Mathematics

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. 24°
B. 56°
C. 127°
D. 156°

Correct Option: Answer is D

Solution:

tanθ=9/20=0.45
θ=tan−1(0.45)
= 24.23°
∴ The bearing of Y from X = 180° – 24.23°
= 155.77°
= 156° (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. Read More »

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 … (i);
xy = 30 … (ii)
From (ii), y=30/x. Putting the value of y in (i), we have
3x + 30/x = 21
⟹ 3x² + 30 = 21x
3x² – 21x + 30 = 0
3x² – 15x – 6x + 30 = 0
3x(x – 5) – 6(x – 5) = 0
(3x – 6)(x – 5) = 0
3x – 6 = 0 ⟹ x = 2.
x – 5 = 0 ⟹ x = 5.
If x = 2, y = 30/2 = 15;
If x = 5, y = 30/5 = 6.

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

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 = 4….(1)
= 2^(2(x-y) )=2^(-5)
2x – 2y = -5 ….(2)
Solve simultaneously,
x +y = 4
2x – 2y = -5
X = ¾ ; y = 13/4

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

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 – 0.18g
= 0.03g
% error = 0.03/0.18×100
= 16.7%

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? Read More »

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. 31°
B. 30°
C. 26°
D. 48°

Correct Option: Answer is B

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

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

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