Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
45201	Solve the Inequality for a	7\|4a-6\|<42	$7 \| 4 a - 6 \| < 42$
45202	Evaluate the Integral	integral of (9x)/( square root of 3x^2+8) with respect to x	$\int \frac{9 x}{\sqrt{3 x^{2} + 8}} d x$
45203	Graph	g(x)=-2x,x>=3; -1/3x-5,x<=3	$g (x) = {\begin{cases} - 2 x, x \geq 3 \\ - \frac{1}{3} x - 5, x \leq 3 \end{cases}$
45204	Evaluate	-(-1)+3(2-(-1))	$- (- 1) + 3 (2 - (- 1))$
45205	Find the Concavity	-1/3x^3-x^2	$- \frac{1}{3} x^{3} - x^{2}$
45206	Factor	1/3xy+5/4xy^2-3/4xy+1/2xy^2-3x^2y+5/6x^2y	$\frac{1}{3} x y + \frac{5}{4} x y^{2} - \frac{3}{4} x y + \frac{1}{2} x y^{2} - 3 x^{2} y + \frac{5}{6} x^{2} y$
45207	Add	-1/4+1/2	$\frac{- 1}{4} + \frac{1}{2}$
45208	Simplify	((1/2)^-4)^2	${({(\frac{1}{2})}^{- 4})}^{2}$
45209	Simplify	(x^(1/2)-y^(1/2))^2	${(x^{\frac{1}{2}} - y^{\frac{1}{2}})}^{2}$
45210	Simplify	(tan(theta)^2+1)/(sec(theta))	$\frac{\tan^{2} (θ) + 1}{\sec (θ)}$
45211	Divide	(6x^3+12-47x^2+17x)÷(6x-5)	$(6 x^{3} + 12 - 47 x^{2} + 17 x) \div (6 x - 5)$
45212	Find the Domain	(x-1)/(4x)	$\frac{x - 1}{4 x}$
45213	Find All Complex Solutions	x^4-x^3-7x^2+x+6=0	$x^{4} - x^{3} - 7 x^{2} + x + 6 = 0$
45214	Factor	(a+b)^3-b^3	${(a + b)}^{3} - b^{3}$
45215	Solve for Y	X+4Y=1	$X + 4 Y = 1$
45216	Subtract	(x^2-8)-(3x^3-6x-4+9x^2)	$(x^{2} - 8) - (3 x^{3} - 6 x - 4 + 9 x^{2})$
45217	Simplify	b^-4c^0d^6	$b^{- 4} c^{0} d^{6}$
45218	Find the Antiderivative	e^x*e^(x+1)	$e^{x} \cdot e^{x + 1}$
45219	Solve the Inequality for c	9- square root of c+4<=6	$9 - \sqrt{c + 4} \leq 6$
45220	Add	(-9x-4/5)+(2x+2/3)	$(- 9 x - \frac{4}{5}) + (2 x + \frac{2}{3})$
45221	Evaluate	(15*360/60)	$(15 \cdot \frac{360}{60})$
45222	Find the Cosine of the Angle	135	$135$
45223	Solve for x	x-81x^-3=0	$x - 81 x^{- 3} = 0$
45224	Evaluate Using the Given Value	d^-3 for d=-2	$d^{- 3}$ for $d = - 2$
45225	Verify the Identity	(x+5)^2=x^2+10x+25	${(x + 5)}^{2} = x^{2} + 10 x + 25$
45226	Solve the Rational Equation for x	1/5 cube root of 3x+10=8	$\frac{1}{5} \sqrt[3]{3 x} + 10 = 8$
45227	Determine if Continuous	f(x)=x^2+3 if x<-2; 5 if x=-2; -3x+1 if x>-2	$f (x) = {\begin{cases} x^{2} + 3 & x < - 2 \\ 5 & x = - 2 \\ - 3 x + 1 & x > - 2 \end{cases}$
45228	Simplify	((8a^4t)/(27at^7))^-2	${(\frac{8 a^{4} t}{27 a t^{7}})}^{- 2}$
45229	Simplify	xy+y/(x^2)	$x y + \frac{y}{x^{2}}$
45230	Find the Exact Value	log base 4 of 1/2	$\log_{4} (\frac{1}{2})$
45231	Graph	(x-1)/(4-x)	$\frac{x - 1}{4 - x}$
45232	Evaluate	(5+2b)+(2b+3/2)	$(5 + 2 b) + (2 b + \frac{3}{2})$
45233	Factor	2x^3+x-3	$2 x^{3} + x - 3$
45234	Solve the Inequality for x	sin(x)<1	$\sin (x) < 1$
45235	Find the Axis of Symmetry	x^2	$x^{2}$
45236	Find the Exact Value	tan(15)tan(30)	$\tan (15) \tan (30)$
