Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
28201	Find the Equation with Real Coefficients	x=sec(t) , y=tan(t)	$x = \sec (t)$ , $y = \tan (t)$
28202	Find the Equation with Real Coefficients	x-2y=1 , y=x^3-5x^2	$x - 2 y = 1$ , $y = x^{3} - 5 x^{2}$
28203	Find the Equation with Real Coefficients	x-3y+3z=-4 , 2x+3y-z=15 , 4x-3y-z=19	$x - 3 y + 3 z = - 4$ , $2 x + 3 y - z = 15$ , $4 x - 3 y - z = 19$
28204	Find the Equation with Real Coefficients	x-3y=4 , 2x-6y=q	$x - 3 y = 4$ , $2 x - 6 y = q$
28205	Find the Equation with Real Coefficients	x-4y-3z=13 , -x-5y-4z=11 , -2x+2y+z=-8	$x - 4 y - 3 z = 13$ , $- x - 5 y - 4 z = 11$ , $- 2 x + 2 y + z = - 8$
28206	Find the Equation with Real Coefficients	x-4z=1 , 2x-y-6z=4 , 2x+3z-2z=8	$x - 4 z = 1$ , $2 x - y - 6 z = 4$ , $2 x + 3 z - 2 z = 8$
28207	Find the Equation with Real Coefficients	a-y+Z=8 , 2y-Z=-7 , 2a+3y=1	$a - y + Z = 8$ , $2 y - Z = - 7$ , $2 a + 3 y = 1$
28208	Find the Equation with Real Coefficients	xy=z^2 , x+y+z=39 , x^2+y^2+z^2=2613	$x y = z^{2}$ , $x + y + z = 39$ , $x^{2} + y^{2} + z^{2} = 2613$
28209	Find the Equation with Real Coefficients	x-y-z=0 , 2y+z=3 , 2x+y=9	$x - y - z = 0$ , $2 y + z = 3$ , $2 x + y = 9$
28210	Find the Equation with Real Coefficients	y=1.5a , b=a+1.5a , c=b+1.5b , d=c+1.5c	$y = 1.5 a$ , $b = a + 1.5 a$ , $c = b + 1.5 b$ , $d = c + 1.5 c$
28211	Find the Equation with Real Coefficients	y=12+2x , y=-16x^2+24x+6	$y = 12 + 2 x$ , $y = - 16 x^{2} + 24 x + 6$
28212	Find the Equation with Real Coefficients	y=2x-8 , 2x-y=8	$y = 2 x - 8$ , $2 x - y = 8$
28213	Find the Equation with Real Coefficients	y=4a-3 , a=-2x-2	$y = 4 a - 3$ , $a = - 2 x - 2$
28214	Find the Equation with Real Coefficients	y=6-2x , 6x+3y=18	$y = 6 - 2 x$ , $6 x + 3 y = 18$
28215	Find the Equation with Real Coefficients	y-3z=0 , 3x+2y=15 , -x-2y+4z=-5	$y - 3 z = 0$ , $3 x + 2 y = 15$ , $- x - 2 y + 4 z = - 5$
28216	Solve in Terms of the Arbitrary Variable a	15x-9y=-11 , 10x+ay=17	$15 x - 9 y = - 11$ , $10 x + a y = 17$
28217	Solve in Terms of the Arbitrary Variable a	2x-2y+3z=2 , (a+3)x+(a-3)y+z=4 , 3x+2y-z=1	$2 x - 2 y + 3 z = 2$ , $(a + 3) x + (a - 3) y + z = 4$ , $3 x + 2 y - z = 1$
28218	Solve in Terms of the Arbitrary Variable A	3x+4y=A , 6x+8y=10	$3 x + 4 y = A$ , $6 x + 8 y = 10$
28219	Solve in Terms of the Arbitrary Variable A	8kNB+(2kN)(1.4m)=0 , (18kN)A+(-38kN)B=0	$8 k N B + (2 k N) (1.4 m) = 0$ , $(18 k N) A + (- 38 k N) B = 0$
