For what values of \( x \) is \( g(x) \cdot f(x) \geq 0 \) if \( x>0 \) ? Determine the positive \( x \)-value for which \( \mathrm{DE}=7,5 \) units.

To determine when \( g(x) \cdot f(x) \geq 0 \) for \( x > 0 \), we need to look at the signs of \( g(x) \) and \( f(x) \). If both functions are positive or both are negative, their product will be non-negative. To find specific points where this holds true, you may need to analyze the functions \( g(x) \) and \( f(x) \)—for instance, finding their roots and intervals of positivity and negativity based on sign changes. Regarding the second part about finding the positive \( x \)-value for which \( \mathrm{DE} = 7.5 \) units, it sounds like a geometry or physics problem, possibly involving distances. Assuming DE refers to distance between points D and E in a coordinate system, this generally involves the distance formula. Set up your equation with the coordinates of points D and E, calculate the distance, and solve for \( x \) accordingly to find the specified distance of 7.5 units. Just remember to double-check if any constraints affect the values of \( x \)!