Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
38501	Simplify	(2x^2-3x-5)/(25-4x^2)	$\frac{2 x^{2} - 3 x - 5}{25 - 4 x^{2}}$
38502	Simplify	(2e^-2)^-4	${(2 e^{- 2})}^{- 4}$
38503	Multiply	(2x^2-11x-21)/(5x^2+16x+3)*(5x+1)/(5x-35)	$\frac{2 x^{2} - 11 x - 21}{5 x^{2} + 16 x + 3} \cdot \frac{5 x + 1}{5 x - 35}$
38504	Solve the System of Equations	x-2y+2z=4 2y-4z=8 -x+4z=2	$x - 2 y + 2 z = 4$ $2 y - 4 z = 8$ $- x + 4 z = 2$
38505	Simplify	(4x^-2)^(-1/2)	${(4 x^{- 2})}^{- \frac{1}{2}}$
38506	Find the Derivative - d/dx	3e^(x-3)	$3 e^{x - 3}$
38507	Verify the Identity	sin(A+B)=cos(pi/2-(A+B))	$\sin (A + B) = \cos (\frac{π}{2} - (A + B))$
38508	Evaluate the Integral	integral from 0 to 2 of (x-x^2)^3(1-2x) with respect to x	$\int_{0}^{2} {(x - x^{2})}^{3} (1 - 2 x) d x$
38509	Simplify	(5x-y^2)(25x^2+5xy^2+y^4)	$(5 x - y^{2}) (25 x^{2} + 5 x y^{2} + y^{4})$
38510	Find the Derivative - d/dx	square root of 1+sin(x)	$\sqrt{1 + \sin (x)}$
38511	Solve the System of Equations	x+2y=-8 y=-3/2x-6	$x + 2 y = - 8$ $y = - \frac{3}{2} x - 6$
38512	Simplify	x/(2x+3)-(2x+1)/(2x-3)	$\frac{x}{2 x + 3} - \frac{2 x + 1}{2 x - 3}$
38513	Find the Exact Value	cos(x)+sin(x)tan(x)	$\cos (x) + \sin (x) \tan (x)$
38514	Evaluate the Function	f(2)=3x^4+x^3-2x^2+x+12	$f (2) = 3 x^{4} + x^{3} - 2 x^{2} + x + 12$
38515	Solve for x	((3/4)(x^(-1/2)))/(y^(-2/3))=a/b	$\frac{(\frac{3}{4}) (x^{- \frac{1}{2}})}{y^{- \frac{2}{3}}} = \frac{a}{b}$
38516	Convert to Radical Form	(5x)-5/4	$(5 x) \frac{- 5}{4}$
38517	Graph	f(x)=x^2+2x-1,x<0; x^2-4x+3,x>=0	$f (x) = {\begin{cases} x^{2} + 2 x - 1, x < 0 \\ x^{2} - 4 x + 3, x \geq 0 \end{cases}$
38518	Graph	y<=5 2x+y<8	$y \leq 5$ $2 x + y < 8$
38519	Simplify	limit as x approaches 1 of x^2-2x+4	$lim_{x \to 1} x^{2} - 2 x + 4$
38520	Find the Parabola Through (4,8) with Vertex (2,4)	(2,4) and (4,8)	$(2, 4)$ and $(4, 8)$
38521	Find the Roots (Zeros)	c(x)=x^4-5x^3-12x^2-22x-40	$c (x) = x^{4} - 5 x^{3} - 12 x^{2} - 22 x - 40$
38522	Evaluate the Limit	limit as x approaches 2 of (x-2)/(h(x+4)-3)	$lim_{x \to 2} \frac{x - 2}{h (x + 4) - 3}$
38523	Solve for x	24.7-2^x=7.8-3.4x	$24.7 - 2^{x} = 7.8 - 3.4 x$
38524	Solve the Function Operation	Given that f(x)=x^2+8x+15 and g(x)=x+5 ; find f(x)*g(x) and express the result in standard form.	Given that $f (x) = x^{2} + 8 x + 15$ and $g (x) = x + 5$ ; find $f (x) \cdot g (x)$ and express the result in standard form.