45237	Convert to Radical Form	p^(1/4)q	$p^{\frac{1}{4}} q$
45238	Solve the Rational Equation for x	(3x)/(x-2)=1+6/(x-2)	$\frac{3 x}{x - 2} = 1 + \frac{6}{x - 2}$
45239	Expand Using Sum/Difference Formulas	x(4x+1)	$x (4 x + 1)$
45240	Simplify	4(6f)+2f	$4 (6 f) + 2 f$
45241	Solve for x	8/(3x-6)=(3x)/(x-2)	$\frac{8}{3 x - 6} = \frac{3 x}{x - 2}$
45242	Find the Length of a	tri{}{45}{2}{45}{}{90}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = & 2 \\ a = \end{matrix} & \begin{matrix} A = & 45 \\ B = & 45 \\ C = & 90 \end{matrix} \end{matrix}$
45243	Simplify	4 square root of 6x*5 square root of 8x^4	$4 \sqrt{6 x} \cdot 5 \sqrt{8 x^{4}}$
45244	Solve the Inequality for x	2/3(1-e^(-x))<=-3	$\frac{2}{3} (1 - e^{- x}) \leq - 3$
45245	Simplify the Radical Expression	8 1/5	$8 \frac{1}{5}$
45246	Factor by Grouping	x^8-y^8	$x^{8} - y^{8}$
45247	Rationalize the Denominator	-1/( square root of 3)	$\frac{- 1}{\sqrt{3}}$
45248	Evaluate the Limit	limit as x approaches negative infinity of (x^2-4)/(x^2+4x+3)	$lim_{x \to - \infty} \frac{x^{2} - 4}{x^{2} + 4 x + 3}$
45249	Solve the Inequality for D	5D-8D-4<=-4+3d	$5 D - 8 D - 4 \leq - 4 + 3 d$
45250	Find the Antiderivative	x*sin(2x)	$x \cdot \sin (2 x)$
45251	Simplify	3x(x-3)+(2x+6)(-x-3)	$3 x (x - 3) + (2 x + 6) (- x - 3)$
45252	Evaluate	(3x/2)(3x/4)=3^6	$(3 \frac{x}{2}) (3 \frac{x}{4}) = 3^{6}$
45253	Simplify	(cot(x)-tan(x))/(sin(x)cos(x))	$\frac{\cot (x) - \tan (x)}{\sin (x) \cos (x)}$
45254	Reduce	(4x+20)/(8x+12)	$\frac{4 x + 20}{8 x + 12}$
45255	Convert to Rectangular	6(cos(pi/2)+isin(pi/2))*4(cos(pi/4)+isin(pi/4))	$6 (\cos (\frac{π}{2}) + i \sin (\frac{π}{2})) \cdot 4 (\cos (\frac{π}{4}) + i \sin (\frac{π}{4}))$
45256	Graph	x<=5 or x>8	$x \leq 5$ or $x > 8$
45257	Solve the Inequality for m	m+17<=-(4m-13)	$m + 17 \leq - (4 m - 13)$
45258	Graph	x^2+y	$x^{2} + y$
45259	Simplify the Radical Expression	cube root of square root of 16	$\sqrt[3]{\sqrt{16}}$
45260	Simplify	(10x^5+1x+8)+(2x^5+8x^2+4)	$(10 x^{5} + 1 x + 8) + (2 x^{5} + 8 x^{2} + 4)$
45261	Solve for x	1/2x-20-x=3(2x-1)-(2x-1)	$\frac{1}{2} x - 20 - x = 3 (2 x - 1) - (2 x - 1)$
45262	Find All Complex Solutions	square root of x-1-5=x-8	$\sqrt{x - 1} - 5 = x - 8$
45263	Solve the Rational Equation for x	square root of 5x+14=x+4	$\sqrt{5 x + 14} = x + 4$
45264	Find dy/dx	y=1/( cube root of x^2-6x)	$y = \frac{1}{\sqrt[3]{x^{2} - 6 x}}$
45265	Solve the Inequality for x	2x>x+7	$2 x > x + 7$
45266	Solve for x	1/4x+2/3-x=3/5x-1/2	$\frac{1}{4} x + \frac{2}{3} - x = \frac{3}{5} x - \frac{1}{2}$
45267	Find the Antiderivative	x^2y	$x^{2} y$
45268	Solve the Rational Equation for x	-6+ square root of x+10=2	$- 6 + \sqrt{x + 10} = 2$
