Mathway | Recent Popular Problems

Recent Popular Problems

Rank	Topic	Problem	Formatted Problem
6101	Find All Complex Solutions	log base 4 of x=1- log base 4 of x-3	$\log_{4} (x) = 1 - \log_{4} (x - 3)$
6102	Simplify	2m(3/2m+1)+3(5/3m-2)	$2 m (\frac{3}{2} m + 1) + 3 (\frac{5}{3} m - 2)$
6103	Solve for x	sec(x)^2-tan(x)^2=1	$\sec^{2} (x) - \tan^{2} (x) = 1$
6104	Simplify	( square root of 16)/( cube root of 2)	$\frac{\sqrt{16}}{\sqrt[3]{2}}$
6105	Solve for x	-1/5(x-4)=-2	$- \frac{1}{5} (x - 4) = - 2$
6106	Solve for x	(6x-1)(6x+1)-4x(9x+2)=-1	$(6 x - 1) (6 x + 1) - 4 x (9 x + 2) = - 1$
6107	Find the Roots (Zeros)	f(x)=(x-1)(x+3)(x^2+1)	$f (x) = (x - 1) (x + 3) (x^{2} + 1)$
6108	Find the Degree, Leading Term, and Leading Coefficient	f(x)=-x+4x^2-x^3	$f (x) = - x + 4 x^{2} - x^{3}$
6109	Simplify	(-5^0)/(2^-2)	$\frac{- 5^{0}}{2^{- 2}}$
6110	Solve the Rational Equation for x	cube root of x=4	$\sqrt[3]{x} = 4$
6111	Simplify	cube root of 10^5* fourth root of 10^5	$\sqrt[3]{10^{5}} \cdot \sqrt[4]{10^{5}}$
6112	Simplify	( square root of 3x^12y^10)/( square root of x^3y^4)	$\frac{\sqrt{3 x^{12} y^{10}}}{\sqrt{x^{3} y^{4}}}$
6113	Divide Using Long Polynomial Division	(2x^4-3x^3-20x^2+72x-63)/(2x-3)	$\frac{2 x^{4} - 3 x^{3} - 20 x^{2} + 72 x - 63}{2 x - 3}$
6114	Graph	x^2+(y- square root of \|x\|)^2=1	$x^{2} + {(y - \sqrt{\| x \|})}^{2} = 1$
6115	Solve for v₁	(p_1v_1)/t_1=(p_2v_2)/t_2	$\frac{p_{1} v_{1}}{t_{1}} = \frac{p_{2} v_{2}}{t_{2}}$
6116	Graph	y>=2x+3 and y<2x-4	$y \geq 2 x + 3$ and $y < 2 x - 4$
6117	Simplify	((-w^-1y)^0)/(4w^-1y^2)	$\frac{{(- w^{- 1} y)}^{0}}{4 w^{- 1} y^{2}}$
6118	Find the Antiderivative	2/(x^3)-3/x	$\frac{2}{x^{3}} - \frac{3}{x}$
6119	Solve for m	-20+m-18=-8m+16	$- 20 + m - 18 = - 8 m + 16$
6120	Solve for x	3/4(x-2y)=12	$\frac{3}{4} (x - 2 y) = 12$
6121	Simplify	(27x^4)/(6x^4)	$\frac{27 x^{4}}{6 x^{4}}$
6122	Find the Excluded Values	((4x-24)/(-3x-15))/((x^2-36)/(x+5))	$\frac{\frac{4 x - 24}{- 3 x - 15}}{\frac{x^{2} - 36}{x + 5}}$
6123	Evaluate	-2(3/2)^-1	$- 2 {(\frac{3}{2})}^{- 1}$
6124	Simplify	(a^3b)^-2(a^3b^4)	${(a^{3} b)}^{- 2} (a^{3} b^{4})$
6125	Simplify	square root of 5-18 square root of 5+4 square root of 5-5 square root of 5	$\sqrt{5} - 18 \sqrt{5} + 4 \sqrt{5} - 5 \sqrt{5}$
6126	Simplify	2^3+3(2)+14÷2	$2^{3} + 3 (2) + 14 \div 2$
6127	Solve for x	-5(x-6)-2=5+(x-1)	$- 5 (x - 6) - 2 = 5 + (x - 1)$
6128	Solve for z	z^2=7	$z^{2} = 7$
6129	Evaluate	ii	$i i$
6130	Find the Excluded Values	(x^2-64)/(x^2+16x+64)	$\frac{x^{2} - 64}{x^{2} + 16 x + 64}$
6131	Simplify	((x^-5)/(x^-2))^-1	${(\frac{x^{- 5}}{x^{- 2}})}^{- 1}$
6132	Simplify	a^4b^3+9a^3b^4-3a^4b^3-4a^3b^4	$a^{4} b^{3} + 9 a^{3} b^{4} - 3 a^{4} b^{3} - 4 a^{3} b^{4}$
6133	Solve the System of Equations	y=x^2+10x+11 y=x^2+x-7	$y = x^{2} + 10 x + 11$ $y = x^{2} + x - 7$
