Find x
1) x^2*23y^2 = 1.78x10^32*z
2) 1.3*10^-4 x=4.7/x -6.3*10^-3
Please help
x^2*23y^2 = 1.78x10^32*z
x^2 = (1.78x10^32 z)/(23y^2)
x^2 = 7.739x10^30 z/y^2
x = 2.782x10^15 √z/y
Ok. I'll take it as written
(1.3*10^-4 x) = (4.7/x) - 6.3*10^-3
1.3*10^-4 x^2 = 4.7 - 6.3*10^-3 x
0.00013x^2 + 0.0063x - 4.7 = 0
x = -215.91, 167.45
I see you're still using x for both a variable and multiplication
How can you get the answer
x = -215.91, 167.45
To find the value of x in the given equations, let's go step by step.
1) x^2*23y^2 = 1.78x10^32*z
First, divide both sides of the equation by 23y^2:
x^2 = (1.78x10^32*z) / (23y^2)
Next, take the square root of both sides to solve for x:
x = √[(1.78x10^32*z) / (23y^2)]
So, x can be found by taking the square root of the quotient [(1.78x10^32*z) divided by (23y^2)].
2) 1.3*10^-4 x = 4.7/x - 6.3*10^-3
First, multiply both sides of the equation by x to eliminate the denominator:
1.3*10^-4 x^2 = 4.7 - 6.3*10^-3x
Next, rearrange the equation to form a quadratic equation:
1.3*10^-4x^2 + 6.3*10^-3x - 4.7 = 0
Now, solve this quadratic equation using the quadratic formula:
x = [-b ± √(b^2 - 4ac)] / (2a)
For our equation, a = 1.3*10^-4, b = 6.3*10^-3, and c = -4.7.
Substituting these values in the quadratic formula:
x = [-6.3*10^-3 ± √((6.3*10^-3)^2 - 4*(1.3*10^-4)*(-4.7))] / (2*(1.3*10^-4))
Simplifying further:
x = [-6.3*10^-3 ± √(3.969*10^-5 + 2.428*10^-4)] / 2.6*10^-4
Finally, calculate the value(s) of x using a calculator or further simplification, as needed.
Please note that the quadratic equation may yield two possible values for x (+ and -).