Help Test on Maths questions?

Question

(B) The instruction on a ready meal indicate that it should be cooked on an oven a temperature of 400F What is this temperatures in degrees Celsius to the nearest degree? Use the formula C=(F-32) x 5/9.

(C) Find the value of 8x + 5y when x=3 and y=-4 ?

(D) Use trial and improvement to find the value of x between 4 and 5 satisfying the equation x^3 - 6x=68
Give your answer correct to one decimal place.

(E) The circumference of the base of a cylinder oil drum is 204cm
(a) Calculate the diameter of the drum.
___________answer in cm?

The drum is 75cm high.
(b) Calculate the volume of the drum. _______answer in cm cubed?

(F) A sum of £800 is invested in a bank for 3 years at rate of 10% per annum compound interest. What is the total amount at the end of 3 years.

(G) The angle of a right angled triangle are (2x+10), (x+20) and 90
Write down an equation for x?

Solve this equation to find the value of x?

Answer 1

(B).

It should be cooked on an oven a temperature (F) = 400F

But  C = (F - 32) × 5 / 9

       C = (400 - 32) × 5 / 9

       C = 368 × 5 / 9

       C = 204.44

This temperature in degrees celsius to the nearest degree = 204⁰C.

 

Answer 2

(C).

Substitute  the values x = 3 and y = -4 in 8x + 5y

8x + 5y = 8(3) + 5(-4)

               = 24 - 20

               = 4.

 

Answer 3

(D).

x³ - 6x = 68

x lies between 4 and 5

let x = 4.5 then the equation becomes

(4.5)³ - 6(4.5) = 68

91.125 -27 = 68

64. 125 = 68  This is wrong

Let x = 4 .6

(4.6)³ - 6(4.6) = 68

97.336 - 27.6 = 68

69.736 = 68 this is wrong

x lies between 4.5 and 4.6

Let x = 4.57

(4.57)³ - 6(4.57) = 68

95.444 - 27.420 = 68

68.024 = 68 (Approximately)

Therefore x = 4.57.

 

Answer 4

The circumference of the base of a cylinder (oil drum)2×π×r = 204cm

2×π×r =204

2r = 204 / π

The diameter of a drum = 2r = 204cm  / π

Substitute π = 3.14

the diameter of a cylinder(2r) = 64.968cm

The  height  of a drum (h) = 75cm

The volume of a drum (V)    = 4 / 3 π×r^2×h = 1 / 3 π × (2r)^2 × h

Substitute π = 3.14 , 2r =64.968 and h = 75

v = 1 / 3× 3.14×(64.968)^2 ×75

Therefore v = 331336cube-cms.

 

 

Comments

E - b) Formula for volume of the cylinder V = π r² h

In this case 2r = 204/3.14

Therfore r = 32.48cm and h = 75 cm

V = 3.14  (32.48)² (75)

V = 248440.8192

Volume of the oil drum  is 248441 cm³

Answer 5

The circumference of the base of a cylinder (oil drum)2×π×r = 204cm

2×π×r =204

2r = 204 / π

The diameter of a drum = 2r = 204cm  / π

Substitute π = 3.14

the diameter of a cylinder = 64.968cm.

Answer 6

(F)

A sum of rupees invested in bank : P = 800

Rate                                              : R = 10%

Time                                              : n = 3 years

The total amount                           :A = p(1 + R / 100)ⁿ

                                                       A = 800(1 + 10 / 100)³

                                                       A = 800(1.1)³

                                                       A = 1064.8.   

 

Answer 7

(G)

The angles of a right angled triangle are (2x + 10)⁰ , (x + 20)⁰ and 90⁰

The sum of the angles = 180⁰

2x + 10 + x + 20 + 90 = 180

3x + 120 = 180

3x = 60

x = 20⁰.