E3AP - Math 03

Determine the differential equation of the family of lines passing through (h,k).

The radius of a snowball rolling down a hill is increasing at a rate of 20 cm/min. How fast is its volume increasing when its diameter is 1 m?

Four fair coins are tossed at once. What is the probability of obtaining three heads and one tail?

The second and sixth terms of a geometric progression are 3/10 and 243/160, respectively. What is the first term of this sequence?

A sinking ship signals to the shore for help. Three individuals spot the signal from shore. The first individual is directly perpendicular to the sinking ship and 20 meters inland. The second individual is also 20 meters inland but 100 meters to the right of the first individual. The third is also 20 meters inland but 125 meters to the right of the first individual. How far off shore is the sinking ship?

Determine the equation that expresses the statement. F is directly proportional to y. Symbols a, b, c, and d are constants.

The final scores of students in a graduate course are distributed normally with a mean of 72 and a standard deviation of 10. What is the probability that a student’s score will be between 65 and 78?

A marksman can hit a bull’s-eye from 100 m with three out of every four shots. What is the probability that he will hit bull’s-eye with at least one of his next three shots?

A balloon is rising vertically over a point A on the ground at the rate of 15 ft./sec. A point B on the ground level with and 30 ft from A. When the balloon is 40 ft. from A, at what rate is its distance from B changing?

Find dy/dx for the parametric equations given: x = 2t² – t and y = t³ – 2t + 1

What is the general solution to the differential equation y”8y’ + 16y = 0?

Find the parametric equation of the line through the point P(-3, 5, 2) and parallel to the line with equation x = 2t + 5, y = -4t and z = - t + 3.

A point is chosen at random inside a circle having a diameter of 8 inches. What is the probability that the point is at least 1.5 in away from the center of the circle?

Find all values of z for which e^3z = 1.

Evaluate tanh (jπ/3).

Determine the possible number of negative roots of x³ + x² - x – 1 = 0.

From past experience, it is known that 90% of one-year-old children can distinguish their mother’s voice from the voice of a similar sounding female. A random sample of 20 one-year-olds is given this voice recognition test. Find the probability that all 20 children recognized their mother’s voice.

How many positive real roots are there in the polynomial x⁴ - 4x³ + 7x² - 6x – 18 = 0?