Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
37501	Find the Exact Value	(tan(45 degrees )+tan(30 degrees ))/(1-tan(45 degrees )tan(30 degrees ))	$\frac{\tan (45 °) + \tan (30 °)}{1 - \tan (45 °) \tan (30 °)}$
37502	Evaluate the Integral	integral of (-3/x+3e^x) with respect to x	$\int (- \frac{3}{x} + 3 e^{x}) d x$
37503	Solve the System of Equations	x^2=2y^2+18 x^2-3y^2=9	$x^{2} = 2 y^{2} + 18$ $x^{2} - 3 y^{2} = 9$
37504	Simplify	(1+ square root of 5)/(5+ square root of 5)	$\frac{1 + \sqrt{5}}{5 + \sqrt{5}}$
37505	Simplify	-3 square root of -49+ cube root of -729+ square root of -4-3 cube root of -64	$- 3 \sqrt{- 49} + \sqrt[3]{- 729} + \sqrt{- 4} - 3 \sqrt[3]{- 64}$
37506	Describe the Transformation	h(x)=1/5f(x)	$h (x) = \frac{1}{5} f (x)$
37507	Evaluate the Limit	limit as x approaches 4 from the right of x^3-cx	$lim_{x \to 4^{+}} x^{3} - c x$
37508	Solve the Function Operation	g(x)=-x+4 ; find g(-4)	$g (x) = - x + 4$ ; find $g (- 4)$
37509	Find the Length of a	tri{}{30}{10}{60}{}{90}	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = \\ c = & 10 \\ a = \end{matrix} & \begin{matrix} A = & 30 \\ B = & 60 \\ C = & 90 \end{matrix} \end{matrix}$
37510	Simplify	(2x^4y^3)/(8xy^2z^2)	$\frac{2 x^{4} y^{3}}{8 x y^{2} z^{2}}$
37511	Simplify	(2x^5-3x^2+4)-(x^5+2x^2+7)	$(2 x^{5} - 3 x^{2} + 4) - (x^{5} + 2 x^{2} + 7)$
37512	Find the Equation with a Point and Slope	What is the equation of the line that passes through the point (8,-8) and has a slope of -2 ?	What is the equation of the line that passes through the point $(8, - 8)$ and has a slope of $- 2$ ?
37513	Solve for h	3(h-2)+1=h+4+2h	$3 (h - 2) + 1 = h + 4 + 2 h$
37514	Solve for k	log base 5 of 3k+12=3/4*( log base 5 of 405- log base 5 of 5)	$\log_{5} (3 k + 12) = \frac{3}{4} \cdot (\log_{5} (405) - \log_{5} (5))$
37515	Graph	f(x)=(1+1/x)^x	$f (x) = {(1 + \frac{1}{x})}^{x}$
37516	Divide Using Synthetic Division	Use synthetic division to find the result when x^3+3x^2-21x-28 is divided by x-4	Use synthetic division to find the result when $x^{3} + 3 x^{2} - 21 x - 28$ is divided by $x - 4$
37517	Evaluate the Limit	limit as x approaches negative infinity of ((x+2)(x+5)(x-5))/(13(x+3)(x+5))	$lim_{x \to - \infty} \frac{(x + 2) (x + 5) (x - 5)}{13 (x + 3) (x + 5)}$
37518	Solve the Function Operation	Given that f(x)=x^2+9x+18 and g(x)=x+3 ; find (f÷g)(x) and express the result in standard form.	Given that $f (x) = x^{2} + 9 x + 18$ and $g (x) = x + 3$ ; find $(f \div g) (x)$ and express the result in standard form.
37519	Solve the System of Equations	y=2x-10 2y=x-8	$y = 2 x - 10$ $2 y = x - 8$
37520	Multiply	(k^2+12k+32)/(k^2+13k+40)*(k^2+5k)/(k^2+6k+8)	$\frac{k^{2} + 12 k + 32}{k^{2} + 13 k + 40} \cdot \frac{k^{2} + 5 k}{k^{2} + 6 k + 8}$
37521	Solve the Rational Equation for x	fourth root of 4x-13=-15	$\sqrt[4]{4 x} - 13 = - 15$
37522	Simplify the Radical Expression	(2^0*2^3)/( square root of 2)	$\frac{2^{0} \cdot 2^{3}}{\sqrt{2}}$
37523	Solve the Inequality for v	5v+10<=-4v-17<9-2v	$5 v + 10 \leq - 4 v - 17 < 9 - 2 v$
37524	Simplify	((ab+b^2)/3)÷((b^3)/(3a))+(a+b)/b	$\frac{a b + b^{2}}{3} \div \frac{b^{3}}{3 a} + \frac{a + b}{b}$
37525	Solve for θ in Degrees	cos(theta)=sin(theta)	$\cos (θ) = \sin (θ)$
37526	Find the Inverse	f(x)=( fifth root of 3(x+8))/10	$f (x) = \frac{\sqrt[5]{3 (x + 8)}}{10}$
37527	Evaluate	8-\|-6\|+3	$8 - \| - 6 \| + 3$
37528	Solve for x	(x+4)/3-(x+7)/2=-1/6	$\frac{x + 4}{3} - \frac{x + 7}{2} = \frac{- 1}{6}$
37529	Solve for A in Degrees	-6cos(A)+8=3cos(A)+8	$- 6 \cos (A) + 8 = 3 \cos (A) + 8$
37530	Find f(g(x))	f(x)=1/(x-4) , g(x)=2/x+4	$f (x) = \frac{1}{x - 4}$ , $g (x) = \frac{2}{x} + 4$
37531	Solve the System of Inequalities	x-2y>-8 x+y>=1	$x - 2 y > - 8$ $x + y \geq 1$
37532	Solve for x	4=1+ square root of x	$4 = 1 + \sqrt{x}$
37533	Factor	2-(x^2+10xy+7y^2)/(x^2+4xy+4y^2)	$2 - \frac{x^{2} + 10 x y + 7 y^{2}}{x^{2} + 4 x y + 4 y^{2}}$
37534	Solve the Function Operation	f(n)=n^2+3n g(n)=-n-3 Find f(g(3))	$f (n) = n^{2} + 3 n$ $g (n) = - n - 3$ Find $f (g (3))$
37535	Solve the Function Operation	Let f(x)=3x-6 and g(x)=x-2 Find f/g and its domain.	Let $f (x) = 3 x - 6$ and $g (x) = x - 2$ Find $\frac{f}{g}$ and its domain.
