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Problem_Solving_05
30問 • 1年前
  • Jacky Shane Luyas Buhia
    • 通報

    問題一覧

  • 1

    Simplify: i²⁹ + i²¹ + i

    A. 3i

  • 2

    Determine the diameter of a closed cylindrical tank having a volume of 11.3 cu.m to obtain minimum surface area.

    C. 2.44

  • 3

    A farmer has enough money to build only 100 meters of fence. What are the dimensions of the field he can enclose the maximum area?

    A. 25 m × 25 m

  • 4

    A fencing is limited to 20 ft length. What is the maximum rectangular area that can be fenced in using two perpendicular corner sides of an existing wall?

    B. 100

  • 5

    A product has a current selling of P 325.00. If its selling price is expected to decline at the rate of 10% per annum because of obsolescence, what will be its selling price four years hence?

    A. P 213.23

  • 6

    If the first term of a G.P. is 9 and the common ratio is -2/3, find the fifth term

    B. 16/9

  • 7

    If the sum is 220 and the first term is 10, find the common difference if the last term is 30.

    A. 2

  • 8

    In how many minutes after 7 o'clock will the hands be directly opposite each other for the first time?

    C. 5.46 minutes

  • 9

    A surveyor wants to know the height of a skyscraper. He places his inclinometer on a tripod 1 m from the ground. At a distance of 50 m from the skyscraper, he records an angle of elevation of 82°.  What is the height of the skyscraper? Give your answer to one decimal place.

    C. 356.8 m

  • 10

    A builder is constructing a roof. The wood he is using for the sloped section of the roof is 4 m long and the peak of the roof needs to be 2 m  high. What angle should the piece of wood make with the base of the roof?

    D. 30°

  • 11

    A helicopter flies 40 km east followed by 105 km south. On what bearing must the helicopter fly to return home directly?

    D. 339°

  • 12

    Find the term involving y⁵ in the expansion of (2x² + y)¹⁰.

    A. 8064 x¹⁰y⁵

  • 13

    Evaluate the log₆(845) = x.

    A. 3.76

  • 14

    What is the value of log to base 10 of 1000³·³ ?

    C. 9.9

  • 15

    Log (MN) is equal to:

    D. Log M + Log N

  • 16

    Find the value of x if log₁₂(x) = 2

    A. 144

  • 17

    Solve for the value of x: log 2x³ + log 6/x = 6.278

    C. 397.56

  • 18

    Given: logb 1024 = 5/2, Find b.

    B. 16

  • 19

    What is the radius of the sphere center at the origin that passes the point 8, 1, 6 ?

    C. √101

  • 20

    If A = -2 - 3i, and B = 3 + 4i, what is A / B ?

    B. - 18 - i / 25

  • 21

    Find the slope of the line 3x + 2y + 1 = 0 ?

    C. - 3/2

  • 22

    What is the moment of inertia of a cylinder of radius 5 m and mass of 5 kg?

    C. 62.5 kg-m²

  • 23

    Two forces of 20 units and 30 units act at right angle. What is the magnitude of the resultant force?

    A. 36

  • 24

    Three forces, 20 N, 30 N and 40 N are in equilibrium. Find the largest angle they make with each other.

    A. 104.48°

  • 25

    An isosceles triangle has a 10 cm base and a 10 cm altitude. Determine the moment of inertia of the triangular area relative to a line parallel to the base and through the upper vertex in cm⁴.

    C. 2500

  • 26

    The cost C of a product is a function of the quantity x of the product: C(x) = x² - 4000x + 50. Find the quantity for which the cost is minimum.

    C. 2000

  • 27

    Radium decomposes at a rate proportional to the amount at any instant. In 100 years, 100 mg of radium decomposes to 96 mg. How many mg will be left after 100 years?

    C. 92.16

  • 28

    Find the general solution of y' = y sec x

    A. y = C (sec x + tan x)

  • 29

    Solve (x + y) dy = (x - y) dx.

    D. x² -2xy + y² = C

  • 30

    An equipment costs P 10,000 with a salvage value of P 500 at the end of 10 years. Calculate the annual depreciation cost by sinking fund method at 4 % interest.

