Final answer:
The quadratic equation 4tx^2 - 7x + 9t = 0 with two equal roots and t > 0 can be solved using the quadratic formula. Plugging the coefficients into the formula, we find that t = 5.
Step-by-step explanation:
The given quadratic equation is 4tx^2 - 7x + 9t = 0. We are told that this equation has two equal roots and t > 0. In order to solve for t, we can rearrange the equation to get 4tx^2 - 7x + 9t = 0.
Next, we can apply the quadratic formula, which states that the solutions to the quadratic equation ax^2 + bx + c = 0 are given by x = (-b ± √(b^2 - 4ac))/(2a). In this case, the quadratic equation is t^2 + 10t - 200 = 0, where a = 1, b = 10, and c = -200.
Plugging these values into the quadratic formula, we get t = (-10 ± √(10^2 - 4*1*(-200)))/(2*1). Simplifying further, we have t = (-10 ± √(100 + 800))/2, t = (-10 ± √900)/2, and t = (-10 ± 30)/2. So the two solutions for t are t = 10/2 = 5 and t = -40/2 = -20. Since t > 0, we can conclude that the value of t is only 5.