# Mathematics

## If P=((Q(R-T))/15 )ã€–^â…“ã€—, make T the subject of the formula.

If P=((Q(R-T))/15 )ã€–^â…“ã€—, make T the subject of the formula.

A. T= (15R-Q)/PÂ³
B. T=Râ€“ 15PÂ³/Q
C. T= (R-15PÂ³)/Q
D. T=(R+PÂ³)/15Q

Correct Option: Answer is B

Solution:
P=((Q(R-T))/15 )ã€–^â…“ã€—
PÂ³ = ((Q(R-T))/15 )
Q(Râˆ’T)=15PÂ³
Râˆ’T=15PÂ³/Q
T=Râ€“ 15PÂ³/Q

## Points X and Y are 20km North and 9km East of point O, respectively. What is the bearing of Y from X? Correct to the nearest degree.

Points X and Y are 20km North and 9km East of point O, respectively. What is the bearing of Y from X? Correct to the nearest degree.
A. 24Â°
B. 56Â°
C. 127Â°
D. 156Â°

Correct Option: Answer is D

Solution:

tanÎ¸=9/20=0.45
Î¸=tanâˆ’1(0.45)
= 24.23Â°
âˆ´ The bearing of Y from X = 180Â° â€“ 24.23Â°
= 155.77Â°
= 156Â° (to the nearest degree)

## Find the value of x and y in the simultaneous equation: 3x + y = 21; xy = 30

Find the value of x and y in the simultaneous equation: 3x + y = 21; xy = 30
A. x = 3 or 7, y = 12 or 8
B. x = 6 or 1, y = 11 or 5
C. x = 2 or 5, y = 15 or 6
D. x = 1 or 5, y = 10 or 7

Correct Option: Answer is C

Solution:
3x + y = 21 â€¦ (i);
xy = 30 â€¦ (ii)
From (ii), y=30/x. Putting the value of y in (i), we have
3x + 30/x = 21
âŸ¹ 3xÂ² + 30 = 21x
3xÂ² â€“ 21x + 30 = 0
3xÂ² â€“ 15x â€“ 6x + 30 = 0
3x(x â€“ 5) â€“ 6(x â€“ 5) = 0
(3x â€“ 6)(x â€“ 5) = 0
3x â€“ 6 = 0 âŸ¹ x = 2.
x â€“ 5 = 0 âŸ¹ x = 5.
If x = 2, y = 30/2 = 15;
If x = 5, y = 30/5 = 6.

## Simplify (0.0839 X 6.381)/5.44 to 2 significant figures.

Simplify (0.0839 X 6.381)/5.44 to 2 significant figures.
A. 0.2809
B. 2.51
C. 3.5
D. 0.098

Correct Option: Answer is D

## If 2^(x+y )=16 and 4^(x-y )=1/32, find the values of x and y.

If 2^(x+y )=16 and 4^(x-y )=1/32, find the values of x and y.
A. x = 3/4, y = 11/4
B. x = 3/4, y = 13/4
C. x = 2/3, y = 4/5
D. x = 2/3, y = 13/4

Correct Option: Answer is B

Solution:
2^(x+y )=16 ; 4^(x-y )=1/32
= 2^(x+y )=2^4
x +y = 4â€¦.(1)
= 2^(2(x-y) )=2^(-5)
2x â€“ 2y = -5 â€¦.(2)
Solve simultaneously,
x +y = 4
2x â€“ 2y = -5
X = Â¾ ; y = 13/4

## Evaluate ( 6/0.32 Ã· 2/0.084)Â¯Â¹ correct to 1 decimal place.

Evaluate ( 6/0.32 Ã· 2/0.084)Â¯Â¹ correct to 1 decimal place.
A. 1.3
B. 2.5
C. 4.6
D. 3.2

Correct Option: Answer is D

## The weight of a day-old chick was measured to be 0.21g. If the actual weight of the chick is 0.18g, what was the percentage error in the measurement?

The weight of a day-old chick was measured to be 0.21g. If the actual weight of the chick is 0.18g, what was the percentage error in the measurement?
A. 15.5%
B. 18.2%
C. 14.8%
D. 16.7%

Correct Option: Answer is D

Solution:
Actual weight = 0.18g
Error = 0.21g â€“ 0.18g
= 0.03g
% error = 0.03/0.18Ã—100
= 16.7%

## The angles of a polygon are given by 2x, 5x, x and 4x respectively. The value of x is

The angles of a polygon are given by 2x, 5x, x and 4x respectively. The value of x is
A. 31Â°
B. 30Â°
C. 26Â°
D. 48Â°

Correct Option: Answer is B

Solution:
Since there are 4 angles given, the polygon is a quadrilateral.
Sum of angle in a quadrilateral = 360Â°
âˆ´ 2x + 5x + x + 4x = 360Â°
12x = 360Â°
x = 30Â°

## If S = (4t + 3)(t â€“ 2), find ds/dt when t = 5 secs.

If S = (4t + 3)(t â€“ 2), find ds/dt when t = 5 secs.
A. 50 units per sec
B. 35 units per sec
C. 22 units per sec
D. 13 units per sec

Correct Option: Answer is B

Solution:
s=(4t+3)(tâˆ’2)
ds/dt=(4t+3)(1)+(tâˆ’2)(4)
= 4t+3+4tâˆ’8
= 8t â€“ 5
ds/dt (t=5secs)=8(5)âˆ’5
= 40 â€“ 5
= 35 units per sec

## Find the value of ( (0.5436)Â²)/(0.017 X 0.219) to 3 significant figures.

Find the value of ( (0.5436)Â²)/(0.017 X 0.219) to 3 significant figures.
A. 46.2
B. 43.1
C. 534
D. 431

Correct Option: Answer is B

Solution:

= ( (0.5436)Â²)/(0.017 X 0.219)
= ( 0.16063)/(0.017 X 0.219) = 43.1 (3 s.f)

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