Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
45301	Find the x and y Intercepts	4x^2+40x+4y^2=0	$4 x^{2} + 40 x + 4 y^{2} = 0$
45302	Find the x and y Intercepts	3x^2+3y^2-24x+12y-15=0	$3 x^{2} + 3 y^{2} - 24 x + 12 y - 15 = 0$
45303	Find the x and y Intercepts	3x+2y=5	$3 x + 2 y = 5$
45304	Find the x and y Intercepts	2x^2+24x+2y^2=0	$2 x^{2} + 24 x + 2 y^{2} = 0$
45305	Find the x and y Intercepts	y=5sin(x)	$y = 5 \sin (x)$
45306	Find the x and y Intercepts	y=2x^2-4x+2	$y = 2 x^{2} - 4 x + 2$
45307	Find the x and y Intercepts	y^2=49+25x^2	$y^{2} = 49 + 25 x^{2}$
45308	Find the x and y Intercepts	y = square root of x-5	$y = \sqrt{x - 5}$
45309	Find the x and y Intercepts	y = square root of x-6	$y = \sqrt{x - 6}$
45310	Find Reduced Row Echelon Form	[[1,3,7,-36],[0,1,3,-14],[0,0,1,-5]]	$[\begin{array}{c} 1 & 3 & 7 & - 36 \\ 0 & 1 & 3 & - 14 \\ 0 & 0 & 1 & - 5 \end{array}]$
45311	Solve the Matrix Equation	[[3,-2],[1,4]][[x],[y]]=[[2],[4]]	$[\begin{array}{c} 3 & - 2 \\ 1 & 4 \end{array}] [\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} 2 \\ 4 \end{array}]$
45312	Find the Center	-x^2+4y^2+8x+16y-64=0	$- x^{2} + 4 y^{2} + 8 x + 16 y - 64 = 0$
45313	Find the Center	9x^2+4y^2+54x-8y+49=0	$9 x^{2} + 4 y^{2} + 54 x - 8 y + 49 = 0$
45314	Find the Distance Between Two Points	(-2.5,pi/6) , (-1.9,-pi/3)	$(- 2.5, \frac{π}{6}) (- 1.9, - \frac{π}{3})$
45315	Find the Roots (Zeros)	1/2cos(2x)	$\frac{1}{2} \cos (2 x)$
45316	Find the Roots (Zeros)	x^3-8x^2+24x-32	$x^{3} - 8 x^{2} + 24 x - 32$
45317	Find the Roots (Zeros)	x^3-4x^2-25x+100	$x^{3} - 4 x^{2} - 25 x + 100$
45318	Find the Roots (Zeros)	x^3-5x^2-2x+24	$x^{3} - 5 x^{2} - 2 x + 24$
45319	Find the Roots (Zeros)	x^3-6x^2+21x-26	$x^{3} - 6 x^{2} + 21 x - 26$
45320	Find the Roots (Zeros)	x^3-2x^2+4x-8	$x^{3} - 2 x^{2} + 4 x - 8$
45321	Find the Roots (Zeros)	x^3-3x^2-16x+48	$x^{3} - 3 x^{2} - 16 x + 48$
45322	Find the Roots (Zeros)	x^3-10x^2+11x+70	$x^{3} - 10 x^{2} + 11 x + 70$
45323	Find the Roots (Zeros)	x^4+13x^2+36	$x^{4} + 13 x^{2} + 36$
45324	Find the Roots (Zeros)	x^4-5x^3+6x^2-x-2	$x^{4} - 5 x^{3} + 6 x^{2} - x - 2$
45325	Find the Roots (Zeros)	x^3	$x^{3}$
45326	Find the Roots (Zeros)	sin(4x+pi)	$\sin (4 x + π)$
45327	Find the Roots (Zeros)	2x^3-23x^2+58x+35	$2 x^{3} - 23 x^{2} + 58 x + 35$
45328	Find the Roots (Zeros)	2x^3-3x^2-10x+15	$2 x^{3} - 3 x^{2} - 10 x + 15$
45329	Find the Roots (Zeros)	2sin(x)^2-3sin(x)+1	$2 \sin^{2} (x) - 3 \sin (x) + 1$
