Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
15601	Find f(g(x))	f(x)=4^x , g(x)=4^(-x)	$f (x) = 4^{x}$ , $g (x) = 4^{- x}$
15602	Find f(g(x))	f(x) = square root of x , g(x)=49-x^2	$f (x) = \sqrt{x}$ , $g (x) = 49 - x^{2}$
15603	Find f(g(x))	f(x) = square root of x+4 , g(x) = square root of x-3	$f (x) = \sqrt{x + 4}$ , $g (x) = \sqrt{x - 3}$
15604	Solve Using a Matrix by Elimination	x-y-2z=-6 , 3x+2y=-25 , -4x+y-z=12	$x - y - 2 z = - 6$ , $3 x + 2 y = - 25$ , $- 4 x + y - z = 12$
15605	Solve Using a Matrix by Elimination	x-z=2 , x+2y=1 , y-3z=3	$x - z = 2$ , $x + 2 y = 1$ , $y - 3 z = 3$
15606	Solve Using a Matrix by Elimination	-x-5y-5z=2 , 4x-5y+4z=19 , x+5y-z=-20	$- x - 5 y - 5 z = 2$ , $4 x - 5 y + 4 z = 19$ , $x + 5 y - z = - 20$
15607	Solve Using a Matrix by Elimination	x-y+z=6 , 5x+y-z=0	$x - y + z = 6$ , $5 x + y - z = 0$
15608	Solve Using a Matrix by Row Operations	2x-2y+3z=2 , 2x-3y+7z=-1 , 4x-3y+2z=0	$2 x - 2 y + 3 z = 2$ , $2 x - 3 y + 7 z = - 1$ , $4 x - 3 y + 2 z = 0$
15609	Solve Using a Matrix by Elimination	9/(x^2)-4/(y^2)+7=0 , 4/(x^2)+1/(y^2)=8	$\frac{9}{x^{2}} - \frac{4}{y^{2}} + 7 = 0$ , $\frac{4}{x^{2}} + \frac{1}{y^{2}} = 8$
15610	Solve Using a Matrix by Elimination	y-z=3-2x , 3x-y-3=-3y , 2z-3=x+3y	$y - z = 3 - 2 x$ , $3 x - y - 3 = - 3 y$ , $2 z - 3 = x + 3 y$
15611	Solve Using a Matrix by Row Operations	2x+y+z=5 , 4x-y-3z=1 , 8x+y-z=5	$2 x + y + z = 5$ , $4 x - y - 3 z = 1$ , $8 x + y - z = 5$
15612	Solve Using a Matrix by Row Operations	2x+y=-4 , -2y+4z=0 , 3x-2z=-11	$2 x + y = - 4$ , $- 2 y + 4 z = 0$ , $3 x - 2 z = - 11$
15613	Solve Using a Matrix by Row Operations	3x-2y+2z-w=2 , 4x+y+z+6w=8 , -3x+2y-2z+w=5 , 5x+3z-2w=1	$3 x - 2 y + 2 z - w = 2$ , $4 x + y + z + 6 w = 8$ , $- 3 x + 2 y - 2 z + w = 5$ , $5 x + 3 z - 2 w = 1$
15614	Solve Using a Matrix by Row Operations	5x+4=-2y , 3x=-y	$5 x + 4 = - 2 y$ , $3 x = - y$
15615	Solve Using a Matrix by Row Operations	5x-2y=27 , -3x+5y=18	$5 x - 2 y = 27$ , $- 3 x + 5 y = 18$
15616	Solve Using a Matrix by Row Operations	x+2=5 , -2x+y=5	$x + 2 = 5$ , $- 2 x + y = 5$
15617	Solve Using a Matrix by Row Operations	-x+3y+z=9 , 2x+5y=27 , 3x+y-2z=-18	$- x + 3 y + z = 9$ , $2 x + 5 y = 27$ , $3 x + y - 2 z = - 18$
15618	Solve Using a Matrix by Row Operations	-x+y+z=-4 , -x+3y-3z=-18 , 7x-3y-15z=0	$- x + y + z = - 4$ , $- x + 3 y - 3 z = - 18$ , $7 x - 3 y - 15 z = 0$
