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 Vsphere = 4/3 πr3 as a function of x (radius), and x (radius) as a function of t (time).

A.   V(t) = 5/2 πt3 C.   V(t) = 9/2 πt3
B.   V(t) = 7/2 πt3 D.   V(t) = 3/2 πt3

 

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 m2 and L = 2,236 m
B.   A = 950,160 m2 and L = 2,122 m
C.   A = 946,350 m2 and L = 2,495 m
D.   A = 939,120 m2 and L = 2,018 m

 

Problem 920 | Additional Centroidal Load to Eliminate Tensile Stress Anywhere Over the Cross Section

Problem 920
A compressive load P = 100 kN is applied, as shown in Fig. 9-8a, at a point 70 mm to the left and 30 mm above the centroid of a rectangular section for which h = 300 mm and b = 250 mm. What additional load, acting normal to the cross section at its centroid, will eliminate tensile stress anywhere over the cross section?
 

920-eccentrically-loaded-rectangular-section.jpg

 

Problem 919 | Additional Axial Compression Load for the Section to Carry No Tensile Stress

Problem 919
From the data in Prob. 918, what additional load applied at the centroid is necessary so that no tensile stress will exist anywhere on the cross-section?
 

Solution 919

Problem 918 | Stress at Each Corner of Eccentrically Loaded Rectangular Section

Problem 918
A compressive load P = 12 kips is applied, as in Fig. 9-8a, at a point 1 in. to the right and 2 in. above the centroid of a rectangular section for which h = 10 in. and b = 6 in. Compute the stress at each corner and the location of the neutral axis. Illustrate the answers with a sketch.
 

figure_9-8a_eccentrically_loaded_column.jpg

 

Eccentrically Loaded Short Compression Member

Consider the cross-section below. A compressive load P is applied at any point (ex, ey) with respect to the principal axes x and y. The moment of P about these axes are respectively
 

$M_x = Pe_y$     and     $M_y = Pe_x$

 

figure_9-9a_eccentrically_loaded_section.jpg

 

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

 

Problem
A salesperson earns \$600 per month plus a commission of 20% of sales. Find the minimum amount of sales needed to receive a total income of at least \$1500 per month.

A.   \$1500 C.   \$4500
B.   \$3500 D.   \$2500

 

Problem
The tide in Bay of Fundy rises and falls every 13 hours. The depth of the water at a certain point in the bay is modeled by a function d = 5 sin (2π/13)t + 9, where t is time in hours and d is depth in meters. Find the depth at t = 13/4 (high tide) and t = 39/4 (low tide).

  1. The depth of the high tide is 15 meters and the depth of the low tide is 3 meters.
  2. The depth of the high tide is 16 meters and the depth of the low tide is 2 meters.
  3. The depth of the high tide is 14 meters and the depth of the low tide is 4 meters.
  4. The depth of the high tide is 17 meters and the depth of the low tide is 1 meter.

 

Problem
The number of hours daylight, D(t) at a particular time of the year can be approximated by
 

$D(t) = \dfrac{K}{2}\sin \left[ \dfrac{2\pi}{365}(t - 79) \right] + 12$

 

for t days and t = 0 corresponding to January 1. The constant K determines the total variation in day length and depends on the latitude of the locale. When is the day length the longest, assuming that it is NOT a leap year?

A.   December 20 C.   June 20
B.   June 19 D.   December 19

 

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