}^{2}}$
48323	Find the Remainder	(2x^6+x^2+2)/(x+2)	$\frac{2 x^{6} + x^{2} + 2}{x + 2}$
48324	Find the Domain	f(x)=(x^2+x-20)/(x^3-4x^2-9x+36)	$f (x) = \frac{x^{2} + x - 20}{x^{3} - 4 x^{2} - 9 x + 36}$
48325	Find dx/dy	(x+y)^2(x-y)^2=x^4+y^4	${(x + y)}^{2} {(x - y)}^{2} = x^{4} + y^{4}$
48326	Simplify the Radical Expression	(x^4y^2)/( fourth root of x^3y^2)	$\frac{x^{4} y^{2}}{\sqrt[4]{x^{3} y^{2}}}$
48327	Evaluate the Integral	integral of (-3x^-2+4+6x^3) with respect to x	$\int (- 3 x^{- 2} + 4 + 6 x^{3}) d x$
48328	Solve the Inequality for x	x+4<5/x	$x + 4 < \frac{5}{x}$
48329	Simplify the Radical Expression	square root of -7* square root of -7	$\sqrt{- 7} \cdot \sqrt{- 7}$
48330	Find the Antiderivative	f(x)=7-6x^2+12x^3	$f (x) = 7 - 6 x^{2} + 12 x^{3}$
48331	Evaluate the Integral	e^( integral of -1 with respect to x)	$e^{\int - 1 d x}$
48332	Evaluate	40% of 85	$40 %$ of $85$
48333	Simplify	sin(x)*(tan(x)+cot(x))	$\sin (x) \cdot (\tan (x) + \cot (x))$
48334	Solve the System of Equations	y=3x^2-7x+1 y=-4x+19	$y = 3 x^{2} - 7 x + 1$ $y = - 4 x + 19$
48335	Simplify	(5x^2+14x-3)/(3x-15x^2)	$\frac{5 x^{2} + 14 x - 3}{3 x - 15 x^{2}}$
48336	Simplify	4*( square root of 2)/2	$4 \cdot \frac{\sqrt{2}}{2}$
48337	Reduce	square root of 108	$\sqrt{108}$
48338	Solve for b	2b-25+5b=7-32	$2 b - 25 + 5 b = 7 - 32$
48339	Simplify	(3x^2y-2xy)(3x^2y+2xy)	$(3 x^{2} y - 2 x y) (3 x^{2} y + 2 x y)$
48340	Solve for u	9=-3/u	$9 = - \frac{3}{u}$
48341	Subtract	-3x^2-4x+3 and 2x^2-x+3	$- 3 x^{2} - 4 x + 3$ and $2 x^{2} - x + 3$
48342	Simplify	((x-1)/(2x-7))/(-1/10)	$\frac{\frac{x - 1}{2 x - 7}}{- \frac{1}{10}}$
48343	Solve the Inequality for x	-2<x<2	$- 2 < x < 2$
48344	Simplify	9 square root of 7+ square root of 6-3 square root of 7+5 square root of 6	$9 \sqrt{7} + \sqrt{6} - 3 \sqrt{7} + 5 \sqrt{6}$
48345	Evaluate	tan((-5pi)/4)	$\tan (\frac{- 5 π}{4})$
48346	Evaluate the Function	f(x+3)=f(x)	$f (x + 3) = f (x)$
48347	Find the Remainder	(-19x^2+3+7x+15x^4)÷(-5x^2+3)	$(- 19 x^{2} + 3 + 7 x + 15 x^{4}) \div (- 5 x^{2} + 3)$
48348	Solve the Function Operation	f(x)=2x+3 g(x)=4x-2 Find (fog)(x)	$f (x) = 2 x + 3$ $g (x) = 4 x - 2$ Find $((f \circ g)) (x)$
48349	Evaluate the Summation	4 sum from k=3 to 6 of -k^2+2k	$4 \sum_{k = 3}^{6} - k^{2} + 2 k$
48350	Solve for x	-\|3+3x\|-2>-11	$- \| 3 + 3 x \| - 2 > - 11$
48351	Simplify	(3m)/(m-6)*(5m^3-30m^2)/(5m^2)	$\frac{3 m}{m - 6} \cdot \frac{5 m^{3} - 30 m^{2}}{5 m^{2}}$
48352	Solve in Terms of the Arbitrary Variable a	y=4x-5 and y=ax+2	$y = 4 x - 5$ and $y = a x + 2$
48353	Solve for x	4(3x-3)^(2/3)=36	$4 {(3 x - 3)}^{\frac{2}{3}} = 36$
48354	Simplify the Radical Expression	(3+ square root of 8)/(2-2 square root of 8)	$\frac{3 + \sqrt{8}}{2 - 2 \sqrt{8}}$
48355	Simplify the Radical Expression	square root of -9+ square root of -25- square root of -5	$\sqrt{- 9} + \sqrt{- 25} - \sqrt{- 5}$
48356	Simplify	(9x-x^2)(3+ square root of x)	$(9 x - x^{2}) (3 + \sqrt{x})$
48357	Solve for v	10^-410^9=10^(v+4)10^(2v-11)	$10^{- 4} \cdot 10^{9} = 10^{v + 4} \cdot 10^{2 v - 11}$
48358	Find the LCM	b+8 , 7b-3	$b + 8$ , $7 b - 3$
48359	Evaluate	x/5+4x+3(x-5)	$\frac{x}{5} + 4 x + 3 (x - 5)$