37536	Solve the Inequality for t	3.5+4t<=39.5	$3.5 + 4 t \leq 39.5$
37537	Factor	x^4-7x^2+6x	$x^{4} - 7 x^{2} + 6 x$
37538	Write Using Positive Exponents	4a^3b^2*3a^-4b^-3	$4 a^{3} b^{2} \cdot 3 a^{- 4} b^{- 3}$
37539	Simplify	(1/x)^4*(1/x)^5	${(\frac{1}{x})}^{4} \cdot {(\frac{1}{x})}^{5}$
37540	Simplify	-(6-3i)/(3+7i)	$- \frac{6 - 3 i}{3 + 7 i}$
37541	Factor	ax^2-(1+ab)xy+by^2	$a x^{2} - (1 + a b) x y + b y^{2}$
37542	Solve the Inequality for k	-8k-12<-9k	$- 8 k - 12 < - 9 k$
37543	Factor	x^4-6x^3-3x^2+52x-60	$x^{4} - 6 x^{3} - 3 x^{2} + 52 x - 60$
37544	Reduce	cube root of square root of 8	$\sqrt[3]{\sqrt{8}}$
37545	Simplify	-(3i)^3	$- {(3 i)}^{3}$
37546	Divide Using Synthetic Division	Use synthetic division to find the result when 3x^4+10x^3+14x^2+12x+5 is divided by x+1	Use synthetic division to find the result when $3 x^{4} + 10 x^{3} + 14 x^{2} + 12 x + 5$ is divided by $x + 1$
37547	Simplify	(2)(-2)-35÷(12-5)	$(2) (- 2) - 35 \div (12 - 5)$
37548	Solve the Inequality for x	-3<(2x-6)/4<5	$- 3 < \frac{2 x - 6}{4} < 5$
37549	Graph	y=x+8 if x<4; 4x-4 if x>=4	$y = {\begin{cases} x + 8 & x < 4 \\ 4 x - 4 & x \geq 4 \end{cases}$
37550	Find the Antiderivative	f(x)=( square root of 2x)/x+3/(x^5)	$f (x) = \frac{\sqrt{2 x}}{x} + \frac{3}{x^{5}}$
37551	Solve for x	3/4x+2/8x=48/8	$\frac{3}{4} x + \frac{2}{8} x = \frac{48}{8}$
37552	Evaluate Using the Given Value	Evaluate 6+x if x=6	Evaluate $6 + x$ if $x = 6$
37553	Solve for x	4/3(x-5/6)=62/9	$\frac{4}{3} (x - \frac{5}{6}) = \frac{62}{9}$
37554	Simplify	fifth root of x^7* cube root of x^2	$\sqrt[5]{x^{7}} \cdot \sqrt[3]{x^{2}}$
37555	Graph	y=1/2(1)^x	$y = \frac{1}{2} {(1)}^{x}$
37556	Simplify	6x^3-3y^2-z+2x^2+3y^2-7z	$6 x^{3} - 3 y^{2} - z + 2 x^{2} + 3 y^{2} - 7 z$
37557	Evaluate	3z+9+14z=4z+5	$3 z + 9 + 14 z = 4 z + 5$
37558	Simplify the Radical Expression	cube root of (5x^3)/(49x^5)	$\sqrt[3]{\frac{5 x^{3}}{49 x^{5}}}$
37559	Find the Derivative - d/dx	6 natural log of x-2^x	$6 \ln (x) - 2^{x}$
37560	Multiply	(x-y-z)(x+y+z)	$(x - y - z) (x + y + z)$
37561	Evaluate	6*6^-1	$6 \times 6^{- 1}$
37562	Multiply	4/3pi6^3	$\frac{4}{3} \cdot π \cdot 6^{3}$
37563	Find the Derivative - d/dx	3(4)^x+5e^x	$3 {(4)}^{x} + 5 e^{x}$
37564	Graph	(1/x)^(-)*5	${(\frac{1}{x})}^{-} \cdot 5$
37565	Find the Derivative - d/dx	-27/( cube root of x-6)	$- \frac{27}{\sqrt[3]{x - 6}}$
37566	Solve the System of Equations	x+2y=-4 4y=3x+12	$x + 2 y = - 4$ $4 y = 3 x + 12$
37567	Evaluate	e^(x-1)-5=5	$e^{x - 1} - 5 = 5$
