Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
30901	Find All Complex Solutions	\|3-x\|-\|x+2\|=5	$\| 3 - x \| - \| x + 2 \| = 5$
30902	Find Amplitude, Period, and Phase Shift	y=cos((6pix)/7+pi/2)	$y = \cos (\frac{6 π x}{7} + \frac{π}{2})$
30903	Solve the System of Equations	2x+2y=12 x+y=6	$2 x + 2 y = 12$ $x + y = 6$
30904	Divide	(-6-4)÷(-5)	$(- 6 - 4) \div (- 5)$
30905	Divide Using Long Polynomial Division	Use the long division method to find the result when 8x^3+24x^2+24x+7 is divided by 2x+1	Use the long division method to find the result when $8 x^{3} + 24 x^{2} + 24 x + 7$ is divided by $2 x + 1$
30906	Evaluate	-cos(pi/4)-sin(pi/4)	$- \cos (\frac{π}{4}) - \sin (\frac{π}{4})$
30907	Find the Derivative - d/dx	tan(x^2)^2	$\tan^{2} (x^{2})$
30908	Describe the Transformation	y=-3 cube root of x-1	$y = - 3 \sqrt[3]{x} - 1$
30909	Solve for x	(2^x-3)(2^x-4)=0	$(2^{x} - 3) (2^{x} - 4) = 0$
30910	Simplify	(-9a^4-9a^3-4a^2)÷9a	$(- 9 a^{4} - 9 a^{3} - 4 a^{2}) \div 9 a$
30911	Evaluate Using L'Hospital's Rule	limit as x approaches -1 of (3 natural log of 3x+4)/(3tan(2x+2))	$lim_{x \to - 1} \frac{3 \ln (3 x + 4)}{3 \tan (2 x + 2)}$
30912	Solve for x	x+3 = square root of x^2+5	$x + 3 = \sqrt{x^{2} + 5}$
30913	Solve for w	525=w^2+4w	$525 = w^{2} + 4 w$
30914	Convert to a Decimal	The fraction -3/5 written as a decimal is	The fraction $- \frac{3}{5}$ written as a decimal is
30915	Simplify	(27k^5m^8)/((4k^3)(9m^2))	$\frac{27 k^{5} m^{8}}{(4 k^{3}) (9 m^{2})}$
30916	Simplify	(xy)/(7x^-4y^-2)	$\frac{x y}{7 x^{- 4} y^{- 2}}$
30917	Solve for x	square root of x=y	$\sqrt{x} = y$
30918	Solve Using the Square Root Property	4x^2+27=x^2	$4 x^{2} + 27 = x^{2}$
30919	Find the Derivative - d/dx	1+1/(2(x+1)^(1/2))	$1 + \frac{1}{2 {(x + 1)}^{\frac{1}{2}}}$
30920	Graph	y>=-3x+7 y>1/2x y<2	$y \geq - 3 x + 7$ $y > \frac{1}{2} x$ $y < 2$
30921	Solve for Q	Q = cube root of 36^(2^-1)+125^(3^-1)-81^(2^-2)	$Q = \sqrt[3]{36^{2^{- 1}} + 125^{3^{- 1}} - 81^{2^{- 2}}}$
30922	Evaluate	(-11x^3y)^-2	${(- 11 x^{3} y)}^{- 2}$
30923	Evaluate	14-3x<-1	$14 - 3 x < - 1$
30924	Verify the Identity	sin(3x)=(sin(x))(4cos(x)^2-1)	$\sin (3 x) = (\sin (x)) (4 \cos^{2} (x) - 1)$
30925	Solve the Function Operation	If g(x)=3x^2+5 and h(x)=x^2-1 ; find (g-h)(x)	If $g (x) = 3 x^{2} + 5$ and $h (x) = x^{2} - 1$ ; find $(g - h) (x)$
30926	Evaluate	(54^3125^28^2)/(6^3*30^6)	$\frac{54^{3} \cdot 125^{2} \cdot 8^{2}}{6^{3} \cdot 30^{6}}$
30927	Expand the Trigonometric Expression	csc(90 degrees -theta)	$\csc (90 ° - θ)$
30928	Divide Using Long Polynomial Division	(x^4-13x-42)/(x^2-x-6)	$\frac{x^{4} - 13 x - 42}{x^{2} - x - 6}$
30929	Solve for x	y=2x^(1/3)	$y = 2 x^{\frac{1}{3}}$
30930	Solve the Inequality for x	x^2-48>-5x+2	$x^{2} - 48 > - 5 x + 2$
30931	Graph	f^-1(x)=1/(f(x))	$f^{- 1} (x) = \frac{1}{f (x)}$
30932	Evaluate Using L'Hospital's Rule	limit as x approaches 0 from the right of (1/x)^x	$lim_{x \to 0^{+}} {(\frac{1}{x})}^{x}$
30933	Simplify	( square root of y^(1/4))^8	${(\sqrt{y^{\frac{1}{4}}})}^{8}$
30934	Evaluate the Function	g(0)=0/( square root of 1-0^2)	$g (0) = \frac{0}{\sqrt{1 - 0^{2}}}$
30935	Find the Equation with a Point and Slope	What is the equation of the line that passes through the point (4,-3) and has a slope of 1 ?	What is the equation of the line that passes through the point $(4, - 3)$ and has a slope of $1$ ?