38525	Simplify	- cube root of 216-2 square root of -4+ cube root of 1	$- \sqrt[3]{216} - 2 \sqrt{- 4} + \sqrt[3]{1}$
38526	Simplify the Radical Expression	3 cube root of 81-2 cube root of 54	$3 \sqrt[3]{81} - 2 \sqrt[3]{54}$
38527	Solve by Substitution	y-5=(x-2)^2 x+2y=6	$y - 5 = {(x - 2)}^{2}$ $x + 2 y = 6$
38528	Simplify	3^2(3^3)^23^-8	$3^{2} \cdot {(3^{3})}^{2} \cdot 3^{- 8}$
38529	Evaluate the Integral	integral of ((x^3)/4+(2x^2)/3-1) with respect to x	$\int (\frac{x^{3}}{4} + \frac{2 x^{2}}{3} - 1) d x$
38530	Simplify	10m^2 fourth root of 162m^7	$10 m^{2} \sqrt[4]{162 m^{7}}$
38531	Evaluate the Integral	integral of (3x^2)/(2 square root of 5-3x^3) with respect to x	$\int \frac{3 x^{2}}{2 \sqrt{5 - 3 x^{3}}} d x$
38532	Evaluate the Integral	integral of r/( square root of r^2-x^2) with respect to r	$\int \frac{r}{\sqrt{r^{2} - x^{2}}} d r$
38533	Simplify the Radical Expression	(4/(64^(5/6)))^(1/2)	${(\frac{4}{64^{\frac{5}{6}}})}^{\frac{1}{2}}$
38534	Solve the System of Inequalities	y<-2x-8 y>=x-5	$y < - 2 x - 8$ $y \geq x - 5$
38535	Simplify	5x square root of 12-6x square root of 75+7x square root of 3	$5 x \sqrt{12} - 6 x \sqrt{75} + 7 x \sqrt{3}$
38536	Simplify	( square root of 5+7)( square root of 6+2)	$(\sqrt{5} + 7) (\sqrt{6} + 2)$
38537	Simplify	(3y+2)/(y^2+5y-24)+7/(y^2+4y-32)	$\frac{3 y + 2}{y^{2} + 5 y - 24} + \frac{7}{y^{2} + 4 y - 32}$
38538	Simplify	((a-b)/(7a+7b))÷((a^2-b^2)/(a^2+8a+16))	$\frac{a - b}{7 a + 7 b} \div \frac{a^{2} - b^{2}}{a^{2} + 8 a + 16}$
38539	Solve for x	2x+8i=6-(2y)i	$2 x + 8 i = 6 - (2 y) i$
38540	Solve the System of Equations	x^2+4y^2=4 x^2+y^2=4	$x^{2} + 4 y^{2} = 4$ $x^{2} + y^{2} = 4$
38541	Find the Antiderivative	square root of x/5	$\sqrt{\frac{x}{5}}$
38542	Simplify	( square root of 3xy)^3	${(\sqrt{3 x y})}^{3}$
38543	Simplify	((x-3)(2x+1))/((2x+1)(2x+5))*((2x+5)(3x-2))/((x-3)(3x-2))	$\frac{(x - 3) (2 x + 1)}{(2 x + 1) (2 x + 5)} \cdot \frac{(2 x + 5) (3 x - 2)}{(x - 3) (3 x - 2)}$
38544	Graph	3cot(pix)	$3 \cot (π x)$
38545	Solve for x	(2x-3)^2-14=2x(x-7)	${(2 x - 3)}^{2} - 14 = 2 x (x - 7)$
38546	Simplify	(4v^2)/( square root of 8v^6)	$\frac{4 v^{2}}{\sqrt{8 v^{6}}}$
38547	Simplify the Matrix	-2u[[7u,3w^2,5u,5]]	$- 2 u [\begin{array}{c} 7 u & 3 w^{2} & 5 u & 5 \end{array}]$
