A ladder that is 5 meters long is leaning against a
wall. The vertical height from the base of the wall to the
top of the ladder is 3 meters. If ∠θ is the angle that the
ladder makes with the ground, what is the approximate
measure of ∠θ?

What is the point of inflection for the function f(x)=2cos4x on the interval (0, pi/2)

More challenges: 1) factor out the indicated quantity.8mn² + 7mn - m : factor out the quantity -m2) factor the polynomial by grouping.2vw + 7cv + 14cw + 49c²3) factor completely using the difference of squares along with factoring by grouping.25v³ - 25v² - 4v + 44) factor the sum of cubes. 125x³ + 645) q³ + 27r³6) factor completely. use difference of squares.729p^6 - 6^67) solve the equation(7x + 4)(9x - 1) = 08) a. find the values of x for which f (x) = 0b. find f (0)f (x) = x² + 2x - 489) find the x and y-intercepts for the function defined by y = f (x)f (x) = (x + 3)(x + 4)(x - 1)²10) factor the trinomial completely by using any method. remember to look for a common factor first. 3v² - 2v - 16

You make a necklace using blue, purple, and green beads in a ration of 1: 1: 2. you use the total of 168 beads. how many green beads in the necklace?