28220	Solve in Terms of the Arbitrary Variable a	a*1=2 , a(n)=3a(n-1)-1	$a \cdot 1 = 2$ , $a (n) = 3 a (n - 1) - 1$
28221	Expand the Logarithmic Expression	log of (x^2)/(yz)	$\log (\frac{x^{2}}{y z})$
28222	Solve in Terms of the Arbitrary Variable a	A=49 , B=64 , a=8	$A = 49$ , $B = 64$ , $a = 8$
28223	Solve in Terms of the Arbitrary Variable a	a=5 , b=8 , C=10	$a = 5$ , $b = 8$ , $C = 10$
28224	Solve in Terms of the Arbitrary Variable a	a=5i+7j , b=-4i+3j	$a = 5 i + 7 j$ , $b = - 4 i + 3 j$
28225	Solve in Terms of the Arbitrary Variable A	A=x-10 , B=4/5x	$A = x - 10$ , $B = \frac{4}{5} x$
28226	Find the Equation with Real Coefficients	f(x)=2x , a=0 , b=6	$f (x) = 2 x$ , $a = 0$ , $b = 6$
28227	Find the Equation with Real Coefficients	fg(7) = square root of x , g(7)=x+9	$f g (7) = \sqrt{x}$ , $g (7) = x + 9$
28228	Find the Equation with Real Coefficients	k=(x+1)/(x-1) , k^2-k=30	$k = \frac{x + 1}{x - 1}$ , $k^{2} - k = 30$
28229	Find the Equation with Real Coefficients	k=0.5 , c=0.2 , f=40	$k = 0.5$ , $c = 0.2$ , $f = 40$
28230	Find the Equation with Real Coefficients	lwh=40 , l=2(w) , h=l+1	$l \cdot w \cdot h = 40$ , $l = 2 (w)$ , $h = l + 1$
28231	Find the Equation with Real Coefficients	p+q=5 , 1/p+1/q=8	$p + q = 5$ , $\frac{1}{p} + \frac{1}{q} = 8$
28232	Find the Equation with Real Coefficients	p+w=300 , p-w=240	$p + w = 300$ , $p - w = 240$
28233	Find the Equation with Real Coefficients	p=144-x^2 , p=48+1/2x^2	$p = 144 - x^{2}$ , $p = 48 + \frac{1}{2} x^{2}$
28234	Find the Equation with Real Coefficients	p=33000+2086 square root of x-1/(8x^2) , x=175	$p = 33000 + 2086 \sqrt{x} - \frac{1}{8 x^{2}}$ , $x = 175$
28235	Find the Equation with Real Coefficients	q=10p+55 , p=500	$q = 10 p + 55$ , $p = 500$
28236	Find the Equation with Real Coefficients	q=30-2p , p=15-1/2q	$q = 30 - 2 p$ , $p = 15 - \frac{1}{2} q$
28237	Find the Equation with Real Coefficients	r=14 , x=4	$r = 14$ , $x = 4$
28238	Find the Equation with Real Coefficients	r=7 , h=3 , k=7	$r = 7$ , $h = 3$ , $k = 7$
28239	Find the Equation with Real Coefficients	sin(x)=12/13 , cos(x)=-5/13	$\sin (x) = \frac{12}{13}$ , $\cos (x) = - \frac{5}{13}$
28240	Find the Equation with Real Coefficients	sin(t)=( square root of 2)/7 , sin(t)^2+cos(t)^2=1	$\sin (t) = \frac{\sqrt{2}}{7}$ , $\sin^{2} (t) + \cos^{2} (t) = 1$