38548	Write the Fraction in Simplest Form	(tan(pi)-tan(x))/(1+tan(pi)tan(x))	$\frac{\tan (π) - \tan (x)}{1 + \tan (π) \tan (x)}$
38549	Simplify	4x^0*2x	$4 x^{0} \cdot 2 x$
38550	Evaluate	(-4)^3+(-4)^2-3*-4+9	${(- 4)}^{3} + {(- 4)}^{2} - 3 \cdot - 4 + 9$
38551	Solve for x	1/5(10x-20)=x-3	$\frac{1}{5} (10 x - 20) = x - 3$
38552	Graph	D={x\|x<=1}	$D = {x \| x \leq 1}$
38553	Evaluate	sin(2*pi/4)	$\sin (2 \cdot \frac{π}{4})$
38554	Simplify	( square root of 9x^2y)/(2x^-4y^2)	$\frac{\sqrt{9 x^{2} y}}{2 x^{- 4} y^{2}}$
38555	Evaluate	6v(2v+3)	$6 v (2 v + 3)$
38556	Evaluate	((2^-1)/(2^0))^3	${(\frac{2^{- 1}}{2^{0}})}^{3}$
38557	Find the Exact Value	2(4i^2)+22	$2 (4 i^{2}) + 22$
38558	Simplify	10/7*9/(2x-7)	$\frac{10}{7} \cdot \frac{9}{2 x - 7}$
38559	Simplify	-3v(-8u^2-8uv-7v^2)	$- 3 v (- 8 u^{2} - 8 u v - 7 v^{2})$
38560	Solve the System of Equations	2x+7y=-5 and -x-6y=10	$2 x + 7 y = - 5$ and $- x - 6 y = 10$
38561	Find the End Behavior	f(x)=x(x-2)(x+2)	$f (x) = x (x - 2) (x + 2)$
38562	Simplify	3x^32x^2y4x^2y	$3 x^{3} \cdot 2 x^{2} y \cdot 4 x^{2} y$
38563	Simplify	(tan((5pi)/8)-tan((3pi)/8))/(1+tan((5pi)/8)tan((3pi)/8))	$\frac{\tan (\frac{5 π}{8}) - \tan (\frac{3 π}{8})}{1 + \tan (\frac{5 π}{8}) \tan (\frac{3 π}{8})}$
38564	Solve for x	(5x-2)^2+35x-14=-12	${(5 x - 2)}^{2} + 35 x - 14 = - 12$
38565	Factor	3/2x^(1/2)+5/2x^(3/2)	$\frac{3}{2} x^{\frac{1}{2}} + \frac{5}{2} x^{\frac{3}{2}}$
38566	Evaluate	square root of cos(x)cos(300x)+ square root of \|x\|-9.3*(-4x^2)^0.01	$\sqrt{\cos (x)} \cdot \cos (300 \cdot x) + \sqrt{\| x \|} - 9.3 \cdot {(- 4 x^{2})}^{0.01}$
38567	Divide Using Long Polynomial Division	Use the long division method to find the result when 16x^3+16x^2+11x+20 is divided by 4x+5	Use the long division method to find the result when $16 x^{3} + 16 x^{2} + 11 x + 20$ is divided by $4 x + 5$
38568	Solve for n	15 is 30% of what number	$15$ is $30 %$ of what number
38569	Simplify	2(a+b)-3(2a+1)-2(b-3)	$2 (a + b) - 3 (2 a + 1) - 2 (b - 3)$
38570	Evaluate the Limit	limit as x approaches 0 of (1-sec(x))/(cos(x)-1)	$lim_{x \to 0} \frac{1 - \sec (x)}{\cos (x) - 1}$
38571	Evaluate the Integral	integral of (2x-x square root of x)/( square root of x) with respect to x	$\int \frac{2 x - x \sqrt{x}}{\sqrt{x}} d x$
38572	Solve for p	p^3-64=0	$p^{3} - 64 = 0$
38573	Simplify	f/(f-g)-g/(g-f)	$\frac{f}{f - g} - \frac{g}{g - f}$
