Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
26301	Simplify	(5/2)^x+(5/2)^(x+3)	${(\frac{5}{2})}^{x} + {(\frac{5}{2})}^{x + 3}$
26302	Write the Fraction in Simplest Form	((3m^4t^5)^2)/(2t^7)	$\frac{{(3 m^{4} t^{5})}^{2}}{2 t^{7}}$
26303	Rationalize the Denominator	( square root of 2+ square root of 3)/( square root of 2- square root of 3)	$\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}}$
26304	Simplify	((3x^2-x-14)/(9x^2-4))÷((x+2)/(3x^2+2x))	$\frac{3 x^{2} - x - 14}{9 x^{2} - 4} \div \frac{x + 2}{3 x^{2} + 2 x}$
26305	Find Amplitude, Period, and Phase Shift	y=1/2cos(3x+pi/2)	$y = \frac{1}{2} \cos (3 x + \frac{π}{2})$
26306	Evaluate	-10+2\|6*(-7)\|	$- 10 + 2 \| 6 \cdot (- 7) \|$
26307	Find the Inflection Points	f(x)=x^2\|x\|	$f (x) = x^{2} \| x \|$
26308	Solve the Inequality for x	(x^(2-36))/(x-6)<=0	$\frac{x^{2 - 36}}{x - 6} \leq 0$
26309	Simplify	cube root of -12x^4y* cube root of 4x^2y^2	$\sqrt[3]{- 12 x^{4} y} \cdot \sqrt[3]{4 x^{2} y^{2}}$
26310	Solve for k	9/(k+3)=3/5	$\frac{9}{k + 3} = \frac{3}{5}$
26311	Solve for x	log of 5x+ log of 2x=1	$\log (5 x) + \log (2 x) = 1$
26312	Simplify	(3-2i^3)-(8+i^2)	$(3 - 2 i^{3}) - (8 + i^{2})$
26313	Solve for V	A=6V^(2/3)	$A = 6 V^{\frac{2}{3}}$
26314	Simplify	x(a-x)(b+x)	$x (a - x) (b + x)$
26315	Evaluate	7/(a-2)=2/3	$\frac{7}{a - 2} = \frac{2}{3}$
26316	Simplify	x^2 square root of 4x	$x^{2} \sqrt{4 x}$
26317	Simplify	-((2a)/(3y))^2	$- {(\frac{2 a}{3 y})}^{2}$
26318	Simplify the Radical Expression	square root of 2( square root of 8-3)	$\sqrt{2} (\sqrt{8} - 3)$
26319	Solve the Inequality for x	(x-4)(3x+1)<(2x-6)(x-2)+4	$(x - 4) (3 x + 1) < (2 x - 6) (x - 2) + 4$
26320	Solve for a	2* natural log of a+3=1/4* natural log of 16+ natural log of a+7	$2 \cdot \ln (a + 3) = \frac{1}{4} \cdot \ln (16) + \ln (a + 7)$
26321	Find the Derivative - d/dx	d/(dx)(x+5)	$\frac{d}{d x} (x + 5)$
26322	Solve for g	-98+2(18g+11)=40g	$- 98 + 2 (18 g + 11) = 40 g$
26323	Simplify	(2x-3y)/(4xy)+(11y-2x)/(4xy)	$\frac{2 x - 3 y}{4 x y} + \frac{11 y - 2 x}{4 x y}$
26324	Evaluate	((9)^-4)/((-3)^-8)	$\frac{{(9)}^{- 4}}{{(- 3)}^{- 8}}$
26325	Find the LCD	(4x)/(x-1) and (2x)/(x-3)	$\frac{4 x}{x - 1}$ and $\frac{2 x}{x - 3}$
26326	Simplify	1/(sin(theta))-(sin(theta)^2)/(sin(theta))	$\frac{1}{\sin (θ)} - \frac{\sin^{2} (θ)}{\sin (θ)}$
26327	Solve for b	limit as x approaches 4 of (x^2+7x+b)/(x^2-6x+8)=15/2	$lim_{x \to 4} \frac{x^{2} + 7 x + b}{x^{2} - 6 x + 8} = \frac{15}{2}$
26328	Find the Maximum/Minimum Value	f(x)=2/5x^5+5x^4+16x^3-15	$f (x) = \frac{2}{5} x^{5} + 5 x^{4} + 16 x^{3} - 15$
26329	Expand the Trigonometric Expression	cos(pi/5+pi/6)	$\cos (\frac{π}{5} + \frac{π}{6})$
26330	Evaluate the Function	f(x)=7x+11 g(x)=-2x+3 h(x)=3x^2+1 (f*g)(x)	$f (x) = 7 x + 11$ $g (x) = - 2 x + 3$ $h (x) = 3 x^{2} + 1$ $(f \cdot g) (x)$
26331	Find All Complex Solutions	8e^x-5=0	$8 e^{x} - 5 = 0$
26332	Determine if Odd, Even, or Neither	f(x)=5\|x\|	$f (x) = 5 \| x \|$