45330	Find the Roots (Zeros)	3x^4-2x^3+74x^2-50x-25	$3 x^{4} - 2 x^{3} + 74 x^{2} - 50 x - 25$
45331	Find the Roots (Zeros)	4+4 square root of 3i	$4 + 4 \sqrt{3 i}$
45332	Find the Roots (Zeros)	7x^3+52x^2+22x+7	$7 x^{3} + 52 x^{2} + 22 x + 7$
45333	Find the Roots (Zeros)	6x^2+x-1	$6 x^{2} + x - 1$
45334	Split Using Partial Fraction Decomposition	(x^2-6x-13)/((x+2)(x^2-1))	$\frac{x^{2} - 6 x - 13}{(x + 2) (x^{2} - 1)}$
45335	Solve by Substitution	2y^2+xy=5 , 4y+x=7	$2 y^{2} + x y = 5$ , $4 y + x = 7$
45336	Solve by Substitution	9x^2+9y^2+85x+18y+9=6x^2-9y^2+50x-18y-9=0	$9 x^{2} + 9 y^{2} + 85 x + 18 y + 9 = 6 x^{2} - 9 y^{2} + 50 x - 18 y - 9 = 0$
45337	Solve by Substitution	x+y=4 y=x^2-8	$x + y = 4$ $y = x^{2} - 8$
45338	Solve by Substitution	x+y=36 , x^2+y^2=72	$x + y = 36$ , $x^{2} + y^{2} = 72$
45339	Solve by Substitution	y=x^2-4x-52x-3y=10	$y = x^{2} - 4 x - 52 x - 3 y = 10$
45340	Solve the Triangle	tri(51/2)(30)(17 square root of 3)(60)()(90)	 $\begin{matrix} Side & Angle \\ \begin{matrix} b = & \frac{51}{2} \\ c = & 17 \sqrt{3} \\ a = \end{matrix} & \begin{matrix} A = & 30 \\ B = & 60 \\ C = & 90 \end{matrix} \end{matrix}$
45341	Split Using Partial Fraction Decomposition	(9x^2-x-18)/(x^3-x)	$\frac{9 x^{2} - x - 18}{x^{3} - x}$
45342	Split Using Partial Fraction Decomposition	(8x+3)/((x+3)(3x-1))	$\frac{8 x + 3}{(x + 3) (3 x - 1)}$
45343	Split Using Partial Fraction Decomposition	(5x-15)/((x-5)(x+1))	$\frac{(5 x - 15)}{(x - 5) (x + 1)}$
45344	Split Using Partial Fraction Decomposition	(-10x^2+27x-14)/((x-1)^3(x+2))	$\frac{- 10 x^{2} + 27 x - 14}{{(x - 1)}^{3} (x + 2)}$
45345	Split Using Partial Fraction Decomposition	35/(2x(3x+7))	$\frac{35}{2 x (3 x + 7)}$
45346	Find the Vertex	f(x)=2x^2-12x+16	$f (x) = 2 x^{2} - 12 x + 16$
45347	Find the Vertex	f(x)=3x^2-24x+47	$f (x) = 3 x^{2} - 24 x + 47$
45348	Find Amplitude, Period, and Phase Shift	f(x)=2tan(3x-pi)	$f (x) = 2 \tan (3 x - π)$
45349	Find the Other Trig Values in Quadrant II	tan(theta)=-8/5	$\tan (θ) = - \frac{8}{5}$
45350	Find the Other Trig Values in Quadrant I	sin(15 degrees )	$\sin (15 °)$
45351	Find the Other Trig Values in Quadrant I	tan(theta)=1/3	$\tan (θ) = \frac{1}{3}$
45352	Find the Other Trig Values in Quadrant II	cos(theta)=-8/9	$\cos (θ) = - \frac{8}{9}$
45353	Multiply the Matrices	[[0.7,0.4],[0.3,0.6]][[0.75],[0.25]]	$[\begin{array}{c} 0.7 & 0.4 \\ 0.3 & 0.6 \end{array}] [\begin{array}{c} 0.75 \\ 0.25 \end{array}]$
