Engr. Christian Baldo

TOPNOTCHER’S BOARD EXAMINATION INSTRUCTION: Select the correct answer for each of the following questions. Mark only one answer for each item by shading the box corresponding to the letter of your choice on the answer sheet provided. STRICTLY NO ERASURES ALLOWED. Use pencil no. 2 only. 1.

The sum of three numbers is 17. The first is 2 times the second. The third is 5 more than the second. Find the value of the largest of the three numbers. a. 6 c. 8 b. 3 d. 10

2.

Two bicyclists 2 km apart start pedalling toward each other with speeds 9 and 10 kph, respectively. A fly flies at 12 kph from one bicycle to the other, turns around instantly, flies back, etc., until the bicyclists meet. How many kilometres did the fly fly? a. 1.26 km c. 1.60 km b. 2.00 km d. 2.40 km

3.

A chemist has 100 cm3 of 20% acid, the rest being water. She adds pure acid to make the solution 33 & 1/3 % acid. How much water must she then add to return it to 20% acid? a. 20.00 cm3 c. 13.33 cm3 3 b. 80.00 cm d. 16.67 cm3

4.

A sequence is defined by 𝑎𝑛 = 𝑎𝑛−1 + 𝑎𝑛−2 + 𝑎𝑛−3 for 𝑛 ≥ 4. Suppose 𝑎4 = 20, 𝑎5 = 36 and 𝑎7 = 121. What is the value of 𝑎1 ? a. 33 c. 4 b. -33 d. -62

5.

If the odd numbers are grouped in the following way: {1}; {3, 5}; {7, 9, 11}; {13, 15, 17, 19} What is the sum of the numbers in the tenth group? a. 505 c. 495 b. 550 d. 441

6.

7.

8.

9.

10.

The following holds for all 𝑥 ≠ 1, 3 𝑓(3𝑥) = 1+𝑥 Find 3𝑓(2). a. 1 c. 9/5 b. -1 d. 2/3 A ticket fee was P10, but then it was reduced. The number of customers increased by 50% but the amount of money received only increased by 20%. How much was the reduced ticket price? a. P7.50 c. P10.91 b. 9.09 d. P8.00 One laser blast will break asteroids larger than 20 kg into three pieces, each one third of the mass of the original. Asteroids smaller than 20 kg are shattered into dust by the laser. How many laser blasts would be required to reduce a 2000 kg asteroid to dust? a. 243 c. 729 b. 364 d. 121 A quart of liquid contains 10% alcohol, and another 3-quart bottle full of liquid contains 30% alcohol. They are mixed together. What is the percentage of alcohol in the mixture? a. 20% c. 15% b. 25% d. 12%

a. b.

4 43

c. d.

56 47

11.

Jem paid $480 to purchase a certain number of items, but the nice vendor gave her two extra. This decreased the price per item by $1. How many items did she receive (including the two extra)? a. 30 c. 36 b. 34 d. 32

12.

A weightless bar that is 5 m long rests against a slope as shown. If its lower tip is moved 10 mm to the right as indicated, how far will its upper tip move up the slope? Initially, the bar is inclined at angle of 30ᵒ with horizontal.

a. b.

9.68 mm 9.86 mm

c. d.

8.96 mm 8.69 mm

13.

An isosceles triangle has two sides of length 10 and one of length 12. Calculate its area. a. 48 sq. units c. 36 sq. units b. 40 sq. units d. 24 sq. units

14.

Find the altitude drawn to the hypotenuse of a right triangle having legs equal to 5 and 12. a. 15 c. 60/13 b. 13 d. 30/13

15.

It is a regular polygon having 44 diagonals. a. octagon c. nonagon b. undecagon d. decagon

16.

The length of each leg of an isosceles triangle is 𝑠 + 1 and the length of the base is 3𝑠 − 2. Determine all possible values of 𝑠. a. 2 c. 2/3 < 𝑠 < 4 b. 𝑠<4 d. 4

17.

Four circles of radius 4 are arranged so that each is tangent to two others and their centers lie on vertices of a square of side 8. A small circle at the center of the square is tangent to the four circles. Find the area of that small circle. a. 1.765 c. 1.576 b. 1.657 d. 1.414

18.

