Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
44401	Solve the System of Equations	x^2-y=1 2x^2+y^2=17	$x^{2} - y = 1$ $2 x^{2} + y^{2} = 17$
44402	Solve Using the Square Root Property	6x^2+125=x^2	$6 x^{2} + 125 = x^{2}$
44403	Find the Domain	(bx+3b)/(x^2-25)*((x-5)^2)/(ax+3a)	$\frac{b x + 3 b}{x^{2} - 25} \cdot \frac{{(x - 5)}^{2}}{a x + 3 a}$
44404	Integrate Using u-Substitution	integral from 0 to 2 of 1/(4+x^2) with respect to x	$\int_{0}^{2} \frac{1}{4 + x^{2}} d x$
44405	Find the Antiderivative	4/(x^2-4)	$\frac{4}{x^{2} - 4}$
44406	Rationalize the Denominator	( square root of 8- square root of 10)/( square root of 10- square root of 2)	$\frac{\sqrt{8} - \sqrt{10}}{\sqrt{10} - \sqrt{2}}$
44407	Simplify	a(a^-3b^-4)^-2b^-3	$a {(a^{- 3} b^{- 4})}^{- 2} b^{- 3}$
44408	Factor	4x^3(x+1)^(-3/2)-x(x+1)^(-1/2)	$4 x^{3} {(x + 1)}^{- \frac{3}{2}} - x {(x + 1)}^{- \frac{1}{2}}$
44409	Simplify	(4x^3y^6z^4)/(8x^6yz^3)	$\frac{4 x^{3} y^{6} z^{4}}{8 x^{6} y z^{3}}$
44410	Find Where Increasing/Decreasing	f(x) = square root of x-7+2	$f (x) = \sqrt{x - 7} + 2$
44411	Solve for h	4 = square root of h-6	$4 = \sqrt{h - 6}$
44412	Write in Standard Form	x^2+(y-3 square root of 2x)^2=1	$x^{2} + {(y - 3 \sqrt{2 x})}^{2} = 1$
44413	Solve the Inequality for x	\|3-2x\|>=4	$\| 3 - 2 x \| \geq 4$
44414	Evaluate	sin(2arccos(( square root of 2)/2))	$\sin (2 \arccos (\frac{\sqrt{2}}{2}))$
44415	Solve for x	2^(x+4)*2^(4x+6)=2^(2x+1)	$2^{x + 4} \cdot 2^{4 x + 6} = 2^{2 x + 1}$
44416	Simplify	2 square root of 18a^6b^2	$2 \sqrt{18} a^{6} b^{2}$
44417	Simplify	square root of 2/( square root of 3)	$\sqrt{\frac{2}{\sqrt{3}}}$
44418	Find the Asymptotes	(3(x+7)(x-7))/(2x(x+7))	$\frac{3 (x + 7) (x - 7)}{2 x (x + 7)}$
44419	Solve the Function Operation	If f(x)=x^2+5x and g(x)=7-x ; find: (f+g)(2)	If $f (x) = x^{2} + 5 x$ and $g (x) = 7 - x$ ; find: $(f + g) (2)$
44420	Evaluate	(3(25)^(1/2))/2	$\frac{3 {(25)}^{\frac{1}{2}}}{2}$
44421	Find dy/dx	y=4/( cube root of -2x-4)	$y = \frac{4}{\sqrt[3]{- 2 x - 4}}$
44422	Evaluate	(2^2)/(2^3)*2^5	$\frac{2^{2}}{2^{3}} \cdot 2^{5}$
44423	Write as a Single Logarithm	2( log base 3 of 20- log base 3 of 4)+0.5 log base 3 of 4	$2 (\log_{3} (20) - \log_{3} (4)) + 0.5 \log_{3} (4)$
44424	Evaluate Using L'Hospital's Rule	limit as x approaches 2 from the right of 8/(x^2-4)-x/(x-2)	$lim_{x \to 2^{+}} \frac{8}{x^{2} - 4} - \frac{x}{x - 2}$
44425	Describe the Transformation	f(x)=1.4^x-1 , g(x)=-1.4^x+6	$f (x) = {1.4}^{x} - 1$ , $g (x) = - {1.4}^{x} + 6$
44426	Evaluate the Limit	limit as x approaches 4 of ( natural log of x- natural log of 4)/(x-4)	$lim_{x \to 4} \frac{\ln (x) - \ln (4)}{x - 4}$
44427	Solve the Rational Equation for x	square root of x+8 = square root of 3x+8	$\sqrt{x + 8} = \sqrt{3 x + 8}$
44428	Evaluate the Integral	integral from 0 to 1 of (x+ square root of x) with respect to x	$\int_{0}^{1} (x + \sqrt{x}) d x$
44429	Evaluate	-2/3(6x-12)<1/2(8-4x)	$- \frac{2}{3} (6 x - 12) < \frac{1}{2} (8 - 4 x)$
