3 questions. Try each one, then open the answer to check yourself and read the explanation.
Find x and y respectively in the subtraction above:
4 2 4 3
− 1 3 x 4
y 3 4 4
Answer: C (4, 2)
The numbers are in base 5. In the fives column you must borrow: (5 + 3) − x = 4 gives x = 4, and in the last column 3 − 1 = y gives y = 2.
Find y if
( 5 −6 )( x ) = ( 7 )
( 2 −7 )( y ) ( −11 )
Answer: D (3)
The matrix equation gives 5x − 6y = 7 and 2x − 7y = −11. Multiply the first by 2 and the second by 5 and subtract: 23y = 69, so y = 3.
PQRS is a desk of dimension 2m × 0.8m which is inclined at 30° to the horizontal. Find the angle θ marked in the figure.
Answer: D (10°)
R is 0.8 sin 30° = 0.4 m above the floor and the diagonal PR = √(22 + 0.82) ≈ 2.15 m, so sin θ ≈ 0.4/2.15 and θ ≈ 10.7°, closest to 10°.