15619	Solve Using a Matrix by Row Operations	x-2y+5z=3 , -2x+6y-11z=1 , 3x-16y+20z=-26	$x - 2 y + 5 z = 3$ , $- 2 x + 6 y - 11 z = 1$ , $3 x - 16 y + 20 z = - 26$
15620	Solve Using a Matrix by Row Operations	x-3y-z=-9 , -x+8y-4z=24 , 2x-15y+7z=-45	$x - 3 y - z = - 9$ , $- x + 8 y - 4 z = 24$ , $2 x - 15 y + 7 z = - 45$
15621	Solve Using an Augmented Matrix	4x-8y+3z=-15 , x+4y-z=0 , 8x-y-z=3	$4 x - 8 y + 3 z = - 15$ , $x + 4 y - z = 0$ , $8 x - y - z = 3$
15622	Solve Using a Matrix by Row Operations	x-2y+3z=6 , 2x+y+z=2 , -2x+4y-6z=-12	$x - 2 y + 3 z = 6$ , $2 x + y + z = 2$ , $- 2 x + 4 y - 6 z = - 12$
15623	Solve Using a Matrix by Row Operations	x-2y+3z=7 , 2x+y+z=4 , -3x+2y-2z=-10	$x - 2 y + 3 z = 7$ , $2 x + y + z = 4$ , $- 3 x + 2 y - 2 z = - 10$
15624	Solve Using an Augmented Matrix	-4x+8y=4 , 4x-5y=1	$- 4 x + 8 y = 4$ , $4 x - 5 y = 1$
15625	Solve Using an Augmented Matrix	3x+2y+4z=25 , 2x-y+z=3 , 6x+5y-z=17	$3 x + 2 y + 4 z = 25$ , $2 x - y + z = 3$ , $6 x + 5 y - z = 17$
15626	Solve Using an Augmented Matrix	-3x-2y=2 , 6x+6y=5	$- 3 x - 2 y = 2$ , $6 x + 6 y = 5$
15627	Find the Determinant	[[-9,-3],[6,12]]	$[\begin{array}{c} - 9 & - 3 \\ 6 & 12 \end{array}]$
15628	Find the Determinant	[[5,7,1],[-2,-1,6],[5,7,1]]	$[\begin{array}{c} 5 & 7 & 1 \\ - 2 & - 1 & 6 \\ 5 & 7 & 1 \end{array}]$
15629	Find the Determinant	[[x,y,z],[u,v,w],[-3,-4,1]]	$[\begin{array}{c} x & y & z \\ u & v & w \\ - 3 & - 4 & 1 \end{array}]$
15630	Find the Inverse	[[-4,-7],[3,5]]^-1	${[\begin{array}{c} - 4 & - 7 \\ 3 & 5 \end{array}]}^{- 1}$
15631	Find the Determinant	[[-5,4,1],[3,-2,7],[2,0,6]]	$[\begin{array}{c} - 5 & 4 & 1 \\ 3 & - 2 & 7 \\ 2 & 0 & 6 \end{array}]$
15632	Find the Inverse	[[10,1],[-1,0]]	$[\begin{array}{c} 10 & 1 \\ - 1 & 0 \end{array}]$
15633	Find the Inverse	-4a=[[4,-2],[0,-5]]	$- 4 a = [\begin{array}{c} 4 & - 2 \\ 0 & - 5 \end{array}]$
15634	Find the Inverse	A=[[a,b],[c,d]]	$A = [\begin{array}{c} a & b \\ c & d \end{array}]$
15635	Find Reduced Row Echelon Form	[[1,1,11000],[0.7,0.8,865]]	$[\begin{array}{c} 1 & 1 & 11000 \\ 0.7 & 0.8 & 865 \end{array}]$
15636	Find Reduced Row Echelon Form	[[1,2,3],[4,5,6]]	$[\begin{array}{c} 1 & 2 & 3 \\ 4 & 5 & 6 \end{array}]$
15637	Find the Inverse	[[7,-9],[-3,4]]	$[\begin{array}{c} 7 & - 9 \\ - 3 & 4 \end{array}]$