44430	Solve by Factoring	5^(x+1)+5^(x-1)=26	$5^{x + 1} + 5^{x - 1} = 26$
44431	Simplify	x^2+1/2(20x^2-10x+6)+2x	$x^{2} + \frac{1}{2} (20 x^{2} - 10 x + 6) + 2 x$
44432	Simplify	(9x^3y^4)÷(x^2)y^2	$9 x^{3} y^{4} \div x^{2} y^{2}$
44433	Evaluate	1/2!	$\frac{1}{2}!$
44434	Solve for d	6 = square root of d/16	$6 = \sqrt{\frac{d}{16}}$
44435	Graph Using a Table of Values	y^2+x=2	$y^{2} + x = 2$
44436	Solve the System of Equations	9y=-17x+72 -72+17x=-9y	$9 y = - 17 x + 72$ $- 72 + 17 x = - 9 y$
44437	Solve for v	-63=4v-8v-15	$- 63 = 4 v - 8 v - 15$
44438	Find the Maximum/Minimum Value	f(x)=(x^2-x-2)/(x^2-6x+9)	$f (x) = \frac{x^{2} - x - 2}{x^{2} - 6 x + 9}$
44439	Solve for x	2(2x-5)=3(x+2)	$2 (2 x - 5) = 3 (x + 2)$
44440	Graph	2x-y<3 x+2y>=4	$2 x - y < 3$ $x + 2 y \geq 4$
44441	Factor	108y-180xy+75x^2y	$108 y - 180 x y + 75 x^{2} y$
44442	Evaluate the Summation	sum from k=0 to 6 of (3/2)*k^2	$\sum_{k = 0}^{6} (\frac{3}{2}) \cdot k^{2}$
44443	Simplify	fifth root of m^5n^-5	$\sqrt[5]{m^{5} n^{- 5}}$
44444	Evaluate the Integral	integral of (15x fourth root of 3x^2+4)/4 with respect to x	$\int \frac{15 x \sqrt[4]{3 x^{2} + 4}}{4} d x$
44445	Find the Exact Value	3*3^3	$3 \cdot 3^{3}$
44446	Find the Holes in the Graph	(x^2+x-6)/(x-2)	$\frac{x^{2} + x - 6}{x - 2}$
44447	Find the Exact Value	arcos (-( square root of 3)/2)	arcos $(- \frac{\sqrt{3}}{2})$
44448	Solve the Inequality for x	30<5x-5(x-6)/2<=60	$30 < 5 x - 5 \frac{x - 6}{2} \leq 60$
44449	Evaluate	60% of 20	$60 %$ of $20$
44450	Graph	f(x)=3x if x<0; x+2 if x>=0	$f (x) = {\begin{cases} 3 x & x < 0 \\ x + 2 & x \geq 0 \end{cases}$
44451	Solve the Inequality for v	\|4v-9\|<=27	$\| 4 v - 9 \| \leq 27$
44452	Find the Roots (Zeros)	3(x+3)^2-81=0	$3 {(x + 3)}^{2} - 81 = 0$
44453	Solve for x in Degrees	8sin(x)tan(x)-7tan(x)=0	$8 \sin (x) \tan (x) - 7 \tan (x) = 0$
44454	Simplify	12/((10x-40)/(4/(2x-8)))	$\frac{12}{\frac{10 x - 40}{\frac{4}{2 x - 8}}}$
44455	Solve for x	3x^2-28=2x^2-3x	$3 x^{2} - 28 = 2 x^{2} - 3 x$
44456	Solve for x	1/6(x+1/5)=-17/15	$\frac{1}{6} (x + \frac{1}{5}) = - \frac{17}{15}$
44457	Solve for z	-6z+1=-4-7z	$- 6 z + 1 = - 4 - 7 z$
44458	Simplify	1/(6^13*8^16)	$\frac{1}{6^{13} \cdot 8^{16}}$
44459	Find the Exact Value	((2^-10)/(4^2))^7	${(\frac{2^{- 10}}{4^{2}})}^{7}$
44460	Simplify/Condense	4 log base 3 of x-1/3 log base 3 of x+6	$4 \log_{3} (x) - \frac{1}{3} \log_{3} (x + 6)$
44461	Evaluate the Limit	limit as x approaches 0 of (e^(-x)-e^x)/(e^(-x)+1)	$lim_{x \to 0} \frac{e^{- x} - e^{x}}{e^{- x} + 1}$
44462	Evaluate	3(4*4)+(12/4)	$3 (4 \cdot 4) + (\frac{12}{4})$
44463	Add	(2y^2-5y+3)+(y^2-2y-5)	$(2 y^{2} - 5 y + 3) + (y^{2} - 2 y - 5)$
44464	Simplify	cube root of (x^24)/27	$\sqrt[3]{\frac{x^{24}}{27}}$
44465	Find the Domain and Range	(2-x)^2+3	${(2 - x)}^{2} + 3$
44466	Divide	( square root of 24)/8	$\frac{\sqrt{24}}{8}$
44467	Simplify the Radical Expression	( square root of 7- square root of 5)/( square root of 12+ square root of 7)	$\frac{\sqrt{7} - \sqrt{5}}{\sqrt{12} + \sqrt{7}}$