28241	Find the Equation with Real Coefficients	a=9 , t(n)=1/3*(t(n-1))	$a = 9$ , $t (n) = \frac{1}{3} \cdot (t (n - 1))$
28242	Find the Equation with Real Coefficients	a*1=5 , a(n)=4(a(n-1))+1	$a \cdot 1 = 5$ , $a (n) = 4 (a (n - 1)) + 1$
28243	Find the Equation with Real Coefficients	a=-1.359 , b=23.831 , r^2=0.6889 , r=0.83	$a = - 1.359$ , $b = 23.831$ , $r^{2} = 0.6889$ , $r = 0.83$
28244	Find the Equation with Real Coefficients	a=15 , b=36	$a = 15$ , $b = 36$
28245	Find the Equation with Real Coefficients	A=33 , a=19 , b=14	$A = 33$ , $a = 19$ , $b = 14$
28246	Find the Equation with Real Coefficients	a=4 , c=7 , B=55	$a = 4$ , $c = 7$ , $B = 55$
28247	Find the Equation with Real Coefficients	a=5 , b=4/5 , c=6	$a = 5$ , $b = \frac{4}{5}$ , $c = 6$
28248	Find the Equation with Real Coefficients	a=5i+7j , b=-4i+3j	$a = 5 i + 7 j$ , $b = - 4 i + 3 j$
28249	Find the Equation with Real Coefficients	ax+by=0 , a^2x+b^2y=1	$a x + b y = 0$ , $a^{2} x + b^{2} y = 1$
28250	Find the Equation with Real Coefficients	B=36 , a=41 , c=17	$B = 36$ , $a = 41$ , $c = 17$
28251	Find the Equation with Real Coefficients	4x-21y-3z=-29 , -10x+44y-28z=44 , 16x-4y+26z=41	$4 x - 21 y - 3 z = - 29$ , $- 10 x + 44 y - 28 z = 44$ , $16 x - 4 y + 26 z = 41$
28252	Find the Equation with Real Coefficients	4x-2y+5z=6 , 6y-12x-15z=7	$4 x - 2 y + 5 z = 6$ , $6 y - 12 x - 15 z = 7$
28253	Find the Equation with Real Coefficients	-4x-y-8z=-6 , y+z=0 , 4x-7y=6	$- 4 x - y - 8 z = - 6$ , $y + z = 0$ , $4 x - 7 y = 6$
28254	Find the Equation with Real Coefficients	5x-10y=30 , x-2y=6 , 4x-8y=24	$5 x - 10 y = 30$ , $x - 2 y = 6$ , $4 x - 8 y = 24$
28255	Find the Equation with Real Coefficients	6x=54 , x+3y=0	$6 x = 54$ , $x + 3 y = 0$
28256	Find the Equation with Real Coefficients	7x-5y=-21 , 2x=3y-6	$7 x - 5 y = - 21$ , $2 x = 3 y - 6$
28257	Find the Equation with Real Coefficients	8x-14y+3=0 , kx-7y+10=0	$8 x - 14 y + 3 = 0$ , $k x - 7 y + 10 = 0$
28258	Find the Equation with Real Coefficients	9a+3b+c=5 , 4a-2b+c=20 , a-b+c=1	$9 a + 3 b + c = 5$ , $4 a - 2 b + c = 20$ , $a - b + c = 1$
28259	Find the Equation with Real Coefficients	2x+y-3z=4 , 4x+2z=10 , -2x+3y-13z=-8	$2 x + y - 3 z = 4$ , $4 x + 2 z = 10$ , $- 2 x + 3 y - 13 z = - 8$
28260	Find the Equation with Real Coefficients	2x-y+5z=17 , y+2z=3 , z=2	$2 x - y + 5 z = 17$ , $y + 2 z = 3$ , $z = 2$