45354	Find the Other Trig Values in Quadrant I	sin(theta)=4/7	$\sin (θ) = \frac{4}{7}$
45355	Find the Other Trig Values in Quadrant I	sin(theta)=3/10	$\sin (θ) = \frac{3}{10}$
45356	Find the Other Trig Values in Quadrant I	tan(theta)=8/5	$\tan (θ) = \frac{8}{5}$
45357	Find the Other Trig Values in Quadrant I	csc(theta)=17/8	$\csc (θ) = \frac{17}{8}$
45358	Find the Other Trig Values in Quadrant I	sin(theta)=2/9	$\sin (θ) = \frac{2}{9}$
45359	Find All Complex Number Solutions	z=1+4i	$z = 1 + 4 i$
45360	Find All Complex Number Solutions	z^4=81i	$z^{4} = 81 i$
45361	Find All Complex Number Solutions	z=5-5i	$z = 5 - 5 i$
45362	Find the Other Trig Values in Quadrant I	cos(theta)=2/9	$\cos (θ) = \frac{2}{9}$
45363	Multiply the Matrices	[[7,7],[1,9]][[-4,4],[7,-9]]	$[\begin{array}{c} 7 & 7 \\ 1 & 9 \end{array}] [\begin{array}{c} - 4 & 4 \\ 7 & - 9 \end{array}]$
45364	Multiply the Matrices	[[4,-5,6]]*[[-4],[6],[9]]	$[\begin{array}{c} 4 & - 5 & 6 \end{array}] \cdot [\begin{array}{c} - 4 \\ 6 \\ 9 \end{array}]$
45365	Multiply the Matrices	[[2,1],[2,-3]][[5/4],[-1/2]]	$[\begin{array}{c} 2 & 1 \\ 2 & - 3 \end{array}] [\begin{array}{c} \frac{5}{4} \\ - \frac{1}{2} \end{array}]$
45366	Multiply the Matrices	[[2,-17,11],[-1,11,-7],[0,3,-2]]*[[1,1,2],[2,4,-3],[3,6,-5]]	$[\begin{array}{c} 2 & - 17 & 11 \\ - 1 & 11 & - 7 \\ 0 & 3 & - 2 \end{array}] \cdot [\begin{array}{c} 1 & 1 & 2 \\ 2 & 4 & - 3 \\ 3 & 6 & - 5 \end{array}]$
45367	Find the Other Trig Values in Quadrant II	sin(theta)=5/7	$\sin (θ) = \frac{5}{7}$
45368	Find the Other Trig Values in Quadrant II	sin(theta)=( square root of 5)/3	$\sin (θ) = \frac{\sqrt{5}}{3}$
45369	Find the Other Trig Values in Quadrant II	cot(theta)=-28/45	$\cot (θ) = - \frac{28}{45}$
45370	Find the Other Trig Values in Quadrant II	csc(theta)=4	$\csc (θ) = 4$
45371	Find the Other Trig Values in Quadrant I	sin(t)=5/6	$\sin (t) = \frac{5}{6}$
45372	Find the Other Trig Values in Quadrant II	sin(A)=3/5	$\sin (A) = \frac{3}{5}$
45373	Find the Other Trig Values in Quadrant II	tan(theta)=-1/3	$\tan (θ) = - \frac{1}{3}$
45374	Find the Other Trig Values in Quadrant III	csc(theta)=-9/8	$\csc (θ) = - \frac{9}{8}$
45375	Find the Other Trig Values in Quadrant III	sin(theta)=-3/7	$\sin (θ) = - \frac{3}{7}$
45376	Find the Other Trig Values in Quadrant III	cot(theta)=14	$\cot (θ) = 14$
