Math Problems: Calculus, Geometry, and More

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What is the rate at which the water level is rising when the water is 6 meters deep?

54π m/min

81π m/min

83π m/min

9π m/min (correct)

A 5 cubic centimeter cube is painted on all its sides. If it is sliced into 1 cubic centimeter cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?

48 (correct)

32

65

54

Find the Laplace transform of the function: f(t) = te^sin(3t)

(s-2)^2 - 2s + 5

5(s+2) + 4s - 13

6(s-2) - 4s + 13

3(s-1) - 9s + 90 (correct)

What is the probability of rolling a prime number when tossing two dice?

13/36 Signup and view all the answers

A line has slope -2 and is a distance of 2 units from the origin. What is the area of the triangle formed by this line and the axes?

7 sq.units Signup and view all the answers

Find the equations of the normal lines to the graph of the relation at the point (4, 2)

3x + 6y = 20 Signup and view all the answers

What is the speed of the tip of her shadow moving towards the base of the lamp?

6 ft/sec Signup and view all the answers

What is the equation of the curve that passes through the point (1, 3) and has a slope of -(1 + y/x) at (x, y)?

y2 – 2xy = 4 Signup and view all the answers

What is the equation of the circle passing through the points (3, 8), (9, 6), and (13, -2)?

(x – 2)2 + (y + 3)2 = 108 Signup and view all the answers

If 1 −2 3 0 −2 2 4 1 1 −6 −8 1 −5, what is the value of?

1 Signup and view all the answers

How many ounces of a 30% salt solution must be added to a 50-oz solution that is 10% salt to make a 20% salt solution?

30 Signup and view all the answers

What is the median of the set of observations: 55, 55, 50, 53, 54, 53, 54, 55, 56, 58, 60, 54, 54, 55, 58, 52, 54, 56, 57, 59?

54 Signup and view all the answers

What is the value of lim (x→∞) (2x+1)/(3x+1)?

2/3 Signup and view all the answers

What is the cross product of the vectors {2, -1, 4} and {6, -2, 1}?

7i - 22j + k Signup and view all the answers

At what point on the curve y = x³ + 3x are the values of y' and y'' equal?

(-1, -4) Signup and view all the answers

What is the derivative of y = √x(1+3x²)²?

1+9x² / 2√x(1+3x²)² Signup and view all the answers

What is the rate of change of the area of a circle with respect to its diameter when the diameter is 10?

5π Signup and view all the answers

What is the maximum area of an isosceles triangle if each of its equal sides has a length of 10 centimeters?

75 cm² Signup and view all the answers

What is the equation of the line in the form of ax + by + c = 0?

7x – 12y – 1 = 0 Signup and view all the answers

What is the length of the graph of the function y = x^5 + 1/3x^3 + 20 from x = 1 to x = 2?

1.221 units Signup and view all the answers

If a radioactive material has a half-life of 1 day, what is the amount of material left after 7 days if there were 500 mg initially?

7.8125 mg Signup and view all the answers

If two aircrafts are 50 km and 72 km away from a point O, and the angle between them is 49°, what is the distance between the two aircrafts?

52.1-km Signup and view all the answers

If y = (2x)sin(x), what is the derivative of y with respect to x?

x(2x) sin(x) ln(2x) + cos(x) Signup and view all the answers

If 30% of teenage consumers receive their spending money from part-time jobs, what is the probability that at least three of five randomly selected teenagers will have part-time jobs?

0.254 Signup and view all the answers

What is the angle between AB and AT?

400 Signup and view all the answers

What is the slant height of the roof of the birdhouse?

12 inches Signup and view all the answers

What is the volume of the box to be made?

8 cubic inches Signup and view all the answers

What is the inverse Laplace of F(s) = 1 / s(s + 1)2?

t^2 + 4e^(-t) + 3t + 1 Signup and view all the answers

What is the work required to lift the bottom end of the chain all the way up to the ceiling?

550 ft-lb Signup and view all the answers

What is the probability that one of the four tested fuses is defective if 10% of a lot is actually defective?

0.40 Signup and view all the answers