28261	Find the Equation with Real Coefficients	2x-y=3 , x+3y=33	$2 x - y = 3$ , $x + 3 y = 33$
28262	Find the Equation with Real Coefficients	35x+14y+11z=74 , 100x+10y+260z=380 , 30x+3y+9z=30	$35 x + 14 y + 11 z = 74$ , $100 x + 10 y + 260 z = 380$ , $30 x + 3 y + 9 z = 30$
28263	Find the Equation with Real Coefficients	36=a+b , 8=1/(1/a+1/b)	$36 = a + b$ , $8 = \frac{1}{\frac{1}{a} + \frac{1}{b}}$
28264	Find the Equation with Real Coefficients	3a-4b+2d=1 , ab+2d=-2 , 2a+2b+3d=-3	$3 a - 4 b + 2 d = 1$ , $a b + 2 d = - 2$ , $2 a + 2 b + 3 d = - 3$
28265	Find the Equation with Real Coefficients	3x+2y+z=4 , 2x-3y-z=5 , 5x+12y+5z=2	$3 x + 2 y + z = 4$ , $2 x - 3 y - z = 5$ , $5 x + 12 y + 5 z = 2$
28266	Find the Equation with Real Coefficients	3x+3y-2z=-1 , 2x-y+z=2 , x-5y+4=3	$3 x + 3 y - 2 z = - 1$ , $2 x - y + z = 2$ , $x - 5 y + 4 = 3$
28267	Find the Equation with Real Coefficients	3x+5y=5 , 2x-y=10	$3 x + 5 y = 5$ , $2 x - y = 10$
28268	Find the Equation with Real Coefficients	3x-4y=4 , 6x-8y=5	$3 x - 4 y = 4$ , $6 x - 8 y = 5$
28269	Find the Equation with Real Coefficients	3x-y-z=7 , 2x+5y+5z=-1 , -7x-8y-8z=9	$3 x - y - z = 7$ , $2 x + 5 y + 5 z = - 1$ , $- 7 x - 8 y - 8 z = 9$
28270	Find the Equation with Real Coefficients	4cos(2x)^2-2=0 , x=pi/8	$4 \cos^{2} (2 x) - 2 = 0$ , $x = \frac{π}{8}$
28271	Find the Equation with Real Coefficients	x^2-7xy+6y^2=0 , x^2+xy=42	$x^{2} - 7 x y + 6 y^{2} = 0$ , $x^{2} + x y = 42$
28272	Find the Equation with Real Coefficients	x^3+4x^2-9x-36=0 , x=3	$x^{3} + 4 x^{2} - 9 x - 36 = 0$ , $x = 3$
28273	Find the Equation with Real Coefficients	16x-32y=20 , -8x+16y=-10	$16 x - 32 y = 20$ , $- 8 x + 16 y = - 10$
28274	Find the Equation with Real Coefficients	1z=2(cos(34)+isin(34)) , 2z=5(cos(10)+isin(10))	$1 z = 2 (\cos (34) + i \sin (34))$ , $2 z = 5 (\cos (10) + i \sin (10))$
28275	Find the Equation with Real Coefficients	2(3)=3(3-1) , 2(3)+2(9)=3(9-1) , 2(3)+2(9)+2(27)=3(27-1) , 2(3)+2(9)+2(27)+2(81)=3(81-1)	$2 (3) = 3 (3 - 1)$ , $2 (3) + 2 (9) = 3 (9 - 1)$ , $2 (3) + 2 (9) + 2 (27) = 3 (27 - 1)$ , $2 (3) + 2 (9) + 2 (27) + 2 (81) = 3 (81 - 1)$
28276	Find the Equation with Real Coefficients	21=-2a^2-2b+c , 12=-a^2-b+c , 16=3a^2+3b+c	$21 = - 2 a^{2} - 2 b + c$ , $12 = - a^{2} - b + c$ , $16 = 3 a^{2} + 3 b + c$
28277	Find the Equation with Real Coefficients	-27a^3+9b-3c+d=-150 , -a+b-c+d=-6 , 8a+4b+2c+d=15 , a+b+c+d=15	$- 27 a^{3} + 9 b - 3 c + d = - 150$ , $- a + b - c + d = - 6$ , $8 a + 4 b + 2 c + d = 15$ , $a + b + c + d = 15$