15638	Find the Inverse	[[5,7],[2,3]]	$[\begin{array}{c} 5 & 7 \\ 2 & 3 \end{array}]$
15639	Find the Inverse	[[7,0],[1,0]]	$[\begin{array}{c} 7 & 0 \\ 1 & 0 \end{array}]$
15640	Find the Inverse	[[3,-2,1],[3,-1,-2],[3,-2,-3]]	$[\begin{array}{c} 3 & - 2 & 1 \\ 3 & - 1 & - 2 \\ 3 & - 2 & - 3 \end{array}]$
15641	Find the Inverse	[[4,3,0],[2,0,1],[-3,x,-1]]=5	$[\begin{array}{c} 4 & 3 & 0 \\ 2 & 0 & 1 \\ - 3 & x & - 1 \end{array}] = 5$
15642	Find the Inverse	[[4,-3],[3,-2]]	$[\begin{array}{c} 4 & - 3 \\ 3 & - 2 \end{array}]$
15643	Find the Inverse	[[-5,1],[-7,1]]	$[\begin{array}{c} - 5 & 1 \\ - 7 & 1 \end{array}]$
15644	Evaluate the Limit	( limit as y approaches 8 of 3-5y^4)/(y^7-2y^3+1)	$\frac{lim_{y \to 8} 3 - 5 y^{4}}{y^{7} - 2 y^{3} + 1}$
15645	Evaluate the Limit	( limit as x approaches -5 of 4x^2+21x+5)/(3x^2+17x+10)	$\frac{lim_{x \to - 5} 4 x^{2} + 21 x + 5}{3 x^{2} + 17 x + 10}$
15646	Evaluate the Limit	( limit as x approaches 8 of 6x+4)/(x^4)	$\frac{lim_{x \to 8} 6 x + 4}{x^{4}}$
15647	Evaluate the Limit	( limit as x approaches 8 of 6x^4-5x^3-2x+1)/(3x^4-2x-7)	$\frac{lim_{x \to 8} 6 x^{4} - 5 x^{3} - 2 x + 1}{3 x^{4} - 2 x - 7}$
15648	Evaluate the Limit	( limit as x approaches 4 of x^2-3x-4)/(\|x^2-25\|-9)	$\frac{lim_{x \to 4} x^{2} - 3 x - 4}{\| x^{2} - 25 \| - 9}$
15649	Evaluate the Limit	( limit as x approaches 4 of (3x^2+2x)-56)/(2x^2+3x-44)	$\frac{lim_{x \to 4} (3 x^{2} + 2 x) - 56}{2 x^{2} + 3 x - 44}$
15650	Evaluate the Limit	( limit as x approaches 2 of 3x^2+2x+1)/(x^3-8)	$\frac{lim_{x \to 2} 3 x^{2} + 2 x + 1}{x^{3} - 8}$
15651	Evaluate the Limit	( limit as x approaches 2 of x^4-16)/(x^2+x-6)	$\frac{lim_{x \to 2} x^{4} - 16}{x^{2} + x - 6}$
15652	Evaluate the Limit	( limit as x approaches -2 of x-2)/(x^2-4)	$\frac{lim_{x \to - 2} x - 2}{x^{2} - 4}$
15653	Evaluate the Limit	( limit as x approaches 2 of x-2)/( square root of x+2-2)	$\frac{lim_{x \to 2} x - 2}{\sqrt{x + 2} - 2}$
15654	Evaluate the Limit	( limit as x approaches 3 of square root of x-2-1)/(x^2-2x-3)	$\frac{lim_{x \to 3} \sqrt{x} - 2 - 1}{x^{2} - 2 x - 3}$
15655	Evaluate the Limit	( limit as x approaches 0 of tan(5x))/(3x)	$\frac{lim_{x \to 0} \tan (5 x)}{3 x}$
15656	Evaluate the Limit	( limit as x approaches 0 of x-tan(x))/(x^3)	$\frac{lim_{x \to 0} x - \tan (x)}{x^{3}}$