Let 𝐴𝐵𝐶𝐷 be a rectangle with 𝐵𝐶 = 2𝐴𝐵, and let 𝐵𝐶𝐸 be an equilateral triangle crossing through the rectangle. If 𝑀 is the midpoint of 𝐸𝐶, find the measure of angle 𝐶𝑀𝐷. a. 120ᵒ c. 50ᵒ b. 75ᵒ d. 60ᵒ

19.

An equilateral triangle is inscribed in a circle. Let 𝐷 and 𝐸 be midpoints of two of its sides and let 𝐹 be the point where the line from 𝐷 through 𝐸 meets the circle. Find the ratio of 𝐷𝐸/𝐸𝐹. a. 1.366 c. 0.618 b. 1.618 d. 0.366

20.

Parallel chords in a circle have length 12 and 16, and the distance between them is 7. Find the length of another parallel chord midway between them. a. 15.78 c. 16.28 b. 7.89 d. 8.14

How many integers between 1 and 99, inclusive, are not divisible by either 3 or 7?

ENGR. CHRISTIAN BALDO

1

TOPNOTCHER’S BOARD EXAMINATION 21.

22.

23.

24.

25.

If all people eat the same amount of pizza, and a pizza 12 inches in diameter serves two people, how many inches in diameter should each of two pizzas be in order to serve three people? Hint: Pizzas are circular and are eaten entirely. a. 18 c. 6√3 b. 9 d. 6√6 Circle B passes through the center of circle A and is tangent to it. Circle C passes through the center of circle B and is tangent to it. What fraction of the area of circle A lies inside circle B but outside circle C? a. 3/16 c. 2/3 b. 1/3 d. 2/9 The point (-3,2) lies in which quadrant? a. I c. III b. II d. IV Which of the following is the equation for the axis of symmetry of 𝑥 = 2𝑦 2 − 12𝑦 + 1? a. 𝑦 = −3 c. 𝑦=3 b. 𝑥=3 d. 𝑥 = −3 What are the asymptotes of the hyperbola whose equation is: (𝑦 + 1)2 (𝑥 − 1)2 − =1 16 4 In slope-intercept form? a. 𝑦 = −2𝑥 + 3, 𝑦 = 2𝑥 − 1 b. 𝑦 = 2𝑥 − 3, 𝑦 = −2𝑥 + 1 c. 𝑦 = −2𝑥 − 3, 𝑦 = 2𝑥 + 1 d. 𝑦 = 2𝑥 + 3, 𝑦 = −2𝑥 − 1

26.

Where is the center of the curve whose equation is given by 𝑥 2 + 𝑦 2 − 6𝑥 + 14𝑦 = 400? a. (6, -14) c. (-6, 14) b. (3, -7) d. (-3, 7)

27.

Find the equation of a parabola with vertex at (1,4) and directrix at 𝑥 = −3. a. 𝑥 − 1 = 8𝑦(𝑦 + 4) b. 16𝑥 = 𝑦 2 + 8𝑦 + 32 c. 𝑥 = 16𝑦 2 + 128𝑦 + 257 d. 𝑦 = 16𝑥 2 − 32𝑥 + 12

28.

Find the value of ℎ𝑘 if 3𝑥 + 𝑘𝑦 + 2 = 0 and 5𝑥 − 𝑦 + ℎ = 0 determine the same line. a. -2/3 c. -2 b. -5/3 d. -7/3

29.

Find the area of the region common to the circles (𝑥 − 3)2 + (𝑦 − 12)2 = 144 and (𝑥 + 4)2 + (𝑦 + 12)2 = 169 a. 0 c. 13π b. 25π d. 12π

30.

31.

32.

The focus of 𝑦 = −0.5𝑥 2 − 𝑥 + 0.5 is (𝑎, 𝑏). Find the value of 𝑎 + 𝑏. a. -1.5 c. 0.5 b. -0.5 d. 1.5 A circle centered at the origin is tangent to the line 𝑥 𝑦 + =1 7 24 What is the length of the radius of the circle? a. 25/2 c. 168/31 b. 625/31 d. 168/25 The foci of the conic 9𝑥 2 + 4𝑦 2 + 36𝑥 − 24𝑦 + 36 = 0 lies along the line given by: a. 𝑥 = −2 c. 𝑥=2

b.

𝑦 = −√5

d.

𝑦 = √5

33.

How many parabolas pass through the points (3,5), (1,4) and (-3,8)? a. 0 c. 2 b. 1 d. infinitely many

34.