    A. P 791.26

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    問題一覧

  • 1

    Simplify: i²⁹ + i²¹ + i

    A. 3i

  • 2

    Determine the diameter of a closed cylindrical tank having a volume of 11.3 cu.m to obtain minimum surface area.

    C. 2.44

  • 3

    A farmer has enough money to build only 100 meters of fence. What are the dimensions of the field he can enclose the maximum area?

    A. 25 m × 25 m

  • 4

    A fencing is limited to 20 ft length. What is the maximum rectangular area that can be fenced in using two perpendicular corner sides of an existing wall?

    B. 100

  • 5

    A product has a current selling of P 325.00. If its selling price is expected to decline at the rate of 10% per annum because of obsolescence, what will be its selling price four years hence?

    A. P 213.23

  • 6

    If the first term of a G.P. is 9 and the common ratio is -2/3, find the fifth term

    B. 16/9

  • 7

    If the sum is 220 and the first term is 10, find the common difference if the last term is 30.

    A. 2

  • 8

    In how many minutes after 7 o'clock will the hands be directly opposite each other for the first time?

    C. 5.46 minutes

  • 9

    A surveyor wants to know the height of a skyscraper. He places his inclinometer on a tripod 1 m from the ground. At a distance of 50 m from the skyscraper, he records an angle of elevation of 82°.  What is the height of the skyscraper? Give your answer to one decimal place.

    C. 356.8 m

  • 10

    A builder is constructing a roof. The wood he is using for the sloped section of the roof is 4 m long and the peak of the roof needs to be 2 m  high. What angle should the piece of wood make with the base of the roof?

    D. 30°

  • 11

    A helicopter flies 40 km east followed by 105 km south. On what bearing must the helicopter fly to return home directly?

    D. 339°

  • 12

    Find the term involving y⁵ in the expansion of (2x² + y)¹⁰.

    A. 8064 x¹⁰y⁵

  • 13

    Evaluate the log₆(845) = x.

    A. 3.76

  • 14

    What is the value of log to base 10 of 1000³·³ ?

    C. 9.9

  • 15

    Log (MN) is equal to:

    D. Log M + Log N

  • 16

    Find the value of x if log₁₂(x) = 2

    A. 144

  • 17

    Solve for the value of x: log 2x³ + log 6/x = 6.278

    C. 397.56

  • 18

    Given: logb 1024 = 5/2, Find b.

    B. 16

  • 19

    What is the radius of the sphere center at the origin that passes the point 8, 1, 6 ?

    C. √101

  • 20

    If A = -2 - 3i, and B = 3 + 4i, what is A / B ?

    B. - 18 - i / 25

  • 21

    Find the slope of the line 3x + 2y + 1 = 0 ?

    C. - 3/2

  • 22

    What is the moment of inertia of a cylinder of radius 5 m and mass of 5 kg?

    C. 62.5 kg-m²

  • 23

    Two forces of 20 units and 30 units act at right angle. What is the magnitude of the resultant force?

    A. 36

  • 24

    Three forces, 20 N, 30 N and 40 N are in equilibrium. Find the largest angle they make with each other.

    A. 104.48°

  • 25

    An isosceles triangle has a 10 cm base and a 10 cm altitude. Determine the moment of inertia of the triangular area relative to a line parallel to the base and through the upper vertex in cm⁴.

    C. 2500

  • 26

    The cost C of a product is a function of the quantity x of the product: C(x) = x² - 4000x + 50. Find the quantity for which the cost is minimum.

    C. 2000

  • 27

    Radium decomposes at a rate proportional to the amount at any instant. In 100 years, 100 mg of radium decomposes to 96 mg. How many mg will be left after 100 years?

    C. 92.16

  • 28

    Find the general solution of y' = y sec x

    A. y = C (sec x + tan x)

  • 29

    Solve (x + y) dy = (x - y) dx.

    D. x² -2xy + y² = C

  • 30

    An equipment costs P 10,000 with a salvage value of P 500 at the end of 10 years. Calculate the annual depreciation cost by sinking fund method at 4 % interest.

    A. P 791.26