During a rainfall, the depth of water in a rain guage increases at a rate modeled by R(t)=0.5+t cos(πt^3/80), where t is the time in hours since the start of the rainfall and R(t) is measured in centimeters per hour. How much did the depth of water in the rain gauge increase from t=0 to t=3 hours

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

Olivia needs to find the number of 1/3 cups are in 3 cups of rice she use the number line below to find 3 / 1/3 how many 1/3 cup servings of rice are in 3 cups of rice

Victoria created the scatterplot below based on the data in the table for the ages and heights of some teachers in her school. she wants to see if a teachers heigh depends on his or her age. what did she do wrong when she created the scatterplot