Evaluate:

1 − cos 𝑥 𝑥→0 𝑥2 c. -1/2 d. 2 lim

35.

a. 1/2 b. 0 Evaluate:

𝜋𝑥

lim(2 − 𝑥)tan( 2 )

a. b. 36.

37.

∞ 535.5

𝑥→0

c. d.

1.9 1

Differentiate: 𝑦 = sec(𝑥 2 + 2) a. 2𝑥 cos(𝑥 2 + 2) b. − cos(𝑥 2 + 2) cot(𝑥 2 + 2) c. 2𝑥 sec(𝑥 2 + 2) tan(𝑥 2 + 2) d. cos(𝑥 2 + 2) Find the slope of the tangent to the curve 𝑦 = 2𝑥 − 𝑥 2 + 𝑥 3 at (0,2). a. -4 c. 3 b. 2 d. 2

38.

Find the equation of the normal to 𝑥 2 + 𝑦 2 = 5 at the point (2,1). Hint: Normal line is a line perpendicular to the tangent. a. 𝑥+𝑦 =1 c. 𝑦 = 2𝑥 b. 2𝑥 + 3𝑦 = 3 d. 𝑥 = 2𝑦

39.

Find the rate of change of the volume of a cube in cm3/s that has surface area changing at a rate of 4 cm2/s when the volume of the cube is 8 cm3. a. 1 c. 3 b. 4 d. 2

40.

Find the absolute maximum value of the function 𝑓(𝑥) = 3𝑥 5 − 5𝑥 3 − 1 on the interval [−2,2]. a. 35 c. 10 b. 44 d. 55

41.

The equation of an ellipse is given by: (𝑥 − 2)2 (𝑦 + 4)2 + =1 𝑎2 𝑏2 Find the rate of change in the area of the ellipse in units/s2 if the minor axis is decreasing at a rate of 0.4 units/s and the major axis is increasing at a rate of 0.6 units/s and the major axis has length 10 units and minor axis has length 6 units. a. 1.588 c. -0.628 b. 2.068 d. -1.885

42.

Find the second derivative of 𝑦 with respect to 𝑥 for the curve given by 𝑥 = 2𝑡 2 and 𝑦 = 4𝑡 − 3. a. 1/(2𝑡 2 ) c. −1/(4𝑡 2 ) b. 1/(2𝑡) d. −1/(4𝑡 3 )

43.

A cylindrical gas tank is to hold 0.9 m3 of fuel. What is the diameter of a tank that will minimize the cost of sheet metal used to construct the tank? a. 0.52 m c. 1.05 m b. 0.67 m d. 1.34 m How many points of inflection does the graph of 𝑦 = 2𝑥 + cos 𝑥 2 have in the interval (0,5)? a. 1 c. 8 b. 5 d. 4

44.

ENGR. CHRISTIAN BALDO

2

TOPNOTCHER’S BOARD EXAMINATION 45.

At what point does the line tangent to 𝑓(𝑥) = 2𝑥 3 − 4𝑥 + 3 at 𝑥 = 3 intersect with the perpendicular to the tangent of 𝑔(𝑥) = 2𝑥 2 − 3/8 at 𝑥 = 0.25? (1/12, 22/3) (−1/12, 13/6) a. c. (−1/12, 11/6) d. (1/6, 11/12) b.

46.

Find the area of the region bounded by the graphs of 𝑦 = 𝑥 2 + 2, 𝑦 = −𝑥, 𝑥 = 0, 𝑥 = 1. a. 17/6 c. 16/7 b. 6/17 d. 7/16

47.

Find the area of the region bounded by the graphs of 𝑓(𝑥) = 2 − 𝑥 2 , 𝑔(𝑥) = 𝑥 a. 4.5 c. 0.2 b. 5.4 d. 2.2

48.

49.

The sine and cosine curves intersect infinitely many times, bounding regions of equal areas. Find the area of one of these regions. a. 2√2 c. 𝜋/2 b. 𝜋 d. 2/𝜋 Find the area of the region between the graphs of 𝑓(𝑥) = 3𝑥 3 − 𝑥 2 − 10𝑥, 𝑔(𝑥) = 2𝑥 − 𝑥 2 a. 21 c. 24 b. 12 d. 42

50.

Find the area of the region bounded by the graphs of 𝑥 = 3 − 𝑦 2 , 𝑥 = 𝑦 + 1. a. 4.5 c. 0.2 b. 5.4 d. 2.2

51.