15657	Evaluate the Limit	( limit as x approaches 1 of square root of 8x+1)/(2(x-1))+(3x)/(1-x^2)	$\frac{lim_{x \to 1} \sqrt{8 x + 1}}{2 (x - 1)} + \frac{3 x}{1 - x^{2}}$
15658	Evaluate the Limit	( limit as x approaches 1 of cube root of x- square root of x^2-x-1)/(x-1)	$\frac{lim_{x \to 1} \sqrt[3]{x} - \sqrt{x^{2} - x} - 1}{x - 1}$
15659	Evaluate the Limit	( limit as x approaches 2 of x^4+x^3-24)/(x^2-4)	$\frac{lim_{x \to 2} x^{4} + x^{3} - 24}{x^{2} - 4}$
15660	Find Reduced Row Echelon Form	[[2,7,15,-12],[4,7,13,-10],[3,6,12,-9]]	$[\begin{array}{c} 2 & 7 & 15 & - 12 \\ 4 & 7 & 13 & - 10 \\ 3 & 6 & 12 & - 9 \end{array}]$
15661	Find Reduced Row Echelon Form	[[6],[4]]	$[\begin{array}{c} 6 \\ 4 \end{array}]$
15662	Find the Determinant	[[4,8,9],[6,6,8],[1,1,1]]	$[\begin{array}{c} 4 & 8 & 9 \\ 6 & 6 & 8 \\ 1 & 1 & 1 \end{array}]$
15663	Find Reduced Row Echelon Form	[[6],[2]]	$[\begin{array}{c} 6 \\ 2 \end{array}]$
15664	Transpose	[[1,2,3,4],[5,6,7,8]]	$[\begin{array}{c} 1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \end{array}]$
15665	Evaluate the Limit	( limit as h approaches 0 of cube root of x+h- cube root of x)/h	$\frac{lim_{h \to 0} \sqrt[3]{x + h} - \sqrt[3]{x}}{h}$
15666	Evaluate the Limit	limit as x approaches 3 of (5x^2-8x-13)/(x^2-5)	$lim_{x \to 3} \frac{5 x^{2} - 8 x - 13}{x^{2} - 5}$
15667	Evaluate the Limit	( limit as x approaches 1/3 of 3x-1)/(9x^2-1)	$\frac{lim_{x \to \frac{1}{3}} 3 x - 1}{9 x^{2} - 1}$
15668	Evaluate the Limit	( limit as x approaches 0 of ( square root of x^2+6x+13)- square root of 13)/x	$\frac{lim_{x \to 0} (\sqrt{x^{2} + 6 x + 13}) - \sqrt{13}}{x}$
15669	Evaluate the Limit	( limit as x approaches 0 of (x+4)^4-256)/x	$\frac{lim_{x \to 0} {(x + 4)}^{4} - 256}{x}$
15670	Evaluate the Limit	( limit as x approaches 0 of x^3)/(tan(x)-sin(x))	$\frac{lim_{x \to 0} x^{3}}{\tan (x) - \sin (x)}$
15671	Find the Variables	[[x],[y],[z]]=[[1.0,0.6,0],[0.9,1.0,0.8],[0.5,0.6,1.0]][[x],[y],[z]]	$[\begin{array}{c} x \\ y \\ z \end{array}] = [\begin{array}{c} 1 & 0.6 & 0 \\ 0.9 & 1 & 0.8 \\ 0.5 & 0.6 & 1 \end{array}] [\begin{array}{c} x \\ y \\ z \end{array}]$
15672	Find the Variables	[[x+1,2,3],[4,y-1,5],[u,-1,z+2]]=[[2x-1,t+1,3],[v+1,-3,5],[-4,w-1,2z-1]]	$[\begin{array}{c} x + 1 & 2 & 3 \\ 4 & y - 1 & 5 \\ u & - 1 & z + 2 \end{array}] = [\begin{array}{c} 2 x - 1 & t + 1 & 3 \\ v + 1 & - 3 & 5 \\ - 4 & w - 1 & 2 z - 1 \end{array}]$