26333	Simplify	( square root of 128)/3+ square root of 243+1/( square root of 2)	$\frac{\sqrt{128}}{3} + \sqrt{243} + \frac{1}{\sqrt{2}}$
26334	Graph	Graph y< = square root of 2x+4-3	Graph $y \leq \sqrt{2 x + 4} - 3$
26335	Find dx/dy	y=x square root of 1-x^2	$y = x \sqrt{1 - x^{2}}$
26336	Find dy/dx	y=x-xsin(x)	$y = x - x \sin (x)$
26337	Divide Using Long Polynomial Division	(x^6-4x^5-7x^3)÷(2x^3)	$(x^{6} - 4 x^{5} - 7 x^{3}) \div (2 x^{3})$
26338	Solve the Inequality for x	1/10-3/4x>=1/2x+3/5	$\frac{1}{10} - \frac{3}{4} x \geq \frac{1}{2} x + \frac{3}{5}$
26339	Solve the Function Operation	f(x)=-x-6 g(x)=3x^2+7x+15 Find: (gof)(x)	$f (x) = - x - 6$ $g (x) = 3 x^{2} + 7 x + 15$ Find: $((g \circ f)) (x)$
26340	Solve for x	x1/(y^4)=2y^2+c	$x \frac{1}{y^{4}} = 2 y^{2} + c$
26341	Simplify	xy-1/(xy)	$x y - \frac{1}{x y}$
26342	Find the Antiderivative	g(x)=(x^2+3x-5)/(x^4)	$g (x) = \frac{x^{2} + 3 x - 5}{x^{4}}$
26343	Find the Domain	square root of square root of x+1+1	$\sqrt{\sqrt{x + 1} + 1}$
26344	Find the Domain	f(x)=5/( square root of x-1-3)	$f (x) = \frac{5}{\sqrt{x - 1} - 3}$
26345	Simplify	(x^3-9x)/(3x^2-6x-9)	$\frac{x^{3} - 9 x}{3 x^{2} - 6 x - 9}$
26346	Find the Domain and Range	y=arcsin((x+1)/2)	$y = \arcsin (\frac{x + 1}{2})$
26347	Simplify	limit as x approaches 0 of (e^(2x)-1)/(e^x-1)	$lim_{x \to 0} \frac{e^{2 x} - 1}{e^{x} - 1}$
26348	Solve for r	2*8^(5r)=28	$2 \cdot 8^{5 r} = 28$
26349	Find the Exact Value	sec(arccot((2 square root of 21)/21))	$\sec (arccot (\frac{2 \sqrt{21}}{21}))$
26350	Convert to Interval Notation	x<-9 and x<9	$x < - 9$ and $x < 9$
26351	Simplify	(-3+ square root of 175)(-5+ square root of 7)	$(- 3 + \sqrt{175}) (- 5 + \sqrt{7})$
26352	Solve the System of Equations	2x-7y=34 and x-y=12	$2 x - 7 y = 34$ and $x - y = 12$
26353	Graph	y+2x^2+32=-16x-1	$y + 2 x^{2} + 32 = - 16 x - 1$
26354	Expand the Logarithmic Expression	log of ( square root of a^3b^5)/(c^7)	$\log (\frac{\sqrt{a^{3} b^{5}}}{c^{7}})$
26355	Write in Exponential Form	fourth root of 5^3* sixth root of 5	$\sqrt[4]{5^{3}} \cdot \sqrt[6]{5}$
26356	Find dy/dx	-4y^2+3-3x^2-4x=0	$- 4 y^{2} + 3 - 3 x^{2} - 4 x = 0$
26357	Solve the Inequality for x	3x^2-5x-12>2x^2-6x-6	$3 x^{2} - 5 x - 12 > 2 x^{2} - 6 x - 6$
26358	Solve for x	3x(x-4)=6	$3 x (x - 4) = 6$
26359	Solve for u	3=7(4-2u)-6u	$3 = 7 (4 - 2 u) - 6 u$
26360	Solve for x	x2/3=25	$x \frac{2}{3} = 25$
26361	Solve the System of Inequalities	-2m<6 and 3m>24	$- 2 m < 6$ and $3 m > 24$
26362	Graph	y=2x-x^2-x^3	$y = 2 x - x^{2} - x^{3}$
26363	Simplify the Matrix	2x-3y+z=4 y-2z+x-5=0 3-2x=4y-z	$2 x - 3 y + z = 4$ $y - 2 z + x - 5 = 0$ $3 - 2 x = 4 y - z$
26364	Expand Using Pascal's Triangle	(2p^4-3t)^4	${(2 p^{4} - 3 t)}^{4}$
26365	Find Amplitude, Period, and Phase Shift	y=2csc(x-pi)+1	$y = 2 \csc (x - π) + 1$
26366	Solve for C in Degrees	cos(C)=0.0698	$\cos (C) = 0.0698$