Find the volume of the solid formed by revolving the region bounded by the graph of 𝑓(𝑥) = √sin 𝑥 about the 𝑥 − 𝑎𝑥𝑖𝑠. a. 3π c. 2π b. π/2 d. π

52.

Find the volume of the solid formed by revolving the region bounded by the graphs of 𝑓(𝑥) = 2 − 𝑥 2 about 𝑦 − 𝑎𝑥𝑖𝑠. a. 10.1 c. 6.3 b. 11.1 d. 3.4

53.

Find the sum of the values for 𝑥 that satisfy the Mean Value Theorem for Integrals for the function 𝑓(𝑥) = (𝑥 − 1)2 Over the interval [4, 7]. a. 4.7 c. 5.6 b. 5.4 d. 4.3

54.

55.

56.

57.

Find the average value of the function 𝑓(𝑥) = sin(2𝑥) from 𝑥 = 0.25𝜋 to 𝑥 = 0.50𝜋. a. 1/𝜋 c. √2/2 b. d. 2/𝜋 √3/2 If two fair dice are rolled, what is the probability that the sum is greater than seven? a. 1/4 c. 5/12 b. 7/12 d. 1/3 How many different arrangements of the letters from the word TENNESSEE are possible? a. 3780 c. 7560 b. 15120 d. 10080 If two fair dice are rolled, what is the probability that two different prime numbers appear? a. 1/6 c. 2/5 b. 1/3 d. ¼

58.

A committee of 2 Democrats and 2 Republicans must be chosen from a group of 10 Democrats and 8 Republicans to advise President Obama. How many different ways can this committee of 4 politicians be formed? a. 5880 c. 630 b. 1260 d. 73

59.

In a class of 30 students, 18 people like M & M’s, 15 like Skittles and 10 like both candies. What is the probability that a student selected at random does not like either candy? a. 13/30 c. 1/5 b. 4/15 d. 8/15

60.

How many 3 digit numbers have exactly one zero? a. 81 c. 162 b. 648 d. 100

61.

What is the probability of getting a total of 9 when three dice are thrown? a. 1/9 c. 25/216 b. 5/36 d. 13/108

Situation 1: Cardo has a large number of colored blocks. The blocks come in the following colros: Red, Orange, Yellow, Green, Blue, Indigo and Violet. Cardo creates every possible 4-block rearrangement of distinct colors, sorts them by alphabetizing them by color name and then spreads them out on a long table. 62. The first rearrangement is BGIO. Cardo’s favourite number is 211. Which rearrangement is in position 211? a. GIBY c. GOBR b. GVOR d. GRIV 63. Cardo’s favourite colors are Green, Blue, Indigo and Violet. How many of the rearrangements contain all four of those colors? a. 24 c. 35 b. 840 d. 120 64. Cardo decided to separate all the rearrangements into sets with the following property: Each set would contain only rearrangements with the same set of four colors. How many different sets would he have? a. 24 c. 35 b. 840 d. 120 65.

How many distinguishable arrangements are there for the letters in “BESTSELLER”? a. 3628800 c. 604800 b. 151200 d. 25200

66.

Solve for 𝑛 such that 𝑛𝐶4 = 5(𝑛𝐶5) a. 3 c. 6 b. 5 d. 10

67.

Tian and Marie are playing tennis. If the odds of Tian winning are 3 to 8, what is the probability that Marie will win? a. 3/8 c. 8/11 b. 5/8 d. 3/11

68.

There are 120 students in the senior class at Adamson University. 57 students take Biology, 62 students take Chemistry and 59 students take Physics. 22 take Biology and Chemistry, 21 take Biology and Physics and 25 take Chemistry and Physics. 10 students take all three classes and every student in the senior class takes at least one of the three sciences. Find the probability of a student taking at least two classes, given that the student is taking Physics.

ENGR. CHRISTIAN BALDO

3

TOPNOTCHER’S BOARD EXAMINATION a. b. 69.

70.

71.

72.

73.

74.

75.

76.

56/59 36/59

c. d.

