# Differential Calculus

**Problem**

Determine the radius of curvature of the curve $x = y^3$ at point (1, 1).

A. 5.27 | C. 5.56 |

B. 5.65 | D. 5.72 |

- Read more about Determine the radius of curvature of the curve x = y^3 at point (1, 1)
- Log in or register to post comments
- 3572 reads

**Problem**

Gas is escaping from a spherical balloon at a constant rate of 2 ft^{3}/min. How fast, in ft^{2}/min, is the outer surface area of the balloon shrinking when the radius is 12 ft?

A. 1/2 | C. 1/3 |

B. 1/5 | D. 1/4 |

**Problem**

Which of the following is the derivative with respect to *x* of $(x + 1)^3 - x^3$?

A. 6x + 3 |
C. 1 + 2x - 3x^{2} |

B. 3x^{2} + 2x + 1 |
D. 6x - 3 |

- Read more about Which of the following is the derivative with respect to x of (x + 1)^3 - x^3?
- Log in or register to post comments
- 137 reads

**Problem**

The formula $v = \sqrt{2gh}$ give the velocity, in feet per second, of an object when it falls *h* feet accelerated by gravity *g*, in feet per second squared. If *g* is approximately 32 feet per second squared, find how far an object has fallen if its velocity is 80 feet per second.

A. 80 feet | C. 70 feet |

B. 100 feet | D. 90 feet |

- Read more about How Far An Object Has Fallen If Its Velocity Is 80 Feet Per Second
- Log in or register to post comments
- 1447 reads

**Problem**

A meteorologist is inflating a spherical balloon with a helium gas. If the radius of a balloon is changing at a rate of 1.5 cm/sec., express the volume *V* of the balloon as a function of time *t* (in seconds). Hint: Use composite function relationship *V*_{sphere} = 4/3 π*r*^{3} as a function of *x* (radius), and *x* (radius) as a function of *t* (time).

A. V(t) = 5/2 πt^{3} |
C. V(t) = 9/2 πt^{3} |

B. V(t) = 7/2 πt^{3} |
D. V(t) = 3/2 πt^{3} |

- Read more about Volume of Inflating Spherical Balloon as a Function of Time
- Log in or register to post comments
- 1400 reads

**Problem**

A farmer owned a square field measuring exactly 2261 m on each side. 1898 m from one corner and 1009 m from an adjacent corner stands Narra tree. A neighbor offered to purchase a triangular portion of the field stipulating that a fence should be erected in a straight line from one side of the field to an adjacent side so that the Narra tree was part of the fence. The farmer accepted the offer but made sure that the triangular portion was a minimum area. What was the area of the field the neighbor received and how long was the fence? Hint: Use the Cosine Law.

A. A = 972,325 m^{2} and L = 2,236 m |

B. A = 950,160 m^{2} and L = 2,122 m |

C. A = 946,350 m^{2} and L = 2,495 m |

D. A = 939,120 m^{2} and L = 2,018 m |

- Read more about Smallest Triangular Portion From A Square Lot
- Log in or register to post comments
- 1507 reads

**Problem**

A rectangular waterfront lot has a perimeter of 1000 feet. To create a sense of privacy, the lot owner decides to fence along three sides excluding the sides that fronts the water. An expensive fencing along the lot’s front length costs Php25 per foot, and an inexpensive fencing along two side widths costs only Php5 per foot. The total cost of the fencing along all three sides comes to Php9500. What is the lot’s dimensions?

A. 300 feet by 100 feet | C. 400 feet by 200 feet |

B. 400 feet by 100 feet | D. 300 feet by 200 feet |

- Read more about Dimensions of the Lot for a Given Cost of Fencing
- Log in or register to post comments
- 703 reads

**Problem**

A conveyor is dispersing sands which forms into a conical pile whose height is approximately 4/3 of its base radius. Determine how fast the volume of the conical sand is changing when the radius of the base is 3 feet, if the rate of change of the radius is 3 inches per minute.

A. 2π ft/min | C. 3π ft/min |

B. 4π ft/min | D. 5π ft/min |

- Read more about Rate of Change of Volume of Sand in Conical Shape
- Log in or register to post comments
- 3767 reads

**Problem**

A Toyota Land Cruiser drives east from point *A* at 30 kph. Another car, Ford Expedition, starting from *B* at the same time, drives S30°W toward *A* at 60 kph. *B* is 30 km from *A*. How fast in kph is the distance between two cars changing after 30 minutes? Hint: Use the Cosine Law.

A. 70 kph | C. 55 kph |

B. 80 kph | D. 60 kph |

- Read more about Velocity of Separation: How fast is the distance between two cars changing?
- Log in or register to post comments
- 3140 reads

**Problem**

Find *y’* if *x* = 2 arccos 2*t* and *y* = 4 arcsin 2*t*.

A. 2 | C. 4 |

B. -2 | D. -4 |

- Read more about Find y’ if x = 2 arccos 2t and y = 4 arcsin 2t
- Log in or register to post comments
- 2973 reads