26367	Evaluate the Integral	integral of x^4-3x^3+6x^2-7 with respect to x	$\int x^{4} - 3 x^{3} + 6 x^{2} - 7 d x$
26368	Solve for x	(x-2)(x-8)=-9	$(x - 2) (x - 8) = - 9$
26369	Write as a Single Logarithm	natural log of x-3 natural log of x+1	$\ln (x) - 3 \ln (x + 1)$
26370	Find the Antiderivative	x^(1/3)+x square root of x-2	$x^{\frac{1}{3}} + x \sqrt{x} - 2$
26371	Find the Domain and Range	f(x)=x+1 if x<=-5; -3 if -5=6	$f (x) = {\begin{cases} x + 1 & x \leq - 5 \\ - 3 & - 5 = 6 \end{cases}$
26372	Solve the Inequality for a	-6a>66	$- 6 a > 66$
26373	Simplify	((5x^2+9x-2)/(2x+6))÷((x^2-4)/(x^2+x-6))	$\frac{5 x^{2} + 9 x - 2}{2 x + 6} \div \frac{x^{2} - 4}{x^{2} + x - 6}$
26374	Solve for f	-8(14f+16)+16f=8(-14f-8)	$- 8 (14 f + 16) + 16 f = 8 (- 14 f - 8)$
26375	Graph	f(x)=x^2-4x+32 ; at (3,0) , t^3	$f (x) = x^{2} - 4 x + 32$ ; at $(3, 0)$ , $t^{3}$
26376	Find the 5th Term	1 , 1/10 , 1/100	$1$ , $\frac{1}{10}$ , $\frac{1}{100}$
26377	Find Where Increasing/Decreasing	f(x)=2 log base 2 of x-2	$f (x) = 2 \log_{2} (x - 2)$
26378	Find Where Increasing/Decreasing	f(x)=x^(2/3)(x^2-4)	$f (x) = x^{\frac{2}{3}} (x^{2} - 4)$
26379	Solve for x	(x^3-x)/(x^2+1)>0	$\frac{x^{3} - x}{x^{2} + 1} > 0$
26380	Solve for x	3/x=2/(5-x)	$\frac{3}{x} = \frac{2}{5 - x}$
26381	Find dy/dx	y=(2x^3+2)^4cos(x)^3	$y = {(2 x^{3} + 2)}^{4} \cos^{3} (x)$
26382	Divide	(6c^2d-14cd^2+2d^3)/2	$\frac{6 c^{2} d - 14 c d^{2} + 2 d^{3}}{2}$
26383	Rationalize the Denominator	8/(-8- square root of 2)	$\frac{8}{- 8 - \sqrt{2}}$
26384	Simplify	( square root of 50)/3+ square root of 147+1/( square root of 2)	$\frac{\sqrt{50}}{3} + \sqrt{147} + \frac{1}{\sqrt{2}}$
26385	Solve the System of Equations	(x-2)^2+(y+1)^2=89 x+y=4	${(x - 2)}^{2} + {(y + 1)}^{2} = 89$ $x + y = 4$
26386	Simplify	1/(x^2)-1/(y^2)	$\frac{1}{x^{2}} - \frac{1}{y^{2}}$
26387	Simplify	(5n)/(30m)+(2m+4n)/(30m)	$\frac{5 n}{30 m} + \frac{2 m + 4 n}{30 m}$
26388	Evaluate	xy>0	$x y > 0$
26389	Find the Derivative - d/dx	natural log of \|1-x\|	$\ln (\| 1 - x \|)$
26390	Evaluate	(pi/2-0)/4	$\frac{\frac{π}{2} - 0}{4}$
26391	Simplify the Radical Expression	(6 square root of 28)/(3 square root of 4)	$\frac{6 \sqrt{28}}{3 \sqrt{4}}$
26392	Integrate By Parts	integral from 0 to 1 of arctan(2x) with respect to x	$\int_{0}^{1} \arctan (2 x) d x$
26393	Simplify	( cube root of -1)^0	${(\sqrt[3]{- 1})}^{0}$
26394	Find the Exact Value	arcsin((-1)^-1)	$\arcsin ({(- 1)}^{- 1})$
26395	Find the Roots (Zeros)	f(x)=-0.3x^2+x+3	$f (x) = - 0.3 x^{2} + x + 3$
26396	Solve the Function Operation	g(a)=-3a-3 f(a)=a^2+5 find (g-f)(a)	$g (a) = - 3 a - 3$ $f (a) = a^{2} + 5$ find $(g - f) (a)$
26397	Graph	f(x)=-1/8(2x-6)^3-2	$f (x) = - \frac{1}{8} {(2 x - 6)}^{3} - 2$
26398	Simplify	square root of x^(3/4)x^-1	$\sqrt{x^{\frac{3}{4}}} x^{- 1}$
26399	Write in Standard Form	(7x^2+3x)-(5x^2+4)	$(7 x^{2} + 3 x) - (5 x^{2} + 4)$
26400	Simplify	(32a^8b^6-12a^5b^4c^2)/(4a^3b^3)	$\frac{32 a^{8} b^{6} - 12 a^{5} b^{4} c^{2}}{4 a^{3} b^{3}}$