15673	Simplify the Matrix	[[0,1,2,3,4,5,6],[3,-2,-7,-2,3,-2,-7]]	$[\begin{array}{c} 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ 3 & - 2 & - 7 & - 2 & 3 & - 2 & - 7 \end{array}]$
15674	Simplify the Matrix	2([[2,-3],[4,1],[-5,0],[2,-3]]-[[-1,0],[4,-6],[-3,-2],[1,-7]])	$2 ([\begin{array}{c} 2 & - 3 \\ 4 & 1 \\ - 5 & 0 \\ 2 & - 3 \end{array}] - [\begin{array}{c} - 1 & 0 \\ 4 & - 6 \\ - 3 & - 2 \\ 1 & - 7 \end{array}])$
15675	Multiply the Matrices	[[cos(pi/2),-sin(pi/2)],[sin(pi/2),cos(pi/2)]][[0,9,0,10],[8,7,0,0]]	$[\begin{array}{c} \cos (\frac{π}{2}) & - \sin (\frac{π}{2}) \\ \sin (\frac{π}{2}) & \cos (\frac{π}{2}) \end{array}] [\begin{array}{c} 0 & 9 & 0 & 10 \\ 8 & 7 & 0 & 0 \end{array}]$
15676	Multiply the Matrices	[[72,0],[0,72]][[3,9],[7,-3]]	$[\begin{array}{c} 72 & 0 \\ 0 & 72 \end{array}] [\begin{array}{c} 3 & 9 \\ 7 & - 3 \end{array}]$
15677	Multiply the Matrices	[[5,-5],[1,1]][[7,1],[0,-1],[3,7]]	$[\begin{array}{c} 5 & - 5 \\ 1 & 1 \end{array}] [\begin{array}{c} 7 & 1 \\ 0 & - 1 \\ 3 & 7 \end{array}]$
15678	Find the Variables	[[5,-3x],[y,-6]]=[[5,18],[-4,-6]]	$[\begin{array}{c} 5 & - 3 x \\ y & - 6 \end{array}] = [\begin{array}{c} 5 & 18 \\ - 4 & - 6 \end{array}]$
15679	Find the Variables	3A+4B=[[9,3],[5,3]][[2,9],[8,8]]	$3 A + 4 B = [\begin{array}{c} 9 & 3 \\ 5 & 3 \end{array}] [\begin{array}{c} 2 & 9 \\ 8 & 8 \end{array}]$
15680	Find the Variables	[[x],[y],[z]]=[[1.0,0.3,0],[0.5,1.0,0.4],[0.4,0.5,1.0]]	$[\begin{array}{c} x \\ y \\ z \end{array}] = [\begin{array}{c} 1 & 0.3 & 0 \\ 0.5 & 1 & 0.4 \\ 0.4 & 0.5 & 1 \end{array}]$
15681	Find the Variables	[[5,1],[-2,-3]][[a],[b]]+[[5],[2]]=[[-11],[-2]]	$[\begin{array}{c} 5 & 1 \\ - 2 & - 3 \end{array}] [\begin{array}{c} a \\ b \end{array}] + [\begin{array}{c} 5 \\ 2 \end{array}] = [\begin{array}{c} - 11 \\ - 2 \end{array}]$
15682	Simplify the Matrix	[[7],[5]]	$[\begin{array}{c} 7 \\ 5 \end{array}]$
15683	Simplify the Matrix	[[1,1,1,15],[0,2,1,14],[1,2,1,19]]	$[\begin{array}{c} 1 & 1 & 1 & 15 \\ 0 & 2 & 1 & 14 \\ 1 & 2 & 1 & 19 \end{array}]$
15684	Simplify the Matrix	[[1,1],[1,2]][[2,-1],[-1,5k]]	$[\begin{array}{c} 1 & 1 \\ 1 & 2 \end{array}] [\begin{array}{c} 2 & - 1 \\ - 1 & 5 k \end{array}]$