30936	Determine if Dependent, Independent, or Inconsistent	3y=9x-6 2y+6x=4	$3 y = 9 x - 6$ $2 y + 6 x = 4$
30937	Evaluate the Summation	sum from k=2 to 5 of k^2+k-2	$\sum_{k = 2}^{5} k^{2} + k - 2$
30938	Simplify the Radical Expression	(4 square root of 5-1)(3+2 square root of 5)	$(4 \sqrt{5} - 1) (3 + 2 \sqrt{5})$
30939	Find the Distance Between Two Points	(6,-1) and (0,7)	$(6, - 1)$ and $(0, 7)$
30940	Find the Product	(x^2+3x-4)/(x^2+4x+4)*(2x^2+4x)/(x^2-4x+3)	$\frac{x^{2} + 3 x - 4}{x^{2} + 4 x + 4} \cdot \frac{2 x^{2} + 4 x}{x^{2} - 4 x + 3}$
30941	Write the Fraction in Simplest Form	((3s^5)^-4)/(6s^3j^-6)	$\frac{{(3 s^{5})}^{- 4}}{6 s^{3} j^{- 6}}$
30942	Evaluate the Function	f(x)=-4x^2+x+5 at x=1	$f (x) = - 4 x^{2} + x + 5$ at $x = 1$
30943	Factor	x^4+7x^3-18x^2-x^2-7x+18	$x^{4} + 7 x^{3} - 18 x^{2} - x^{2} - 7 x + 18$
30944	Graph	y<-5x+3y	$y < - 5 x + 3 y$
30945	Solve the System of Equations	y=x+4 y-4=x	$y = x + 4$ $y - 4 = x$
30946	Factor	p(x)=x^3+x^2+9x+9	$p (x) = x^{3} + x^{2} + 9 x + 9$
30947	Simplify	((x+1)/(x+1)*(x^2-1)/(4x^2-40x))÷((x^2+9x-10)/(x^2-100))	$\frac{x + 1}{x + 1} \cdot \frac{x^{2} - 1}{4 x^{2} - 40 x} \div \frac{x^{2} + 9 x - 10}{x^{2} - 100}$
30948	Simplify	(3xy^3)^3(2x)	${(3 x y^{3})}^{3} (2 x)$
30949	Graph	x-2y<-2 2x+y>3	$x - 2 y < - 2$ $2 x + y > 3$
30950	Graph	f(x)=-(3x-1)/(x-3)	$f (x) = - \frac{3 x - 1}{x - 3}$
30951	Solve for a	9x^2-24x+16=(ax-b)^2	$9 x^{2} - 24 x + 16 = {(a x - b)}^{2}$
30952	Describe the Transformation	g(x)=3(1/(x+1))-2	$g (x) = 3 (\frac{1}{x + 1}) - 2$
30953	Simplify	4/x-2/(x(x+1))-2/(x+1)	$\frac{4}{x} - \frac{2}{x (x + 1)} - \frac{2}{x + 1}$
30954	Multiply	(6mn-9)(m^2n-7)	$(6 m n - 9) (m^{2} n - 7)$
30955	Simplify	(4x^3+56x^2+160x)/(x+10)(81-x^2)/(-x-9)(3x)/(x^2-5x-36)	$\frac{4 x^{3} + 56 x^{2} + 160 x}{x + 10} \cdot \frac{81 - x^{2}}{- x - 9} \cdot \frac{3 x}{x^{2} - 5 x - 36}$
30956	Solve for x	-16+5x=4(3x+7)	$- 16 + 5 x = 4 (3 x + 7)$
30957	Simplify	tan(x)*tan(x)	$\tan (x) \cdot \tan (x)$
30958	Simplify the Radical Expression	(4 square root of 6)( square root of -5)	$(4 \sqrt{6}) (\sqrt{- 5})$
30959	Simplify	((x^2y^2z^2)^5)/((x^3y^3z^3)^7)	$\frac{{(x^{2} y^{2} z^{2})}^{5}}{{(x^{3} y^{3} z^{3})}^{7}}$
30960	Simplify	\|-1+i\|	$\| - 1 + i \|$
30961	Solve the Function Operation	If f(x)=3x+6 then find f^-1(x)	If $f (x) = 3 x + 6$ then find $f^{- 1} (x)$
30962	Find dy/dx	y=3 square root of 2x^2-x-4	$y = 3 \sqrt{2 x^{2} - x - 4}$
30963	Divide Using Long Polynomial Division	(x^3-3x^2+x-3)/(x^2+1)	$\frac{x^{3} - 3 x^{2} + x - 3}{x^{2} + 1}$
30964	Simplify	(-6^8)/(-6^5)	$\frac{- 6^{8}}{- 6^{5}}$
30965	Simplify	( cube root of 10)/( cube root of 625)	$\frac{\sqrt[3]{10}}{\sqrt[3]{625}}$
30966	Find Amplitude, Period, and Phase Shift	y=4+3sin(pi/3x-pi/16)	$y = 4 + 3 \sin (\frac{π}{3} x - \frac{π}{16})$