45269	Find the Inverse	y=(2x+3)/(x-1)	$y = \frac{2 x + 3}{x - 1}$
45270	Simplify	(-(35p^6q^8)/(5r^-5))^2	${(- \frac{35 p^{6} q^{8}}{5 r^{- 5}})}^{2}$
45271	Find the Domain and Range	f(x) = square root of 2x-2	$f (x) = \sqrt{2} x - 2$
45272	Simplify	cot(x)sin(x)sec(x)^2	$\cot (x) \sin (x) \sec^{2} (x)$
45273	Find the Roots (Zeros)	x^4-5x^3+9x^2-9x=0	$x^{4} - 5 x^{3} + 9 x^{2} - 9 x = 0$
45274	Solve for x	0.5^(x+2)>9	${0.5}^{x + 2} > 9$
45275	Solve for x	square root of x-x+6=0	$\sqrt{x} - x + 6 = 0$
45276	Find f(g(x))	f(x)=x+4 g(x)=x^2	$f (x) = x + 4$ $g (x) = x^{2}$
45277	Multiply	square root of 2x^2* square root of 4x	$\sqrt{2 x^{2}} \cdot \sqrt{4 x}$
45278	Factor	12x^-6+7x^-5+x^-4	$12 x^{- 6} + 7 x^{- 5} + x^{- 4}$
45279	Factor	9x^2(x+6)-(x+6)	$9 x^{2} (x + 6) - (x + 6)$
45280	Calculate the Square Root	fourth root of 256(5x-2)^12	$\sqrt[4]{256 {(5 x - 2)}^{12}}$
45281	Simplify	((6a^3b^4)/(z^2y^4))^-3*((2zy)/(3ab))^-2	${(\frac{6 a^{3} b^{4}}{z^{2} y^{4}})}^{- 3} \cdot {(\frac{2 z y}{3 a b})}^{- 2}$
45282	Evaluate the Limit	limit as x approaches 3 of (x^2-9)(x-3)/(\|x-3\|)	$lim_{x \to 3} (x^{2} - 9) \frac{x - 3}{\| x - 3 \|}$
45283	Evaluate the Limit	limit as x approaches ( square root of 3)/2 of (arcsin(x)-arcsin(( square root of 3)/2))/(x-( square root of 3)/2)	$lim_{x \to \frac{\sqrt{3}}{2}} \frac{\arcsin (x) - \arcsin (\frac{\sqrt{3}}{2})}{x - \frac{\sqrt{3}}{2}}$
45284	Simplify	(7(3)^4)^0	${(7 {(3)}^{4})}^{0}$
45285	Solve by Substitution	x^2+y^2=49 y=7-x	$x^{2} + y^{2} = 49$ $y = 7 - x$
45286	Solve the Inequality for x	10/(x+2)<=5	$\frac{10}{x + 2} \leq 5$
45287	Simplify	(x^3-x^2y)-(xy^2+y^3)+(x^2y+xy^2)	$(x^{3} - x^{2} y) - (x y^{2} + y^{3}) + (x^{2} y + x y^{2})$
45288	Solve the Inequality for h	4h-13<-5	$4 h - 13 < - 5$
45289	Solve the System of Inequalities	16x^2+4y^2<=64 y>=-x^2+2	$16 x^{2} + 4 y^{2} \leq 64$ $y \geq - x^{2} + 2$
45290	Solve for n	m=n-18	$m = n - 18$
45291	Simplify	square root of 5( square root of 15x+3)	$\sqrt{5} (\sqrt{15 x} + 3)$
45292	Solve for x	3x-1<=2x+4	$3 x - 1 \leq 2 x + 4$
45293	Find the End Behavior	B(x)=7x^4-5x^3+10x^2-4x+1	$B (x) = 7 x^{4} - 5 x^{3} + 10 x^{2} - 4 x + 1$
45294	Solve for x	3x-5 = square root of 6x+5	$3 x - 5 = \sqrt{6 x + 5}$
45295	Combine Like Terms	-3y+12x-y-3x	$- 3 y + 12 x - y - 3 x$
45296	Evaluate	1/2(1-0.97)	$\frac{1}{2} (1 - 0.97)$
45297	Solve for h	15 = square root of 2(9.8)h	$15 = \sqrt{2 (9.8) h}$
45298	Solve the Inequality for x	2x-16>4x	$2 x - 16 > 4 x$
45299	Solve the Matrix Equation	[[4],[8],[6]]+2[[x],[y],[5z]]=[[-4],[-22],[16]]	$[\begin{array}{c} 4 \\ 8 \\ 6 \end{array}] + 2 [\begin{array}{c} x \\ y \\ 5 z \end{array}] = [\begin{array}{c} - 4 \\ - 22 \\ 16 \end{array}]$
45300	Evaluate	-3x^2=150	$- 3 x^{2} = 150$