15685	Simplify the Matrix	[[-4,-5],[-6,-1]][[-6,-3],[5,2]]	$[\begin{array}{c} - 4 & - 5 \\ - 6 & - 1 \end{array}] [\begin{array}{c} - 6 & - 3 \\ 5 & 2 \end{array}]$
15686	Simplify the Matrix	[[2,3],[4,5]][[3],[4]]	$[\begin{array}{c} 2 & 3 \\ 4 & 5 \end{array}] [\begin{array}{c} 3 \\ 4 \end{array}]$
15687	Find the Determinant	A=[[5,0,4],[-8,4,0],[6,-4,4]]	$A = [\begin{array}{c} 5 & 0 & 4 \\ - 8 & 4 & 0 \\ 6 & - 4 & 4 \end{array}]$
15688	Find the Determinant	[[1,0,1],[8,-54,1],[-1,-7,-1]]	$[\begin{array}{c} 1 & 0 & 1 \\ 8 & - 54 & 1 \\ - 1 & - 7 & - 1 \end{array}]$
15689	Find the Determinant	[[4/5,4],[2/3,5]]	$[\begin{array}{c} \frac{4}{5} & 4 \\ \frac{2}{3} & 5 \end{array}]$
15690	Find the Determinant	A=[[-8,4],[2,-1]]	$A = [\begin{array}{c} - 8 & 4 \\ 2 & - 1 \end{array}]$
15691	Find the Determinant	[[2,-2],[7,-7]]	$[\begin{array}{c} 2 & - 2 \\ 7 & - 7 \end{array}]$
15692	Find the Determinant	[[-2,5,4],[3,-2,1],[1,6,-3]]	$[\begin{array}{c} - 2 & 5 & 4 \\ 3 & - 2 & 1 \\ 1 & 6 & - 3 \end{array}]$
15693	Find the Determinant	[[10,-13,1],[-10,6,1],[-9,5,1]]	$[\begin{array}{c} 10 & - 13 & 1 \\ - 10 & 6 & 1 \\ - 9 & 5 & 1 \end{array}]$
15694	Find the Determinant	[[-1,cos(c),cos(b)],[cos(c),-1,cos(a)],[cos(b),cos(a),-1]]	$[\begin{array}{c} - 1 & \cos (c) & \cos (b) \\ \cos (c) & - 1 & \cos (a) \\ \cos (b) & \cos (a) & - 1 \end{array}]$
15695	Multiply the Matrices	[[1,5,6],[2,-4,0]][[6,4],[-2,0],[8,0]]	$[\begin{array}{c} 1 & 5 & 6 \\ 2 & - 4 & 0 \end{array}] [\begin{array}{c} 6 & 4 \\ - 2 & 0 \\ 8 & 0 \end{array}]$
15696	Multiply the Matrices	3[[-3,2,0],[1,-1,-2]]	$3 [\begin{array}{c} - 3 & 2 & 0 \\ 1 & - 1 & - 2 \end{array}]$
15697	Multiply the Matrices	[[0,-2],[3,2],[1,-5]][[-2,3,1],[3,-2,4]]	$[\begin{array}{c} 0 & - 2 \\ 3 & 2 \\ 1 & - 5 \end{array}] [\begin{array}{c} - 2 & 3 & 1 \\ 3 & - 2 & 4 \end{array}]$
15698	Subtract the Matrices	[[1,0],[0,1]][[0.8,0.1],[0.1,0.7]]	$[\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}] [\begin{array}{c} 0.8 & 0.1 \\ 0.1 & 0.7 \end{array}]$
15699	Add	[[1,3,x],[3,-4,-6],[4,6,9]]=51	$[\begin{array}{c} 1 & 3 & x \\ 3 & - 4 & - 6 \\ 4 & 6 & 9 \end{array}] = 51$
15700	Subtract the Matrices	[[3,5,8],[0,4,-1],[3,1,0]]-[[-2,3,-2],[-4,2,3],[7,-8,4]]	$[\begin{array}{c} 3 & 5 & 8 \\ 0 & 4 & - 1 \\ 3 & 1 & 0 \end{array}] - [\begin{array}{c} - 2 & 3 & - 2 \\ - 4 & 2 & 3 \\ 7 & - 8 & 4 \end{array}]$