Aplane rises from take-off and flies at an angle of 4° with the horizontal runway. when it has gained 450 feet, find the distance, to the nearest foot, the plane has flown. an airplane is at vertex b of a right triangle that has a horizontal side a c, a vertical side b c of length 450 feet, and a dashed hypotenuse a b of unknown length c that rises from left to right. angle c is the right angle and angle a measures 4°.

Eric has challenged himself to walk 24,000 steps in 4 days. if eric walks the same number of steps each day, which function represents the number of steps eric still needs to walk to reach his goal with respect to the number of days since he started his challenge? a. y = 8,000x − 24,000 b. y = -8,000x + 24,000 c. y = 6,000x − 24,000 d. y = -6,000x + 24,000

On a string instrument, the length of a string varies inversely as the frequency of its vibrations. an 11-inch string has a frequency of 400 cylces per second. find the frequency of a 10-icnch string.

Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x^2 + 3x + 4, [−1, 1] no, f is continuous on [−1, 1] but not differentiable on (−1, 1). no, f is not continuous on [−1, 1]. yes, f is continuous on [−1, 1] and differentiable on (−1, 1) since polynomials are continuous and differentiable on . there is not enough information to verify if this function satisfies the mean value theorem. yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem.