Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
32101	Find the Quotient	(5x^4-3x^3-24x^2+2x-5)/(x+2)	$\frac{5 x^{4} - 3 x^{3} - 24 x^{2} + 2 x - 5}{x + 2}$
32102	Find the Difference Quotient	2x^2	$2 x^{2}$
32103	Simplify	(x^(1/2))/(-3x^(4/3))	$\frac{x^{\frac{1}{2}}}{- 3 x^{\frac{4}{3}}}$
32104	Graph	(x^2+y^2-1)^3=x^2 y^3	${(x^{2} + y^{2} - 1)}^{3} = x^{2}$ $y^{3}$
32105	Solve the Inequality for x	(3x-5)/4-(x-6)/12<1	$\frac{3 x - 5}{4} - \frac{x - 6}{12} < 1$
32106	Simplify	2/( square root of 5+1)	$\frac{2}{\sqrt{5 + 1}}$
32107	Solve for x	square root of x-3 = square root of x-3	$\sqrt{x - 3} = \sqrt{x - 3}$
32108	Add	(a-5)/(15a^2b^3)+8/(24ab^3)	$\frac{a - 5}{15 a^{2} b^{3}} + \frac{8}{24 a b^{3}}$
32109	Find Amplitude, Period, and Phase Shift	f(x)=1/7cot(8theta-120)	$f (x) = \frac{1}{7} \cot (8 θ - 120)$
32110	Solve for x	5y^2*(2y^3)^x=80y^14	$5 y^{2} \cdot {(2 y^{3})}^{x} = 80 y^{14}$
32111	Solve for y	5y^3-3y^2+8y=0	$5 y^{3} - 3 y^{2} + 8 y = 0$
32112	Solve for x	(x+5)2/3=4	$(x + 5) \frac{2}{3} = 4$
32113	Multiply	a(a+b)	$a (a + b)$
32114	Combine Like Terms	(3-6n^5-8n^4)-(-6n^4-3n-8n^5)	$(3 - 6 n^{5} - 8 n^{4}) - (- 6 n^{4} - 3 n - 8 n^{5})$
32115	Simplify	(3n^(1/5))(9n^(4/5))	$(3 n^{\frac{1}{5}}) (9 n^{\frac{4}{5}})$
32116	Find the Domain and Range	y=sin(x-pi/4)	$y = \sin (x - \frac{π}{4})$
32117	Solve the System of Inequalities	2x+5y<10 3x-4y>=-8	$2 x + 5 y < 10$ $3 x - 4 y \geq - 8$
32118	Solve for c	2=c^2+c	$2 = c^{2} + c$
32119	Graph	x>-3 and x<2	$x > - 3$ and $x < 2$
32120	Simplify	( sixth root of 4)÷( cube root of 3)	$\sqrt[6]{4} \div \sqrt[3]{3}$
32121	Evaluate	(3v+2)-(2/3v-1/4)	$(3 v + 2) - (\frac{2}{3} v - \frac{1}{4})$
32122	Evaluate the Integral	integral from 2 to 4 of (1/2x^3-3x+2) with respect to x	$\int_{2}^{4} (\frac{1}{2} x^{3} - 3 x + 2) d x$
32123	Evaluate the Integral	integral from 0 to 4 of 24-(6x^3)/12 with respect to x	$\int_{0}^{4} 24 - \frac{6 x^{3}}{12} d x$
32124	Find the Derivative - d/dt	2e^(3t)-e^(2t)	$2 e^{3 t} - e^{2 t}$
32125	Factor by Grouping	125-x^3	$125 - x^{3}$
32126	Simplify the Radical Expression	i^5	$i^{5}$
32127	Add	(-3d^2-8+2d)+(4d-12+d^2)	$(- 3 d^{2} - 8 + 2 d) + (4 d - 12 + d^{2})$
32128	Find the Domain and Range	f(x)=-3+2	$f (x) = - 3 + 2$
32129	Solve for m	square root of 25-25 = square root of 10+3m	$\sqrt{25 - 25} = \sqrt{10 + 3 m}$
32130	Plot	tan(theta)>0 , sin(theta)<0	$\tan (θ) > 0$ , $\sin (θ) < 0$
32131	Graph	f(x)=-1 if x<-1; x if -1<=x<=1; 1 if x>1	$f (x) = {\begin{cases} - 1 & x < - 1 \\ x & - 1 \leq x \leq 1 \\ 1 & x > 1 \end{cases}$
32132	Find the Tangent Line at (1/2,8)	f(t)=t^-3 ;, (1/2,8)	$f (t) = t^{- 3}$ ;, $(\frac{1}{2}, 8)$
32133	Solve the System of Equations	x-3y=5 and 8x-7y=6	$x - 3 y = 5$ and $8 x - 7 y = 6$
32134	Rationalize the Denominator	(3 square root of 11- square root of 3)/( square root of 11+ square root of 3)	$\frac{3 \sqrt{11} - \sqrt{3}}{\sqrt{11} + \sqrt{3}}$
32135	Find the Product	1/3(2a^3b)(6b^3)	$\frac{1}{3} (2 a^{3} b) (6 b^{3})$
32136	Solve for k	-(-(-k))-(-2)(-2+k)=-k-(4k+3)	$- (- (- k)) - (- 2) (- 2 + k) = - k - (4 k + 3)$
32137	Divide	(-2/3)÷(2/3)	$- \frac{2}{3} \div \frac{2}{3}$