45377	Find Trig Functions Using Identities	cos(theta)=2/3 , tan(theta)<0	$\cos (θ) = \frac{2}{3}$ , $\tan (θ) < 0$
45378	Find Trig Functions Using Identities	csc(x)sec(x)cot(x)=csc(x)^2	$\csc (x) \sec (x) \cot (x) = \csc^{2} (x)$
45379	Find Trig Functions Using Identities	sin(theta)(tan(theta)+cot(theta))=sec(theta)	$\sin (θ (\tan (θ) + \cot (θ))) = \sec (θ)$
45380	Determine if Rational	2pi	$2 π$
45381	Find the Tangent Given the Point	(10,-8)	$(10, - 8)$
45382	Find the Tangent Given the Point	p=(-2/3,( square root of 5)/3)	$p = (- \frac{2}{3}, \frac{\sqrt{5}}{3})$
45383	Expand the Logarithmic Expression	log of (x^2 square root of 1-x)/(10(x+1)^3)	$\log (\frac{x^{2} \sqrt{1 - x}}{10 {(x + 1)}^{3}})$
45384	Expand the Logarithmic Expression	log of (x^3 cube root of 1-x)/(100(x+2)^3)	$\log (\frac{x^{3} \sqrt[3]{1 - x}}{100 {(x + 2)}^{3}})$
45385	Expand the Logarithmic Expression	log of a/(b^3c^7)	$\log (\frac{a}{b^{3} c^{7}})$
45386	Expand the Logarithmic Expression	log of (xy)^(1/3)	$\log ({(x y)}^{\frac{1}{3}})$
45387	Expand the Logarithmic Expression	log of xz^3	$\log (x z^{3})$
45388	Expand the Logarithmic Expression	log of y^5x	$\log (y^{5} x)$
45389	Expand the Logarithmic Expression	log of y^4z	$\log (y^{4} z)$
45390	Expand the Logarithmic Expression	log of yx^2	$\log (y x^{2})$
45391	Expand the Logarithmic Expression	log of square root of x^4y^-7	$\log (\sqrt{x^{4} y^{- 7}})$
45392	Expand the Logarithmic Expression	log of e/13	$\log (\frac{e}{13})$
45393	Expand the Logarithmic Expression	natural log of (2a)/b	$\ln (\frac{2 a}{b})$
45394	Expand the Logarithmic Expression	natural log of square root of x+1(y^2+1)^(3/2)e^(3/2)	$\ln (\sqrt{x + 1} \cdot {(y^{2} + 1)}^{\frac{3}{2}} \cdot e^{\frac{3}{2}})$
45395	Expand the Logarithmic Expression	natural log of (e^6)/14	$\ln (\frac{e^{6}}{14})$
45396	Expand the Logarithmic Expression	natural log of (x^7 square root of p^5q^3)/(e^9)	$\ln (\frac{x^{7} \sqrt{p^{5} q^{3}}}{e^{9}})$
45397	Expand the Logarithmic Expression	natural log of (x^8 square root of p^3q)/(e^2)	$\ln (\frac{x^{8} \sqrt{p^{3} q}}{e^{2}})$
45398	Expand the Logarithmic Expression	natural log of 36d	$\ln (36 d)$
45399	Expand the Logarithmic Expression	natural log of ( cube root of xy)/(t^(4/3))	$\ln (\frac{\sqrt[3]{x y}}{t^{\frac{4}{3}}})$
45400	Add	3(cos(60 degrees )+isin(60 degrees ))+2(cos(35 degrees )+isin(35 degrees ))	$3 (\cos (60 °) + i \sin (60 °)) + 2 (\cos (35 °) + i \sin (35 °))$