Stumps

Question 1

Set 1 Problem 37: A pyramid having an altitude of h is divided into 3 parts by 2 planes passed parallel to the base. These planes are at distances of h/3 and 2/3h from the base. Determine the volume of the middle part if the volume of the pyramid is 180 cm³.

Answer 1

46.67 cm³ (p.12)

Question 2

Set 1 Problem 66: A vat with 2,000 liters of beer contains 4% alcohol (by volume). Beer with 6% alcohol is pumped into the vat at a rate of 20 liters/minute and the mixture is pumped out at the same rate. What is the percentage of alcohol after an hour?

Answer 2

4.9% (p.16)

Question 3

Set 2 Problem 23: Find the dy²/dx² of y=sin²3x.

Answer 3

18cos6x (p.26)

Question 4

Set 2 Problem 39: Solve the differential equation (D²+1)y=0 where D is a differential operator.

Answer 4

y=C1cosx+C2sinx (p.29)

Question 5

Set 2 Problem 57: The probability of Steve Carry to hit a 3-point is 0.80. How many attempts will he make in order to make sure of at least 90% having a 3-point shot?

Answer 5

4 (p.32)

Question 6

Set 2 Problem 71: Evaluate the limit of (1-sinx) to the power 1/x as x approaches zero.

Answer 6

1/e (p.36)

Question 7

Set 2 Problem 72: One ship is sailing south at a rate of 5 knots, and another east at a rate of 10 knots. At 2 P.M. the second ship was at the place occupied by the first ship one hour before. At what time was the distance between them not changing?

Answer 7

1:48 P.M. (p.36)

Question 8

Ship A left a port at 12:00 noon and sails N 42°18’ E at a rate of 3 mph. At 2:00 PM, ship B starts from the same port and goes S 44°28’ E at a rate of 4 mph. Compute the following.
Set 3 Problem 22: What time after 12:00 noon when B is directly south of A?

Answer 8

9:07 PM (p.44)

Question 9

Set 3 Problem 23: Two secants PAB and PCD are drawn to a circle from external point P and intersect the circle at A, B, C, and D, with A and C nearer to P. Angle PBC = 42°, angle BPC = 30°, BC is the diameter of the circle, and PA = 25 cm. Compute the distance AB.

Answer 9

16.03 cm (p.45)

Question 10

Set 3 Problem 64: Find the value x_0 as prescribed by the generalized law of the mean, given f(x)=3x+1 and g(x)=x²-1, 0≤x≤3.

Answer 10

3/2 (p.53)

Question 11

Set 4 Problem 47: A model of a boat is made to scale 1:100. If the mass of the model is 10 g, what is the mass of the actual boat in kg. The model and the actual are made of the same material.

Answer 11

10,000 kg (p.67)

Question 12

Set 7 Problem 25: Find the general solution of the differential equation, y”-7y’+12y=0.

Answer 12

Equation 7.1 (p.115)

Question 13

Set 9 Problem 44: Represent the family of curves y=e^(-cx) by a differential equation.

Answer 13

xy=ylny (p.152)

Question 14

Set 10 Problem 9:. Solve the differential equation: y’=cscx+ycotx; if y=1 when x=π/2.

Answer 14

y=cosx-sinx (p.163)