32138	Evaluate	y=(1/2)^-2	$y = {(\frac{1}{2})}^{- 2}$
32139	Expand the Logarithmic Expression	natural log of (x square root of y)/(zw^3)	$\ln (\frac{x \sqrt{y}}{z w^{3}})$
32140	Solve the System of Equations	a^2+2b^2=10 3a^2-b^2=9	$a^{2} + 2 b^{2} = 10$ $3 a^{2} - b^{2} = 9$
32141	Find dx/dy	y=1/(sin(20x))	$y = \frac{1}{\sin (20 x)}$
32142	Graph	y=(x+1)^(1/2)+8	$y = {(x + 1)}^{\frac{1}{2}} + 8$
32143	Evaluate	(1/( square root of x+h)-1/( square root of x))/h	$\frac{\frac{1}{\sqrt{x + h}} - \frac{1}{\sqrt{x}}}{h}$
32144	Simplify	(16^(2/5)*8^(2/5))/(4^(2/5))	$\frac{16^{\frac{2}{5}} \cdot 8^{\frac{2}{5}}}{4^{\frac{2}{5}}}$
32145	Solve the Inequality for c	(c+9)/-5<-2	$\frac{c + 9}{- 5} < - 2$
32146	Simplify	(-ab)(-b^2c^2)(-a^2b^2)	$(- a b) (- b^{2} c^{2}) (- a^{2} b^{2})$
32147	Simplify	1/(x-y)+2/(y-x)	$\frac{1}{x - y} + \frac{2}{y - x}$
32148	Simplify the Radical Expression	(7+ square root of 12)(7- square root of 12)	$(7 + \sqrt{12}) (7 - \sqrt{12})$
32149	Evaluate	(6^(1/2)*4^(1/3))^2	${(6^{\frac{1}{2}} \cdot 4^{\frac{1}{3}})}^{2}$
32150	Factor	(x+y)^2+6x(x+y)+8x^2	${(x + y)}^{2} + 6 x (x + y) + 8 x^{2}$
32151	Simplify	(3a^2+a+5)-(2a-5)	$(3 a^{2} + a + 5) - (2 a - 5)$
32152	Simplify	4/(9x)-(3x)/7	$\frac{4}{9 x} - \frac{3 x}{7}$
32153	Solve the Inequality for x	x>=-6-1/4(-6x+5)	$x \geq - 6 - \frac{1}{4} (- 6 x + 5)$
32154	Add	8 square root of 3+-10 square root of 3	$8 \sqrt{3} + - 10 \sqrt{3}$
32155	Verify the Identity	(cos(x)sin(x))/(cot(x))=1-cos(x)^2	$\frac{\cos (x) \sin (x)}{\cot (x)} = 1 - \cos^{2} (x)$
32156	Simplify	(sin(x)^4)/(cos(x)^2)	$\frac{\sin^{4} (x)}{\cos^{2} (x)}$
32157	Find the Inverse	F(x)=x^3-5/6	$F (x) = x^{3} - \frac{5}{6}$
32158	Graph Using a Table of Values	h(x)=5\|x-6\|-8	$h (x) = 5 \| x - 6 \| - 8$
32159	Evaluate the Integral	integral of ((3w^2)/2-2/(3w^2)) with respect to w	$\int (\frac{3 w^{2}}{2} - \frac{2}{3 w^{2}}) d w$
32160	Simplify the Radical Expression	(3 square root of 8)/(8 square root of 5)	$\frac{3 \sqrt{8}}{8 \sqrt{5}}$
32161	Solve for x	x^3+3x^2=24x+72	$x^{3} + 3 x^{2} = 24 x + 72$
32162	Evaluate	-54/50-40/100+1.65	$- \frac{54}{50} - \frac{40}{100} + 1.65$
32163	Find the Derivative - d/dx	((5x)/(6-5x^3))^3	${(\frac{5 x}{6 - 5 x^{3}})}^{3}$
32164	Divide	1/22/1	$\frac{1}{2} \cdot \frac{2}{1}$
32165	Solve for x	y=2(x-a)	$y = 2 (x - a)$
32166	Solve for a	2a-7=2a	$2 a - 7 = 2 a$
32167	Simplify	fifth root of (9x^11y^2)/(32xy^7)	$\sqrt[5]{\frac{9 x^{11} y^{2}}{32 x y^{7}}}$
32168	Solve the Function Operation	f(x)=x-6 if x<0; 3 if x=0; 6x-9 if x>0 Find f(0)	$f (x) = {\begin{cases} x - 6 & x < 0 \\ 3 & x = 0 \\ 6 x - 9 & x > 0 \end{cases}$ Find $f (0)$
32169	Find the Roots (Zeros)	(x-2)^2(x+3)(x+1)^2	${(x - 2)}^{2} (x + 3) {(x + 1)}^{2}$
32170	Simplify	-4(x+1/16)	$- 4 (x + \frac{1}{16})$
32171	Evaluate	80% of 25	$80 %$ of $25$
32172	Simplify	(8-2i^4)+(3-7i^8)-(4+i^9)	$(8 - 2 i^{4}) + (3 - 7 i^{8}) - (4 + i^{9})$
32173	Simplify	(cos(A)+cos(B))/(sin(A)-sin(B))+(sin(A)+sin(B))/(cos(A)-cos(B)) ?	$\frac{\cos (A) + \cos (B)}{\sin (A) - \sin (B)} + \frac{\sin (A) + \sin (B)}{\cos (A) - \cos (B)}$ ?