26/59 23/59

In 2005, the total debt (credit cards, auto loans, home mortgages, etc.) amounted to more than 100% of total disposable income for the average P.H. household. If your total disposable income is P250000, how much interest can you expect to pay when the average interest rate on your debt is 12% per year? a. P20000 c. P50000 b. P30000 d. P25000 A recent government study reported that a college degree is worth an extra $23000 per year in income compared to what a high-school graduate makes. If the interest rate is 6% per year and you work for 40 years, what is the future compound amount of this extra income? a. $3255596 c. $87512 b. $3559526 d. P78215 A micro-brewery is considering the installation of a newly designed boiler system that burns the dried, spent malt and barley grains from the brewing process. The boiler will produce process steam that powers the majority of the brewery’s energy operations, saving $450000 per year over the boiler’s expected life of 10 years. If the interest rate is 12% per year, how much money can the brewery afford to invest in the new boiler system? a. $2254590 c. $2452095 b. $2245095 d. $2542590 If you purchase a car from CEWO Sports Cars, you expect to have four free oil changes per yaer during the five years you keep the car. Each oil change would normally cost you Php 1500. If you save your money in a mutual fund earning 2% per quarter, how much are the oil changes worth to you at the time you buy the car? a. P24527 c. P24527 b. P24257 d. P22457 You borrow Php 750000 from your credit union to purchase a used car. The interest rate on your loan is 0.25% per month and you will make a total of 36 monthly payments. What is your monthly payment? a. P21825 c. P25128 b. P22581 d. P25182 What lump amount would a father on the day his son is born have to be paid into an account bearing interest of 12% per year in order to provide withdrawals of P100000 on each of the son’s 18th, 19th, 20th and 21st birthdays? a. P44223 c. P42342 b. P42243 d. P43224 Suppose that certain end of year cash flows are expected to be P5000 for the second year, P10000 for the third year and P15000 for the fourth year and that, if interest is 15% per year, find the uniform annual equivalent value at the end of each of the four years. a. P6236 c. P6623 b. P6632 d. P6326 When you take your first job, you decide to start saving right away for your retirement. You put P5000 per year into the company’s 401k plan, which averages 8% interest per year. Five years

later, you move to another job and start a new 401k plan. You never get around to merging the funds in the two plans. If the first plan continued to earn interest at the rate of 8% per year for 35 years after you stopped making contributions, how much is the account worth? a. P436379 c. P436973 b. P437693 d. P433697 77.

On your 23rd birthday, you decide to invest P22500 in a mutual fund earning 7% per year. You will continue to make annual deposits of P22500 until you retire at age 63. You expect to increase your annual deposits by an average of 4% each year during this time. How much money will you have accumulated in your mutual fund when you retire? a. P507490 c. P504790 b. P509740 d. P509470

78.

Permanent mineral rights on a parcel of land are purchased for an initial lump-sum payment of Php 1000000. Profits from mining activities are Php 120000 each year and these profits are expected to continue indefinitely. Calculate the interest rate earned on the initial investment. a. 8% c. 10% b. 12% d. 9%

79.

Php 1000 is deposited in a savings account that pays 6% annual interest and no money is withdrawn for three years. Find the account balance after three years. a. P1282 c. P1213 b. P1123 d. P1191

80.

Determine the amount of money a person must deposit 3 years from now in order to withdraw P20000 per year for 10 years beginning 15 years from now at an interest rate of 10% per year. a. P30100 c. P34402 b. P38600 d. P43073

81.

A 2-m high cylindrical tank has a diameter of 1.5 m. Upon suspending vertically by its sides, the force exerted on the tank at the bottom if it’s half full is closest to a. 34.67 kN c. 69.34 kN b. 17.34 kN d. 14.14 kN

82.

The base dimensions of a rectangular swimming pool is 22 m x 10 m. If the pool is filled with water up to a depth of 3.2 m, which of the following most nearly gives the maximum hydrostatic force on the pool’s side faces? a. 1079 kN c. 1105 kN b. 502 kN d. 3453 kN

83.

A rectangular plate 1.5 m x 3.75 m is immersed vertically in water in such a way that its longer dimension coincides with the water surface. Calculate the total hydrostatic force acting on the plate. a. 41.39 kN c. 155.20 kN b. 103.46 kN d. 55.18 kN

84.

A solid sphere with radius 1.2 m floats half submerged in a liquid whose specific gravity is 1.15. Which of the following most nearly gives the weight of concrete required as an external anchor to just submerge the sphere completely? The sphere and the concrete will be interconnected by a tension rope with negligible mass. The density of the concrete is 2400 kg/m3.

ENGR. CHRISTIAN BALDO

4

TOPNOTCHER’S BOARD EXAMINATION a. b.

