answer:To differentiate the given function, we can use the sum rule and the power rule of differentiation. The sum rule states that the derivative of a sum of functions is equal to the sum of the derivatives of each function. The power rule states that the derivative of x^n is equal to n x^{n-1}. Applying these rules, we have: f'(x) = frac{d}{dx} left[ e^{frac{5 x}{2}-frac{17}{2}}-frac{1}{e^2} right] f'(x) = frac{d}{dx} left[ e^{frac{5 x}{2}-frac{17}{2}} right] - frac{d}{dx} left[ frac{1}{e^2} right] f'(x) = left( frac{5}{2} right) e^{frac{5 x}{2}-frac{17}{2}} - 0 f'(x) = frac{5}{2} e^{frac{5 x}{2}-frac{17}{2}} Therefore, the derivative of the given function is frac{5}{2} e^{frac{5 x}{2}-frac{17}{2}}. The answer is f'(x) = frac{5}{2} e^{frac{5 x}{2}-frac{17}{2}}

answer:Potential causes for a delayed period include pregnancy, thyroid gland imbalances, hormonal fluctuations, high stress levels, significant changes in physical activity, and illness or infections. It is important to note that these factors can affect menstrual cycles differently, and consulting a healthcare professional can provide more accurate insights into your specific situation.

answer:We can use the following kinematic equation to find the velocity of the garbage can just before it hits the ground: {eq}displaystyle v_f^2 = v_i^2 + 2gd {/eq} where: * {eq}displaystyle v_f{/eq} is the final velocity * {eq}displaystyle v_i{/eq} is the initial velocity (0 m/s, since the can was dropped) * {eq}displaystyle g{/eq} is the acceleration due to gravity (9.81 m/s²) * {eq}displaystyle d{/eq} is the distance fallen (43.0 m) Plugging in the values, we get: {eq}begin{align} displaystyle v_f^2 &= 0^2 + 2(9.81 m/s^2)(43.0 m) &= 843.66 m^2/s^2 v_f &= sqrt{843.66 m^2/s^2} &approx boxed{29.0 m/s} end{align} {/eq} Therefore, the velocity of the garbage can just before it hits the ground is approximately 29.0 m/s.

answer:The geometric mean of a set of numbers is the nth root of the product of the numbers. In this case, we have five numbers, so the geometric mean would be the fifth root of the product of 1, 100000, 625, -3125, and 6. However, since -3125 is a negative number, the product of the numbers will also be negative. The fifth root of a negative number is not a real number, so the geometric mean of the given set of numbers cannot be calculated. The geometric mean cannot be calculated for the given set of numbers because it includes a negative number (-3125). The geometric mean is only defined for positive numbers.