SET 4 (p. 55) Flashcards
- A 3-degree simple curve has an external distance of 9.12 m. What is the central angle using chord basis?
24.80°
- An employee is earning P25,000 a month and he can afford to purchase a car which will require a down payment of P115,000 and a monthly amortization of 30% of his salary. What is the maximum value of a car that he can purchase if the balance is paid by end of the month payments in 4 years, the first payment is due at the end of the first month. Money is worth 18% compounded monthly?
P370,319 (p. 61)
- Find the area of a piece of land with an irregular boundary as follows:
(p. 11)
The stations are on a straight line boundary. Use Trapezoidal Rule.
170.65 m²
- Mc Naldo’s Deli offers a lunch special in which you can choose a sandwich, a side dish, and a beverage. If there are 10 different sandwiches, 12 different side dishes, and 7 different beverages from which to choose, how many lunch special can you order?
840
- Compute the total number of 8-letter arrangements of the letters of the word ENGINEER.
3,360 (p. 62)
- It is the term of the angle that the sides of a soil bank or pile naturally form with the horizontal when the excavated soil is dumped onto the pile.
Angle of repose
- A machine has a first cost of P 580,000 and estimated to have a book value of P 42,000 at the end of its 10-year operational life. Money is worth 12%. Compute the book value after 4 years using the Declining Balance Method.
P 202,936 (p. 62)
24: Find the sum to infinity of the series 4, 4/3, 4/9,…..
6 (p. 63)
- A triangle has vertices at A(1,3), B(7,0), and C(4,6). Locate the coordinates the orthocenter.
(3,4) (p. 63)
Find the capacity of the following tanks whose shape and dimensions are given:
30: A tank in the form of a cylinder with diameter 6 m and a height of 7.5 m.
212.06 m^3 (p. 64)
- Find the angle between the curves xy = 4 and x^2 = 2y.
71.57°
- How long will it take in years money to quadruple if it earns 14% compounded continuously?
10 (p. 65)
37: What is the derivative of 4cos(2-x^3)?
12x^2sin(2-x^3) (p. 65)
38: A closed traverse has the following data:
(p. 12)
Compute the distance CD in meters.
77.60 m
- Determine the capitalized cost of an equipment whose first cost is P284,600 with a salvage value of P 5,000 after its life of 5 years. Money is worth 10%.
P 724,578
- A projectile is thrown from the top of a building 30 m high above the ground with a velocity of 300 m/s directed at an angle of 20° from the horizontal. How long will the ball hit the ground?
32.2 sec
- Given the inequality 3 < x < 7 and 6 > x > 2. What are the possible values of x?
3 < x < 6
45: How many integers do the solutions of the inequalities 3x - 5 > 7 and x < or equal to 18 - x share?
5
46: Find the solution set: |3-2x|≥7
(-∞,-2)U(5,∞) (p. 66)
- The volume of a square prism is numerically equal to its lateral area. Calculate the length of the side of the base if its height is not equal to the length of its base.
4 (p. 67)
- A point within a equilateral triangle has distances of 3 m, 4 m, and 5 m respectively from the vertices.
Compute the distance from the circumcenter of the circle to one of the sides.
1.95 m
- Given the following notes from BM_12 to BM_14:
(p. 12)
Compute the difference in elevation between BM_12 and BM_13.
4.51 m
59:. A highway curve having a radius of 340 ft is banked so that there will be no lateral pressure on the car’s wheel at a speed of 45 kph. What is the angle of elevation of the embankment in degrees?
8.74°
- The slope of a line joining a moving point (1,-5) is always twice the slope of the line joining it to the origin. Find the equation of the locus of the moving point.
xy+5x+2y=0 (p. 69)
- Find the first derivative of y=x^lnx.
1-lnx^2x
68: Find the equation of the normal to the curve y + (x+y)^(1/2) = x at (3, 1).
5x + 3y = 18 (p. 70)
- Find the area bounded by the parabolas x = y² - 4y and x = 2y - y².
9
- Given that cos A = 3s. Find the tangent of A.
((1-9s^2)^1/2)/3s (p. 71)
- There exists a value of x such that the tangent of the expression (2x+18) is equal to the cotangent of the expression (4x-12). The value of x could be
14°
74: A tangent and a secant are drawn to a circle from the same external point. If the internal segment of the secant is 6 units and the tangent is 8 units long to the point of tangency, determine the length of the secant.
11.44 units (p. 72)