38574	Solve the Inequality for x	7 square root of 3x+9-12<=30	$7 \sqrt{3 x + 9} - 12 \leq 30$
38575	Solve for x	x+a=b/3x	$x + a = \frac{b}{3} x$
38576	Find the Domain and Range	f(x)=(x+3)^2-2 , x<=-3	$f (x) = {(x + 3)}^{2} - 2$ , $x \leq - 3$
38577	Simplify	( fourth root of 32)÷( fourth root of 2)	$\sqrt[4]{32} \div \sqrt[4]{2}$
38578	Evaluate	(x^-4y^-5y^2)/x	$\frac{x^{- 4} y^{- 5} y^{2}}{x}$
38579	Simplify	(21x+12)/(7x+4)*1/(x-2)	$\frac{21 x + 12}{7 x + 4} \cdot \frac{1}{x - 2}$
38580	Evaluate	3 square root of 4a=42	$3 \sqrt{4 a} = 42$
38581	Simplify the Radical Expression	fourth root of 36x^6	$\sqrt[4]{36 x^{6}}$
38582	Solve the Inequality for x	2x^2-3x+4>0	$2 x^{2} - 3 x + 4 > 0$
38583	Find the Slope	(-4,-8) and (-1,6)	$(- 4, - 8)$ and $(- 1, 6)$
38584	Solve for k	1+ square root of k+1=9	$1 + \sqrt{k + 1} = 9$
38585	Graph	f(x)=x^2+1 if x<1; (x-2)^2 if x>=1	$f (x) = {\begin{cases} x^{2} + 1 & x < 1 \\ {(x - 2)}^{2} & x \geq 1 \end{cases}$
38586	Simplify	(4y^2(x^2)^5)/(x^2x^5)	$\frac{4 y^{2} \cdot {(x^{2})}^{5}}{x^{2} \cdot x^{5}}$
38587	Find the x and y Intercepts	f(x)=-4(2x+1)^2(x+2)^2(x^2+9)(x^2-5)	$f (x) = - 4 {(2 x + 1)}^{2} {(x + 2)}^{2} (x^{2} + 9) (x^{2} - 5)$
38588	Solve the System of Equations	y=x^2+4x-1 and y+3=x	$y = x^{2} + 4 x - 1$ and $y + 3 = x$
38589	Find the Domain	p(x)=2 square root of -1/2x+4	$p (x) = 2 \sqrt{- \frac{1}{2} x + 4}$
38590	Solve for x	2-3/4x=1/2x-1/2	$2 - \frac{3}{4} x = \frac{1}{2} x - \frac{1}{2}$
38591	Evaluate	7^(3y-8)=7^13	$7^{3 y - 8} = 7^{13}$
38592	Simplify	4yi^2+8yi^4	$4 y i^{2} + 8 y i^{4}$
38593	Divide	((x^3)/(x^2-4))÷((2x)/(x^2-7x+10))	$\frac{x^{3}}{x^{2} - 4} \div \frac{2 x}{x^{2} - 7 x + 10}$
38594	Evaluate	( square root of 3)(2 square root of 5)-4 square root of 15	$(\sqrt{3}) (2 \sqrt{5}) - 4 \sqrt{15}$
38595	Simplify	(5xy+3x^2y^2)/(xy^3)	$\frac{5 x y + 3 x^{2} y^{2}}{x y^{3}}$
38596	Evaluate	20% of 200	$20 %$ of $200$
38597	Determine if True	sec(theta)+tan(theta)=1/(sec(theta)-tan(theta))	$\sec (θ) + \tan (θ) = \frac{1}{\sec (θ) - \tan (θ)}$
38598	Find the Derivative - d/dx	(2 square root of x)/5	$\frac{2 \sqrt{x}}{5}$
38599	Evaluate Using L'Hospital's Rule	limit as x approaches -1 of (2 natural log of -x)/(e^(3x+3)-1)	$lim_{x \to - 1} \frac{2 \ln (- x)}{e^{3 x + 3} - 1}$
38600	Solve the Inequality for x	2x+5y<10	$2 x + 5 y < 10$