78.39 kN 40.83 kN

c. d.

69.99 kN 60.86 kN

Situation 2: A semi-circular plate whose radius is 0.75 m is placed vertically in oil of specific gravity 0.905 such that its diameter is parallel to the oil surface and lies above the semi-circular arc. If the distance from the oil surface to the diameter is 2.5 m. 85. Which of the following most nearly gives the distance from the oil surface to the centroid of the plate? a. 2.18 m c. 2.82 m b. 3.25 m d. 0.32 m 86. Which of the following most nearly gives the moment of inertia of the plate with respect to a horizontal axis passing through the centroid? a. 0.0347 m4 c. 0.1243 m4 b. 0.0548 m4 d. 0.0621 m4 87. Which of the following most nearly gives the location of the force acting on one side of the plate from the plate’s centroid? a. 64.51 mm c. 96.91 mm b. 13.95 mm d. 21.63 mm 88. Calculate the maximum force acting on one side of the plate. a. 2.55 kN c. 25.49 kN b. 17.10 kN d. 22.11 kN Situation 3: An isosceles triangular plate whose base is 3.5 m is immersed vertically in water such that its base is parallel to and 2.5 m from the water surface. The triangle is positioned in a way that the other vertex lies below the base. 89. Calculate the hydrostatic force acting on the plate if it has a perimeter of 10 m. a. 42.92 kN c. 148.19 kN b. 160.46 kN d. 199.93 kN 90. Calculate the hydrostatic force acting on the plate if it has an area of 8.75 m2. a. 255.47 kN c. 500.72 kN b. 316.78 kN d. 357.66 kN 91. Calculate the perimeter of the plate if the hydrostatic force acting on the plate is 585 kN. a. 14.2 m c. 12.5 m b. 14.5 m d. 18.0 m Situation 4: A 15 m high vertical wall separates seawater (𝑠. 𝑔. = 1.031) from freshwater. The wall is placed on a support that cannot be subjected to horizontal forces. 92. Calculate the net hydrostatic force acting on the wall if the depth of seawater at one side of the wall is 13 m while the other is full of freshwater up to the top of the wall. a. 248.98 kN c. 283.20 kN b. 34.21 kN d. 308.89 kN 93. If a cable whose tensile capacity is 60 MPa is used to balance the hydrostatic forces in the previous problem, which of the following most nearly gives its required cross-sectional area? a. 4720 mm2 c. 4150 mm2 2 b. 571 mm d. 5149 mm2 94. If the seawater’s depth is 7 m, calculate the required depth of the freshwater to maintain the wall’s equilibrium state. a. 8.886 m c. 7.108 m b. 8.314 m d. 7.072 m 95.

96.

A 14 m long rectangular barge sinks 12 mm in water upon adding a mass of 1000 kg at its center. Calculate the change in its wetted surface area in contact with water. Assume that the portion of the barge above the initial water level is dry. a. 6720 cm2 c. 2395 cm2 b. 4789 cm2 d. 3360 cm2

Situation 5: The 2 m wide gate is hinged at point 𝐻. The liquid has a specific gravity of 1.18.

97.

Determine the hydrostatic force acting on the gate. a. 262 kN c. 94 kN b. 309 kN d. 111 kN

98.

Calculate the required force 𝑇 to hold the gate in the position as shown. a. 31 kN c. 103 kN b. 87 kN d. 37 kN

99.

A wooden cube whose edge is 30 cm is to be submerged partially to an oil-water system having a huge area. The depth of oil above the water surface is 15 cm. Calculate the surface area of the wood that is not in contact with any of the liquids. The densities of the wood and oil are 721 kg/m 3 and 903 kg/m3 respectively. a. 830 cm2 c. 207 cm2 b. 1107 cm2 d. 1730 cm2

Situation 6: A 15.1 m x 10.3 m x 4.1 m wooden block floats in a liquid whose specific gravity is 0.815. A couple holds the block in the position shown.

100.

Calculate the buoyant force. a. 1865 kN b. 1235 kN

c. d.

5098 kN 2289 kN

Determine the value of the water depth ℎ if a force of 350 kN is needed to open the gate in a manner shown below. The 3 m wide gate appears to be a 90ᵒ arc of a circle with a radius of 𝑅 = 1.3 𝑚. a. 9.62 m c. 7.43 m b. 9.43 m d. 8.83 m

ENGR. CHRISTIAN BALDO

5