48360	Graph	-1/3x+5<3	$- \frac{1}{3} x + 5 < 3$
48361	Evaluate	n^(1/2)+6n^(1/4)-16=0	$n^{\frac{1}{2}} + 6 n^{\frac{1}{4}} - 16 = 0$
48362	Solve the Rational Equation for y	square root of 4y=10	$\sqrt{4 y} = 10$
48363	Evaluate	\|i\|	$\| i \|$
48364	Solve the System of Equations	x-2y=6 y=2x	$x - 2 y = 6$ $y = 2 x$
48365	Find dy/dx	y=(4x^3)/(2x^2-5)	$y = \frac{4 x^{3}}{2 x^{2} - 5}$
48366	Simplify	3/4*12/27	$\frac{3}{4} \cdot \frac{12}{27}$
48367	Simplify	fourth root of square root of z^5	$\sqrt[4]{\sqrt{z^{5}}}$
48368	Simplify	(2t^3)/( square root of 4t^5)	$\frac{2 t^{3}}{\sqrt{4 t^{5}}}$
48369	Solve for t	-3t+9>=-21	$- 3 t + 9 \geq - 21$
48370	Simplify the Radical Expression	eighth root of 49a^8b^2	$\sqrt[8]{49 a^{8} b^{2}}$
48371	Find the Quotient	(-19x^2+3+7x+15x^4)÷(-5x^2+3)	$(- 19 x^{2} + 3 + 7 x + 15 x^{4}) \div (- 5 x^{2} + 3)$
48372	Simplify	(3^2*3^-4)^4	${(3^{2} \times 3^{- 4})}^{4}$
48373	Solve for m	c=3m+2	$c = 3 m + 2$
48374	Find the Slope	(12,0) and (2,-5)	$(12, 0)$ and $(2, - 5)$
48375	Find the Holes in the Graph	H(x)=(4x^2-80x+364)/(x^2-18x+77)	$H (x) = \frac{4 x^{2} - 80 x + 364}{x^{2} - 18 x + 77}$
48376	Evaluate the Limit	limit as x approaches 3 of (x+9)/(5-x)	$lim_{x \to 3} \frac{x + 9}{5 - x}$
48377	Find the Roots (Zeros)	4x^3-3x^2+1	$4 x^{3} - 3 x^{2} + 1$
48378	Simplify	((x+1)/(x^2))/(1/x+(x+1)/x)	$\frac{\frac{x + 1}{x^{2}}}{\frac{1}{x} + \frac{x + 1}{x}}$
48379	Find dx/dy	y=(4x^3)/(2x^2-5)	$y = \frac{4 x^{3}}{2 x^{2} - 5}$
48380	Find the Asymptotes	y=(5x^3-4)/(x^2+4x-5)	$y = \frac{5 x^{3} - 4}{x^{2} + 4 x - 5}$
48381	Divide	((x+2)/(x-4))÷(1/(3x-12))	$\frac{x + 2}{x - 4} \div \frac{1}{3 x - 12}$
48382	Convert to Radical Form	square root of x^(3/4)x^-1	$\sqrt{x^{\frac{3}{4}} x^{- 1}}$
48383	Solve for x	square root of x+2=2x+1	$\sqrt{x + 2} = 2 x + 1$
48384	Solve for x	2(3-5(6+x))=15x	$2 (3 - 5 (6 + x)) = 15 x$
48385	Find the Domain and Range	y=cos(x-pi/2)	$y = \cos (x - \frac{π}{2})$
48386	Find the Roots (Zeros)	3x^4-9x^3+x^2-3x	$3 x^{4} - 9 x^{3} + x^{2} - 3 x$
48387	Solve for x	1/(x-a)+1/(x+a)=2/(x-1)	$\frac{1}{x - a} + \frac{1}{x + a} = \frac{2}{x - 1}$
48388	Graph	\|2x+2\|-7<=-5	$\| 2 x + 2 \| - 7 \leq - 5$
48389	Evaluate	11x^3*7x^(7/3)	$11 x^{3} \cdot 7 x^{\frac{7}{3}}$
48390	Solve the Absolute Value Inequality for w	\|3-6w\|=39	$\| 3 - 6 w \| = 39$
48391	Multiply	(4t+4)/(t-5)*(t^2-t-20)	$\frac{4 t + 4}{t - 5} \cdot (t^{2} - t - 20)$
48392	Find the Degree	f(x)=2-11x+2x^2	$f (x) = 2 - 11 x + 2 x^{2}$
48393	Subtract	7/12-(4x)/(3x)	$\frac{7}{12} - \frac{4 x}{3 x}$
48394	Simplify	-9/(2 square root of 45)	$- \frac{9}{2 \sqrt{45}}$
48395	Solve the Function Operation	f(x)=5 fifth root of x+7 ; find f^-1(x)	$f (x) = 5 \sqrt[5]{x + 7}$ ; find $f^{- 1} (x)$
48396	Evaluate	csc(0 degrees )	$\csc (0 °)$
48397	Convert to a Percentage	22 is what percent of 40	$22$ is what percent of $40$
48398	Solve the Inequality for x	y<4x-5	$y < 4 x - 5$
48399	Simplify	1/2a^3b^2-2a^2b^3-a^3b^2-2/3a^2b^3	$\frac{1}{2} a^{3} b^{2} - 2 a^{2} b^{3} - a^{3} b^{2} - \frac{2}{3} a^{2} b^{3}$
48400	Solve the Inequality for x	(x-1)(3x-4)>=0	$(x - 1) (3 x - 4) \geq 0$