Solved Math Problems with Step-by-Step Solutions - Desklib

Q 13.
Answer
(9 + i)(5 + 2i) = 45 + 18i + 5i + 2i2
= 45 + 23i + 2i2
[i2 = −1]
= 45 + 23i − 2
= 43 + 23i
Q 14.
Answer
x + 4
x − 2 ≥ 0
The numerator x + 4 is 0 at x = −4, the denominator x − 2 is 0 at x = 2.
To check the interval of solution the number line is divided into three regions:
x < −4, −4 < x < 2 and x > 2. Each region is tested to check if satisfies
the inequality.
region x f (x) check
x < −4 −5 1
7 ≥ 0
−4 < x < 2 1 −5 ≤ 0
x > 2 3 7 ≥ 0
Thus the region x < −4 and x > 2 satisfy the inequality. Additionally, at
x = −4, f (x) = 0, therefore the inequality is satisfied. The solution interval
is
(−∞, −4] ∪ (2, ∞)
Q 15.
Answer
T (t) = 75 + 110e−0.075t
when t = 12
T (12) = 75 + 110e−0.075×12 ≈ 120◦F
1

Q 16.
Answer
log2
( 1
16
)
Property of logarithms:
loga (an) = n
log2
( 1
16
)
= log2
( 1
24
)
= log2 (2−4)
= −4
Q 17.
Answer
95x−2 = 81
95x−2 = 92
=⇒ 5x − 2 = 2
∴ x = 0.8
Q 18.
Answer
Compound interest formula:
A = P
(
1 + r
n
)nt
where, A is the amount accumulated at the end of the period, r is the rate
of interest, n is the frequency of compounding and t is the total time over
which the interest was compounded. P is the principal amount.
For double growth: A/P = 2. The given rate of interest is 3.2 %. Interest
2