30967	Find the Exact Value	arcsin(cot((3pi)/4))	$\arcsin (\cot (\frac{3 π}{4}))$
30968	Find the Derivative - d/dx	arcsin(e^(3x))	$\arcsin (e^{3 x})$
30969	Find the Exact Value	tan(arcsin(3/5)-arctan(1/4))	$\tan (\arcsin (\frac{3}{5}) - \arctan (\frac{1}{4}))$
30970	Evaluate	cube root of x=3 cube root of 7	$\sqrt[3]{x} = 3 \sqrt[3]{7}$
30971	Find g(h(x))	g(x)=3x h(x)=x-4	$g (x) = 3 x$ $h (x) = x - 4$
30972	Solve for x	3^(8x^2+6x)-12=-81^(x^2+(3x)/4)	$3^{8 x^{2} + 6 x} - 12 = - 81^{x^{2} + \frac{3 x}{4}}$
30973	Solve for x	4(4+2x)-6(7x-10)=-80	$4 (4 + 2 x) - 6 (7 x - 10) = - 80$
30974	Solve the Function Operation	f(x)=3x^2-11 Find f(-5)	$f (x) = 3 x^{2} - 11$ Find $f (- 5)$
30975	Find the Roots (Zeros)	-9x^2+12x-4=0	$- 9 x^{2} + 12 x - 4 = 0$
30976	Simplify	(4/(2y)-1/(2y))/(4/(2y)+3/y)	$\frac{\frac{4}{2 y} - \frac{1}{2 y}}{\frac{4}{2 y} + \frac{3}{y}}$
30977	Solve the Inequality for X	X^3-4X^2-X+4>=0	$X^{3} - 4 X^{2} - X + 4 \geq 0$
30978	Factor	factor 9y^2-25	factor $9 y^{2} - 25$
30979	Solve for x	x/(x+9)-1/(9-x)=(2x)/(x^2-81)	$\frac{x}{x + 9} - \frac{1}{9 - x} = \frac{2 x}{x^{2} - 81}$
30980	Solve the System of Equations	x+y=5 y=x+1	$x + y = 5$ $y = x + 1$
30981	Graph	(9-x)/7=y	$\frac{9 - x}{7} = y$
30982	Write in Standard Form	(x^2+2x-2)(x^2+x+10)	$(x^{2} + 2 x - 2) (x^{2} + x + 10)$
30983	Simplify	cube root of 64/(x^2)	$\sqrt[3]{\frac{64}{x^{2}}}$
30984	Find dy/dx	f(x)=e^(xy)	$f (x) = e^{x y}$
30985	Evaluate	5/6*1/4+3/8	$\frac{5}{6} \cdot \frac{1}{4} + \frac{3}{8}$
30986	Simplify	1/(x^2-1)+2/(x^2+x)	$\frac{1}{x^{2} - 1} + \frac{2}{x^{2} + x}$
30987	Subtract	(x+7)/(x+5)-(7x)/(x^2-3x-40)	$\frac{x + 7}{x + 5} - \frac{7 x}{x^{2} - 3 x - 40}$
30988	Find the Product	(3xy)^2	${(3 x y)}^{2}$
30989	Evaluate the Limit	limit as x approaches 0 of (5x^4-3x^3+7x+2)^5	$lim_{x \to 0} {(5 x^{4} - 3 x^{3} + 7 x + 2)}^{5}$
30990	Solve for p	p-5(p+4)=p-(8-p)	$p - 5 (p + 4) = p - (8 - p)$
30991	Evaluate	((3 square root of 3)/2)^2	${(\frac{3 \sqrt{3}}{2})}^{2}$
30992	Write in y=mx+b Form	0=-3x-4-2y	$0 = - 3 x - 4 - 2 y$
30993	Solve the Rational Equation for x	square root of x/10 = square root of 3x-58	$\sqrt{\frac{x}{10}} = \sqrt{3 x - 58}$
30994	Factor	-45x^4+42x^3+1272x^2-1050x-3675	$- 45 x^{4} + 42 x^{3} + 1272 x^{2} - 1050 x - 3675$
30995	Evaluate	i^9i^25i^12*i^16	$i^{9} \cdot i^{25} \cdot i^{12} \cdot i^{16}$
30996	Evaluate the Integral	integral of (3x^3)(3x^2) with respect to x	$\int (3 x^{3}) (3 x^{2}) d x$
30997	Simplify	(5x^4)/(5x^-3)	$\frac{5 x^{4}}{5 x^{- 3}}$
30998	Find the Holes in the Graph	f(x)=(2x^2+5x-3)/(x+3)	$f (x) = \frac{2 x^{2} + 5 x - 3}{x + 3}$
30999	Simplify	(2ab)^2(3a^2b^3)	${(2 a b)}^{2} (3 a^{2} b^{3})$
31000	Factor by Grouping	x^4-100y^2	$x^{4} - 100 y^{2}$