28278	Find the Equation with Real Coefficients	x^2+2y^2=2 , 2x^2-3y=15	$x^{2} + 2 y^{2} = 2$ , $2 x^{2} - 3 y = 15$
28279	Find the Union of the Inequalities	x=y , x+y=12	$x = y$ , $x + y = 12$
28280	Find the Union of the Inequalities	x>0 , y>0 , x+y<10 , x^2+y^2=9	$x > 0$ , $y > 0$ , $x + y < 10$ , $x^{2} + y^{2} = 9$
28281	Find the Union of the Inequalities	5x+6y=30 , 10x+y=30	$5 x + 6 y = 30$ , $10 x + y = 30$
28282	Find the Union of the Inequalities	cos(x)>0 , tan(x)<0	$\cos (x) > 0$ , $\tan (x) < 0$
28283	Find the Union of the Inequalities	x+2y=4 , 3x-y>2	$x + 2 y = 4$ , $3 x - y > 2$
28284	Find the Union of the Inequalities	x-7y<7 , 7x+y>7	$x - 7 y < 7$ , $7 x + y > 7$
28285	Find the Union of the Inequalities	x-y=3 , 2x+3y=6 , y=2	$x - y = 3$ , $2 x + 3 y = 6$ , $y = 2$
28286	Find the Union of the Inequalities	y=1/2x+2 , y<-2/3x-1	$y = \frac{1}{2} x + 2$ , $y < - \frac{2}{3} x - 1$
28287	Find the Union of the Inequalities	y=x^2-2 , x^2+y^2<16	$y = x^{2} - 2$ , $x^{2} + y^{2} < 16$
28288	Find the Union of the Inequalities	y=2 , y>8	$y = 2$ , $y > 8$
28289	Find the Union of the Inequalities	y=3x-1 , y=-3x-1 , x=3	$y = 3 x - 1$ , $y = - 3 x - 1$ , $x = 3$
28290	Find the Union of the Inequalities	y=-5x+4 , 2x-y<-5	$y = - 5 x + 4$ , $2 x - y < - 5$
28291	Find the Union of the Inequalities	y=x-3 , y>-x+2	$y = x - 3$ , $y > - x + 2$
28292	Find the Union of the Inequalities	10x+6y=60 , 10/3x+8/3y=32/3	$10 x + 6 y = 60$ , $\frac{10}{3} x + \frac{8}{3} y = \frac{32}{3}$
28293	Find the Union of the Inequalities	2x+3y=18 , 3x+2y=18	$2 x + 3 y = 18$ , $3 x + 2 y = 18$
28294	Find the Union of the Inequalities	2x+3y=3 , x+y=1	$2 x + 3 y = 3$ , $x + y = 1$
28295	Find the Union of the Inequalities	2x-4y=8 , 3x-2y>6	$2 x - 4 y = 8$ , $3 x - 2 y > 6$
28296	Find the Union of the Inequalities	3x+5y=20 , 3x+1y=16 , -2x+1y=2 , x=0 , y=0	$3 x + 5 y = 20$ , $3 x + 1 y = 16$ , $- 2 x + 1 y = 2$ , $x = 0$ , $y = 0$
28297	Find the Union of the Inequalities	x=5 , y=3 , 2x+3y=37	$x = 5$ , $y = 3$ , $2 x + 3 y = 37$
28298	Find the Union of the Inequalities	x>1 , x>5	$x > 1$ , $x > 5$
28299	Find the Intersection of the Inequalities	cos(x)>0 , csc(x)<0	$\cos (x) > 0$ , $\csc (x) < 0$
28300	Find the Intersection of the Inequalities	tan(x)<0 , csc(x)<0	$\tan (x) < 0$ , $\csc (x) < 0$