Find the velocity, v(t), for an object moving along the x-axis if the acceleration, a(t), is a(t) = 2t + sin(t) and v(0) = 4. (4 points)
a.) v(t) = t2 + cos(t) + 3
b.) v(t) = 2 + cos(t) + 1
c.) v(t) = t2 - cos(t) + 5
d.) v(t) = t2 + sin(t) + 4

! i think the answer is d

Airplane speeds are measured in three different ways: (1) indicated speed, (2) true speed, and (3) ground speed. the indicated airspeed is the airspeed given by an instrument called an airspeed indicator. a plane’s indicated airspeed is different from its true airspeed because the indicator is affected by temperature changes and different altitudes of air pressure. the true airspeed is the speed of the airplane relative to the wind. ground speed is the speed of the airplane relative to the ground. for example, a plane flying at a true airspeed of 150 knots into a headwind of 25 knots will have a ground speed of 125 knots. the problems below refer to static and dynamic pressure. static pressure is used when a body is in motion or at rest at a constant speed and direction. dynamic pressure is used when a body in motion changes speed or direction or both. a gauge compares these pressures, giving pilots an indicated airspeed. in problem #s 1 and 2, use the following information. the indicated airspeed s (in knots) of an airplane is given by an airspeed indicator that measures the difference p (in inches of mercury) between the static and dynamic pressures. the relationship between s and p can be modeled by s=136.4p√+4.5. 1. find the differential pressure when the indicated airspeed is 157 knots. 2. find the change in the differential pressure of an airplane that was traveling at 218 knots and slowed down to195 knots. in problem #s 3 and 4, use the following information. the true airspeed t (in knots) of an airplane can be modeled by t=(1+a50,000) ⋅ s, where a is the altitude (in feet) and s is the indicated airspeed (in knots). 3. write the equation for true airspeed t in terms of altitude and differential pressure p. 4. a plane is flying with a true airspeed of 280 knots at an altitude of 20,000 feet. estimate the differential pressure. explain why you think your estimate is correct.

An entertainment firm offer serveral dj choices and light shows that range in price based on the rental time period. the djs cost between $219 and $369 per night and the light shows cost between $159 and $309 per night. if you are booking both a dj and a light show write a compound inequality that represents the possible total amount you would pay x

The function p(x) is an odd degree polynomial with a negative leading coefficient. if q(x) = x3 + 5x2 - 9x - 45, which statement is true? a. as x approaches negative infinity, p(x) approaches positive infinity and q(x) approaches negative infinity. b. as x approaches negative infinity, p(x) and q(x) approach positive infinity. c. as x approaches negative infinity, p(x) and q(x) approach negative infinity. d. as x approaches negative infinity, p(x) approaches negative infinity and q(x) approaches positive infinity.