6134	Solve for x	(3x+1)/(x+2)-(x-1)/(x-2)=1	$\frac{3 x + 1}{x + 2} - \frac{x - 1}{x - 2} = 1$
6135	Find the Derivative - d/dx	(sin(-x))	$(\sin (- x))$
6136	Simplify	2x1/(x^-3)x^-2	$2 x \cdot \frac{1}{x^{- 3}} \cdot x^{- 2}$
6137	Find the Product	5x^2y^3*(-2 3/4xy^6)	$5 x^{2} y^{3} \cdot (- 2 \frac{3}{4} x y^{6})$
6138	Solve by Substitution	d+e=2 d-e=4	$d + e = 2$ $d - e = 4$
6139	Solve for H	sin(-67.3)=-12/H	$\sin (- 67.3) = - \frac{12}{H}$
6140	Simplify	((7r^5k)/(4r^2k^3))^2	${(\frac{7 r^{5} k}{4 r^{2} k^{3}})}^{2}$
6141	Solve for m	-54=10-(m-10)^(3/2)	$- 54 = 10 - {(m - 10)}^{\frac{3}{2}}$
6142	Simplify	cube root of a/b	$\sqrt[3]{\frac{a}{b}}$
6143	Simplify	(8m^2)/(10m^3+60m^2)-(6m^2-12m)/(10m^3+60m^2)	$\frac{8 m^{2}}{10 m^{3} + 60 m^{2}} - \frac{6 m^{2} - 12 m}{10 m^{3} + 60 m^{2}}$
6144	Solve for x	(3x)/7+2/7=2	$\frac{3 x}{7} + \frac{2}{7} = 2$
6145	Divide	(x^2+2x+4)÷(x^3-8)	$(x^{2} + 2 x + 4) \div (x^{3} - 8)$
6146	Find the Derivative - d/dt	2+5arctan(t/2)	$2 + 5 \arctan (\frac{t}{2})$
6147	Simplify	w^-2(4w)^2	$w^{- 2} {(4 w)}^{2}$
6148	Determine if a Polynomial	c^4 square root of 5+b^3-cb^4	$c^{4} \sqrt{5} + b^{3} - c b^{4}$
6149	Simplify	(-2f)/(d^5)((df^5)/(-2f^10))^2	$\frac{- 2 f}{d^{5}} {(\frac{d f^{5}}{- 2 f^{10}})}^{2}$
6150	Find the Reference Angle	sin(pi/3)	$\sin (\frac{π}{3})$
6151	Solve for θ	sin(2theta)- square root of 2cos(theta)=0	$\sin (2 θ) - \sqrt{2} \cos (θ) = 0$
6152	Simplify the Radical Expression	square root of 3+2 square root of 3	$\sqrt{3} + 2 \sqrt{3}$
6153	Factor	5x+xy+5y+y^2	$5 x + x y + 5 y + y^{2}$
6154	Find the Domain and Range	1/(\|x\|)	$\frac{1}{\| x \|}$
6155	Find the Exact Value	3 square root of 12+2 square root of 108-3 square root of 48	$3 \sqrt{12} + 2 \sqrt{108} - 3 \sqrt{48}$
6156	Graph	y=-1/2x^2-3/2x+2	$y = - \frac{1}{2} x^{2} - \frac{3}{2} x + 2$
6157	Evaluate	(5x^4y^2+20xy^6-10x)÷5xy^2	$(5 x^{4} y^{2} + 20 x y^{6} - 10 x) \div 5 x y^{2}$
6158	Find the Antiderivative	2/(4x-3)	$\frac{2}{4 x - 3}$
6159	Solve for x	3(2x-5)+2x+3=1	$3 (2 x - 5) + 2 x + 3 = 1$
6160	Solve for x	3x(2x-1)-12(2x-1)=0	$3 x (2 x - 1) - 12 (2 x - 1) = 0$
6161	Simplify	(4v^2+3v)-(6v-7+7v^2)	$(4 v^{2} + 3 v) - (6 v - 7 + 7 v^{2})$
6162	Find the x and y Intercepts	f(x)=-2+ log base 5 of -x	$f (x) = - 2 + \log_{5} (- x)$
6163	Simplify	16 root of (m^-5)/(m^-1)	$\sqrt[16]{\frac{m^{- 5}}{m^{- 1}}}$
6164	Subtract	(-7m^4-9m^3+3m)-(-2m^4+5m^3-9m^2+4m)	$(- 7 m^{4} - 9 m^{3} + 3 m) - (- 2 m^{4} + 5 m^{3} - 9 m^{2} + 4 m)$
6165	Write the Fraction in Simplest Form	(20t^2)/((5t)^2)	$\frac{20 t^{2}}{{(5 t)}^{2}}$
6166	Simplify the Radical Expression	square root of 20- square root of 5	$\sqrt{20} - \sqrt{5}$
6167	Find the Reference Angle	tan(pi/3)	$\tan (\frac{π}{3})$
6168	Solve for x	x+3=(10-x)/3	$x + 3 = \frac{10 - x}{3}$
6169	Evaluate	-2(3/2)^-2	$- 2 {(\frac{3}{2})}^{- 2}$
6170	Solve for s	n=s*(p-v)-f	$n = s \cdot (p - v) - f$
6171	Graph	x^2+y>-4	$x^{2} + y > - 4$
6172	Find the Exact Value	(81 1/4)^4	${(81 \frac{1}{4})}^{4}$
6173	Rewrite the Cartesian Equation as a Polar Equation	x^2+(y-2)^2=4	$x^{2} + {(y - 2)}^{2} = 4$
6174	Solve the Absolute Value Inequality for u	9x-7i>3(3x-7u)	$9 x - 7 i > 3 (3 x - 7 u)$
6175	Factor	p^2-6-q*(p^2-6)^2	$p^{2} - 6 - q \cdot {(p^{2} - 6)}^{2}$
6176	Solve for x	(1/3)^(x+3)=10	${(\frac{1}{3})}^{x + 3} = 10$
6177	Evaluate the Integral	integral from 0 to pi of integral from 0 to 2pi of 0 with respect to theta with respect to x	$\int_{0}^{π} \int_{0}^{2 π} 0 d θ d x$
6178	Write the Fraction in Simplest Form	((4m^4)^2)/(12m^5)	$\frac{{(4 m^{4})}^{2}}{12 m^{5}}$
6179	Solve for x	3arctan(x)+arccot(x)=pi	$3 \arctan (x) + arccot (x) = π$
6180	Solve for x	2/7=-(8x)/7+6/7	$\frac{2}{7} = - \frac{8 x}{7} + \frac{6}{7}$
6181	Write in Standard Form	f(x)=(2x^3)/3+5/3+15x	$f (x) = \frac{2 x^{3}}{3} + \frac{5}{3} + 15 x$
6182	Evaluate the Limit	limit as x approaches 0 of ( square root of 1+x-1)/( square root of 4+x-2)	$lim_{x \to 0} \frac{\sqrt{1 + x} - 1}{\sqrt{4 + x} - 2}$
6183	Simplify	(3^-1)/((3^2)^-6)	$\frac{3^{- 1}}{{(3^{2})}^{- 6}}$
6184	Graph	y=(x^2-4x+3)/(x^2-9)	$y = \frac{x^{2} - 4 x + 3}{x^{2} - 9}$
6185	Simplify	fifth root of (3072h^8)/(243f^5)	$\sqrt[5]{\frac{3072 h^{8}}{243 f^{5}}}$
6186	Simplify	(1-sin(theta)^2)tan(theta)sec(theta)	$(1 - \sin^{2} (θ)) \cdot \tan (θ) \cdot \sec (θ)$
6187	Solve for b	6(1 1/4+b)=10	$6 (1 \frac{1}{4} + b) = 10$
6188	Evaluate the Integral	integral of 2/( square root of x^3) with respect to x	$\int \frac{2}{\sqrt{x^{3}}} d x$
6189	Solve for θ in Radians	csc(theta)=-(2 square root of 3)/3	$\csc (θ) = - \frac{2 \sqrt{3}}{3}$
6190	Find Amplitude, Period, and Phase Shift	y=3sin(-x/3)	$y = 3 \sin (- \frac{x}{3})$
6191	Evaluate the Function	p(x)=2x^3+4x^2+6x+7 , x=1/2	$p (x) = 2 x^{3} + 4 x^{2} + 6 x + 7$ , $x = \frac{1}{2}$
6192	Simplify	(x^3+4x^2-12x)/(x^2+x-30)	$\frac{x^{3} + 4 x^{2} - 12 x}{x^{2} + x - 30}$
6193	Solve for x	2x^3+2x-3=-0.5\|x-4\|	$2 x^{3} + 2 x - 3 = - 0.5 \| x - 4 \|$
6194	Find the End Behavior	f(x)=-738x^3+18x^5+4392x+159x^4-1884x^2-3x^6+8640	$f (x) = - 738 x^{3} + 18 x^{5} + 4392 x + 159 x^{4} - 1884 x^{2} - 3 x^{6} + 8640$
6195	Find the Roots (Zeros)	-2cos(5/4x)	$- 2 \cos (\frac{5}{4} x)$
6196	Graph	2x-y^2=4y+10	$2 x - y^{2} = 4 y + 10$
6197	Solve the Inequality for x	x^2+x-6>=-4	$x^{2} + x - 6 \geq - 4$
6198	Solve for m	(2m-7)/(3n)=3	$\frac{2 m - 7}{3 n} = 3$
6199	Simplify	7y^2-5y+9y-5y^2	$7 y^{2} - 5 y + 9 y - 5 y^{2}$
6200	Simplify	(2p^3)^0(p^4)	${(2 p^{3})}^{0} (p^{4})$