How To Solve These Equations? Need A Clue/Hint

[mymachine]

Homework Statement

$F(t)=$

$\frac{1}{6}(7-t)^{2}(1,2)+\frac{1}{3}(-t^{2}+12t-34)(3,5)+\frac{1}{6}(t-5)^{2}(6,2)$__________if__________$5≤t<7$

and

$\frac{1}{3}(8-t)^{2}(3,5)+\frac{1}{3}(-2t^{2}+30t-110)(6,2)+\frac{1}{3}(t-7)^{2}(9,4)$__________if__________$7≤t≤8$

Homework Equations

None

The Attempt at a Solution

None because I don't understand

I wouldn't ask if I do understand.

This is a spline equation.

Thank you

 

[SammyS]

Homework Statement

$F(t)=$

$\frac{1}{6}(7-t)^{2}(1,2)+\frac{1}{3}(-t^{2}+12t-34)(3,5)+\frac{1}{6}(t-5)^{2}(6,2)$__________if__________$5≤t<7$

and

$\frac{1}{3}(8-t)^{2}(3,5)+\frac{1}{3}(-2t^{2}+30t-110)(6,2)+\frac{1}{3}(t-7)^{2}(9,4)$__________if__________$7≤t≤8$

Homework Equations

None

The Attempt at a Solution

None because I don't understand

I wouldn't ask if I do understand.

This is a spline equation.

Thank you

The title of you thread mentions "solving these equations", but there's nothing to solve.

It looks as though F(t) is a piecewise defined function.

Are the quantities which look like points actually supposed to be position vectors? (I'm referring to (1, 2), (3, 5), and (6, 2) in the first expression.)

 

[mymachine]

The title of you thread mentions "solving these equations", but there's nothing to solve.

I am not sure.

It looks as though F(t) is a piecewise defined function.

Yes, it might be.

Are the quantities which look like points actually supposed to be position vectors? (I'm referring to (1, 2), (3, 5), and (6, 2) in the first expression.)

It looks like a cartesian coordinate to me.

What should I do?

Should I multiply them?

Note this is a function of spline.