Math Problems: Calculus, Geometry, and More
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Questions and Answers

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

  • 54Ï€ m/min
  • 81Ï€ m/min
  • 83Ï€ m/min
  • 9Ï€ 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?

<p>13/36 (A)</p> 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?

<p>7 sq.units (C)</p> Signup and view all the answers

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

<p>3x + 6y = 20 (C)</p> Signup and view all the answers

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

<p>6 ft/sec (A)</p> 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)?

<p>y2 – 2xy = 4 (D)</p> Signup and view all the answers

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

<p>(x – 2)2 + (y + 3)2 = 108 (A)</p> 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?

<p>1 (A)</p> 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?

<p>30 (B)</p> 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?

<p>54 (A)</p> Signup and view all the answers

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

<p>2/3 (A)</p> Signup and view all the answers

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

<p>7i - 22j + k (A)</p> Signup and view all the answers

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

<p>(-1, -4) (C)</p> Signup and view all the answers

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

<p>1+9x² / 2√x(1+3x²)² (A)</p> 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?

<p>5Ï€ (D)</p> 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?

<p>75 cm² (B)</p> Signup and view all the answers

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

<p>7x – 12y – 1 = 0 (B)</p> 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?

<p>1.221 units (A)</p> 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?

<p>7.8125 mg (D)</p> 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?

<p>52.1-km (B)</p> Signup and view all the answers

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

<p>x(2x) sin(x) ln(2x) + cos(x) (A)</p> 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?

<p>0.254 (D)</p> Signup and view all the answers

What is the angle between AB and AT?

<p>400 (A)</p> Signup and view all the answers

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

<p>12 inches (A)</p> Signup and view all the answers

What is the volume of the box to be made?

<p>8 cubic inches (A)</p> Signup and view all the answers

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

<p>t^2 + 4e^(-t) + 3t + 1 (D)</p> 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?

<p>550 ft-lb (D)</p> 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?

<p>0.40 (C)</p> Signup and view all the answers

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