Chapter 1.1, Problem 22ES

answer the question in image.

x If f(x) = = L* f(t)dt then find the value of ƒ (ln 7). f: R R is continuous everywhere.

An eccentric, compressive 270-lb force P is applied to the end of a cantilever beam. Replace P with an equivalent force-couple system at G.

100 identical balls are rolling along a straight line. They all have speed equal to v, but some of them might move in opposite directions. When two of them collide they immediately switch their direction and keep the speed v. What is the maximum number of collisions that can happen?  Let f(w) be a function of vector w Є RN, i.e. f(w) = 1+e Determine the first derivative and matrix of second derivatives off with respect to w.   Let A Є RN*N be a symmetric, positive definite matrix and bЄ RN a vector. If x ER, evaluate the integral Z(A,b) = e¯xAx+bx dx as a function of A and b. John throws a fair die with faces labelled 1 to 6. ⚫ He gains 10 points if the die shows 1. ⚫ He gains 1 point if the die shows 2 or 4. • No points are allocated otherwise. Let X be the random variable describing John's gain at each throw. Determine the variance of X.

A 20 lb horizontal force P acts on a bell crank as shown below. (a) Replace P with an equivalent force-couple system at B. (b) Find the two vertical forces at C and D which are equivalent to the couple found in part a

Please solve and explain

i need help please hand written

Not use ai please

i need help please hand written