44468	Simplify	(-2+ square root of 3)/( square root of 3- square root of 15)	$\frac{- 2 + \sqrt{3}}{\sqrt{3} - \sqrt{15}}$
44469	Solve for k	1/2k+2=5+5/6k	$\frac{1}{2} k + 2 = 5 + \frac{5}{6} k$
44470	Find the Product	(12x^2+7y^3)(4x^2+7y^3)	$(12 x^{2} + 7 y^{3}) (4 x^{2} + 7 y^{3})$
44471	Find the Derivative - d/dx	(1- square root of x)*(1- cube root of x)	$(1 - \sqrt{x}) \cdot (1 - \sqrt[3]{x})$
44472	Solve for b	12(b+2)=8(b+5)	$12 (b + 2) = 8 (b + 5)$
44473	Simplify	(a-b^3+3c)(a-b^3-3c)	$(a - b^{3} + 3 c) (a - b^{3} - 3 c)$
44474	Simplify	square root of cube root of square root of y	$\sqrt{\sqrt[3]{\sqrt{y}}}$
44475	Find the GCF	16bc^2+24bc	$16 b c^{2} + 24 b c$
44476	Evaluate	(5^(1/4))+6(405^(1/4))	$(5^{\frac{1}{4}}) + 6 (405^{\frac{1}{4}})$
44477	Divide	((3x^2)/(3x))÷((x^2-9)/(x^2-10x+21))	$\frac{3 x^{2}}{3 x} \div \frac{x^{2} - 9}{x^{2} - 10 x + 21}$
44478	Evaluate	f(-1)=3(2)^x	$f (- 1) = 3 {(2)}^{x}$
44479	Solve for x	1/3(x-6)=1/9x-5/3	$\frac{1}{3} (x - 6) = \frac{1}{9} x - \frac{5}{3}$
44480	Solve for u	u+3/4=1/8	$u + \frac{3}{4} = \frac{1}{8}$
44481	Solve the Absolute Value Inequality for x	15=\|10-3x\|	$15 = \| 10 - 3 x \|$
44482	Solve the Inequality for x	1<=\|x\|<=4	$1 \leq \| x \| \leq 4$
44483	Find the Antiderivative	4sec(3x)tan(3x)	$4 \sec (3 x) \tan (3 x)$
44484	Graph	y<=(-1/3)x+4	$y \leq (- \frac{1}{3}) x + 4$
44485	Evaluate	(pi*5^2)/2	$\frac{π \cdot 5^{2}}{2}$
44486	Solve the System of Equations	y=x+z+5 z=-3y-3 2x-y=-4	$y = x + z + 5$ $z = - 3 y - 3$ $2 x - y = - 4$
44487	Evaluate	1/2(7+5^3)	$\frac{1}{2} (7 + 5^{3})$
44488	Evaluate the Limit	limit as x approaches 0 from the right of 9x-8 square root of x	$lim_{x \to 0^{+}} 9 x - 8 \sqrt{x}$
44489	Simplify	(x+h)^2-x^2	${(x + h)}^{2} - x^{2}$
44490	Evaluate	3(cos(pi/6)+isin(pi/6))	$3 (\cos (\frac{π}{6}) + i \sin (\frac{π}{6}))$
44491	Evaluate the Limit	limit as x approaches infinity of (-2x^4)/(3x^2-1)	$lim_{x \to \infty} \frac{- 2 x^{4}}{3 x^{2} - 1}$
44492	Evaluate the Integral	integral from 0 to 3 of (3/4y-1/4y^2) with respect to y	$\int_{0}^{3} (\frac{3}{4} y - \frac{1}{4} y^{2}) d y$
44493	Evaluate the Integral	integral from -2 to 6 of [4y-(y^2-12)] with respect to y	$\int_{- 2}^{6} [4 y - (y^{2} - 12)] d y$
44494	Divide Using Long Polynomial Division	Use the long division method to find the result when 3x^3+23x^2+23x+6 is divided by 3x+2	Use the long division method to find the result when $3 x^{3} + 23 x^{2} + 23 x + 6$ is divided by $3 x + 2$
44495	Solve the System of Equations	y=x-2 y=x^2-2	$y = x - 2$ $y = x^{2} - 2$
44496	Factor by Grouping	10a-25+5b	$10 a - 25 + 5 b$
44497	Simplify the Radical Expression	fourth root of (x^4y^24)/81	$\sqrt[4]{\frac{x^{4} y^{24}}{81}}$
44498	Simplify	(1-1/(x+2))/(1+3/(x-2))	$\frac{1 - \frac{1}{x + 2}}{1 + \frac{3}{x - 2}}$
44499	Convert to a Percentage	3/42*100%	$\frac{3}{42} \cdot 100 %$
44500	Solve for x	5/4(x-5/2)=-5/8	$\frac{5}{4} (x - \frac{5}{2}) = - \frac{5}{8}$