solve for unknowns

[fun4life]

hi sorry I am posting 2 questions of different topics but they are similar in way to find value for unknowns


1)t[sup:2uzd8z5n]1/2[/sup:2uzd8z5n](t[sup:2uzd8z5n]1/2[/sup:2uzd8z5n] -6)=-9 Ans says t=9.I am not getting it how to start with?
2)y=x[sup:2uzd8z5n]n[/sup:2uzd8z5n]where n is any integer,Given that the curve passes between the points (2,200) and(2,2000) determine the value of n. ans is 9

Please help to solve it.

 

[mmm4444bot]

1)t[sup984kxhb]1/2[/sup984kxhb](t[sup984kxhb]1/2[/sup984kxhb] -6)=-9 Ans says t=9.I am not getting it how to start with? Start by using the Distributive Property to expand the lefthand side.

Next, move all terms to one side, with zero on the other side.

[t^(1/2)]^2 - 9*[t^(1/2)] - 9 = 0

This is quadratic form. Let's make a temporary substitution, to see it more clearly.

Let z = t^(1/2)

z^2 - 9z - 9 = 0

Find the solutions for z, in this quadratic equation.

Then reverse the substitution by setting each solution equal to t^(1/2), and solve for t.



2)y=x[sup984kxhb]n[/sup984kxhb]where n is any integer,Given that the curve passes between the points (2,200) and(2,2000) determine the value of n. ans is 9

Please help to solve it.



Okay, on this one, you can start by experimenting.

Substitute some integers for n into the formula y=x^n, and then calculate the value of y when x is 2.

When you find n that yields a value for y between 200 and 2000, that's the answer.

 

[fun4life]

Re:

1)t[sup:3987lc7z]1/2[/sup:3987lc7z](t[sup:3987lc7z]1/2[/sup:3987lc7z] -6)=-9 Ans says t=9.I am not getting it how to start with? Start by using the Distributive Property to expand the lefthand side.

Next, move all terms to one side, with zero on the other side.

[t^(1/2)]^2 - 9*[t^(1/2)] - 9 = 0

This is quadratic form. Let's make a temporary substitution, to see it more clearly.

Let z = t^(1/2)

z^2 - 9z - 9 = 0

Find the solutions for z, in this quadratic equation.

Then reverse the substitution by setting each solution equal to t^(1/2), and solve for t.



2)y=x[sup:3987lc7z]n[/sup:3987lc7z]where n is any integer,Given that the curve passes between the points (2,200) and(2,2000) determine the value of n. ans is 9

Please help to solve it.



Hold on.

yes for the second queation there is adiagram but don't know how to post it here.but that is also not very useful.It is just a sketch.

thanks for the 1st one I got it thanking you I was trying to mulptiply bysqrt t on both sides...and got lost..thank you

 

[mmm4444bot]

yes for the second queation there is adiagram but don't know how to post it here.

I edited my first post. Check it out again, for the second exercise.

It looks to me like there are three solutions for n.