37568	Find the LCM	x , x^2	$x$ , $x^{2}$
37569	Graph	2x=-2/3y	$2 x = - \frac{2}{3} y$
37570	Find the Equation Using Point-Slope Formula	(1,-1) y=3/2x+5	$(1, - 1)$ $y = \frac{3}{2} x + 5$
37571	Simplify	square root of -4* square root of 2* square root of -8* square root of 4	$\sqrt{- 4} \cdot \sqrt{2} \cdot \sqrt{- 8} \cdot \sqrt{4}$
37572	Simplify the Radical Expression	9^(1/3)*81^(1/3)	$9^{\frac{1}{3}} \cdot 81^{\frac{1}{3}}$
37573	Solve for x	7 2/5=2/3x-4 1/2	$7 \frac{2}{5} = \frac{2}{3} x - 4 \frac{1}{2}$
37574	Solve for y	(x+2)+(2y-1)i=-1+5i	$(x + 2) + (2 y - 1) i = - 1 + 5 i$
37575	Solve Using the Quadratic Formula	(7w-10)+4=0	$(7 w - 10) + 4 = 0$
37576	Evaluate the Integral	integral from 3 to 5 of (2x^2+x+4)/(x-1) with respect to x	$\int_{3}^{5} \frac{2 x^{2} + x + 4}{x - 1} d x$
37577	Write in Standard Form	(-4-7i)*(3+i)	$(- 4 - 7 i) \cdot (3 + i)$
37578	Simplify	x^-5x^(2/3)	$x^{- 5} x^{\frac{2}{3}}$
37579	Graph	y>x 2 y<=x-2	$y > x$ $2$ $y \leq x - 2$
37580	Solve for y	y=(100(0.02)+x(0.005))/(100+x)	$y = \frac{100 (0.02) + x (0.005)}{100 + x}$
37581	Solve the Rational Equation for x	fourth root of 3x-5=-8	$\sqrt[4]{3 x - 5} = - 8$
37582	Graph	F(x)=1/(-x^2)	$F (x) = \frac{1}{- x^{2}}$
37583	Simplify	( cube root of u^4)( cube root of 2u^8)	$(\sqrt[3]{u^{4}}) (\sqrt[3]{2 u^{8}})$
37584	Solve for x	y=(100(0.02)+x(0.005))/(100+x)	$y = \frac{100 (0.02) + x (0.005)}{100 + x}$
37585	Find the Inverse	y=(2x-1)^2-2	$y = {(2 x - 1)}^{2} - 2$
37586	Solve for a	-2a-4+a=-a-4	$- 2 a - 4 + a = - a - 4$
37587	Solve for x	1=1/x	$1 = \frac{1}{x}$
37588	Find the Derivative - d/dt	y=e^t(cos(2t)+2sin(2t))	$y = e^{t} (\cos (2 t) + 2 \sin (2 t))$
37589	Add	(-6x+3)-(-2x^2+6x-10)	$(- 6 x + 3) - (- 2 x^{2} + 6 x - 10)$
37590	Simplify	(3x+1)+( square root of 3x-6+1)	$(3 x + 1) + (\sqrt{3 x - 6} + 1)$
37591	Solve for x	3/5(x+1/6)=-23/10	$\frac{3}{5} (x + \frac{1}{6}) = - \frac{23}{10}$
37592	Solve the System of Equations	x^2+y^2=169 x^2+y=13	$x^{2} + y^{2} = 169$ $x^{2} + y = 13$
37593	Evaluate	(-7-(-4))^3+2^4	${(- 7 - (- 4))}^{3} + 2^{4}$
37594	Simplify	(2x^5-6x^2+4x^4y)/(2x)	$\frac{2 x^{5} - 6 x^{2} + 4 x^{4} y}{2 x}$
37595	Simplify	((2+2^3)^2)/5	$\frac{{(2 + 2^{3})}^{2}}{5}$
37596	Graph	f(x^2)	$f (x^{2})$
37597	Find the Reference Angle	(-(7pi)/6)	$(- \frac{7 π}{6})$
37598	Solve by Factoring	18x^3=50x	$18 x^{3} = 50 x$
37599	Find Where Increasing/Decreasing	y=5/2x^4	$y = \frac{5}{2} x^{4}$
37600	Simplify	(x1/4)/(x1/5)	$\frac{x \frac{1}{4}}{x \frac{1}{5}}$