32174	Find the Equation with a Point and Slope	What is the equation of the line that passes through the point (6,-5) and has a slope of -3/2 ?	What is the equation of the line that passes through the point $(6, - 5)$ and has a slope of $- \frac{3}{2}$ ?
32175	Evaluate	(sec(x))/(sin(x))-(sin(x))/(cos(x))	$\frac{\sec (x)}{\sin (x)} - \frac{\sin (x)}{\cos (x)}$
32176	Evaluate	(-pi/2)/2	$\frac{- \frac{π}{2}}{2}$
32177	Solve by Factoring	30x^2-10=5x^2-1	$30 x^{2} - 10 = 5 x^{2} - 1$
32178	Solve the Function Operation	((((3,2-1,7))÷0,3)/(((29/35-3/7)4)÷0,2)-((33/20-1,5)1,5)/((2,44+39/25)*1/8))÷62 1/20+1 , 364÷0 , 124	$(\frac{(3, 2 - 1, 7) \div 0, 3}{(\frac{29}{35} - \frac{3}{7}) \times 4 \div 0, 2} - \frac{(\frac{33}{20} - 1, 5) \times 1, 5}{(2, 44 + \frac{39}{25}) \times \frac{1}{8}}) \div 62 \frac{1}{20} + 1$ , $364 \div 0$ , $124$
32179	Find the Derivative - d/dt	e^(-(t-3)^2)	$e^{- {(t - 3)}^{2}}$
32180	Solve the Inequality for x	3(-3+7x)<=-93	$3 (- 3 + 7 x) \leq - 93$
32181	Simplify	(-1b-2)^3	${(- 1 b - 2)}^{3}$
32182	Solve for r	1-5r=-2r^2	$1 - 5 r = - 2 r^{2}$
32183	Find Where Increasing/Decreasing	f(x)=- square root of x^3+8	$f (x) = - \sqrt{x^{3} + 8}$
32184	Graph Using a Table of Values	y=1/(3x)	$y = \frac{1}{3 x}$
32185	Solve the System of Equations	x^2+y^2=25 x-y^2=-5	$x^{2} + y^{2} = 25$ $x - y^{2} = - 5$
32186	Find the Antiderivative	f(x)=cos(pi/6-5x)	$f (x) = \cos (\frac{π}{6} - 5 x)$
32187	Evaluate	(729^2+21879^227)/(39^327^2+16236243*12)	$\frac{729^{2} + 2187 \cdot 9^{2} \cdot 27}{3 \cdot 9^{3} \cdot 27^{2} + 162 \cdot 36 \cdot 243 \cdot 12}$
32188	Solve the Inequality for x	6(2x+1/2)+3<=-3	$6 (2 x + \frac{1}{2}) + 3 \leq - 3$
32189	Solve for x	(5- square root of x)^2=y-20 square root of 2	${(5 - \sqrt{x})}^{2} = y - 20 \sqrt{2}$
32190	Solve the Inequality for x	log base 5 of x+5>=2	$\log_{5} (x + 5) \geq 2$
32191	Graph	0>=x+4 or 9	$0 \geq x + 4$ or $9$
32192	Solve by Completing the Square	x^2+18x+c=25+c	$x^{2} + 18 x + c = 25 + c$
32193	Divide	( square root of 2)/2( square root of 2)/2	$\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2}$
32194	Write in Standard Form	2x(3x^3+5y)	$2 x (3 x^{3} + 5 y)$
32195	Find Where Increasing/Decreasing	f(x)=-1/3\|x-2\|+4	$f (x) = - \frac{1}{3} \| x - 2 \| + 4$
32196	Simplify	2a^3(5a^2-7a)+(3a^4-a^5)	$2 a^{3} (5 a^{2} - 7 a) + (3 a^{4} - a^{5})$
32197	Evaluate	(4/(4^-3))^-2	${(\frac{4}{4^{- 3}})}^{- 2}$
32198	Simplify	((x^2)/(x-1))/((3x^2)/(x+4))	$\frac{\frac{x^{2}}{x - 1}}{\frac{3 x^{2}}{x + 4}}$
32199	Simplify	(4m2)5m	$(4 m \cdot 2) \cdot 5 m$
32200	Simplify the Radical Expression	( cube root of 4)÷( cube root of 6)	$\sqrt[3]{4} \div \sqrt[3]{6}$