Q 1.. Answer. [Property :. [Property : (an)1/m = an/m].

Q 1.
Answer
[Property :
[Property : (
an)1
/m =
an/m]
Q 2.
Answer
y = −2
x2 + 2
x + 2
The vertex form of a quadratic equation
y =
ax2 +
bx +
c is:
y =
a(
x −
h)2 +
k
where, (
h,k) are coordinates of vertex of the parabola (
y), given
by
&
k =
f(
h)
Comparing,
1

ax2 +
bx +
c ~ −2
x2 + 2
x + 2
we have,
a = −2,
b = 2 and
c = 2. Therefore,
Thus, the vertex form is
Now, when
x = 6:
Q 3.
Side length = 5
a + 4
b
Answer
The box is in shape of a cube.
Volume of a cube = (side)3
Since, side = 5
a + 4
b,
Volume = (5
a + 4
b)3
[Formula : (
x +
y)3 =
x3 +
y3 + 3
x2
y + 3
xy2]
= (5
a)3 + (4
b)3 + 3(5
a)2(4
b) +
3(5
a)(4
b)2 ∴Volume = 125
a3 + 64
b3 + 300
a2
b
+ 240
ab2
Q 4.
Answer
2

For a function
f(
x), the transformed function
g(
x):
g(
x) =
f(
x −
h) +
k
represents a horizontal shift of
h to the right and a vertical shift
of
k upwards. Since,
f(
x) is to be shifted by four units to the left,
the transformed function
g(
x) is
g(
x) =
f(
x + 4)
Q 5.
Answer
The cost of making
x T-shirts is
C(
X) = 20 + 8
x
Revenue generated from selling
x T-shirts is
S(
x) = 12
x
Net profit from selling
x T-shirts:
P(
x) =
S(
x) −
C(
x)
Implies,
P(
x) = 12
x − (20 + 8
x) = 4
x − 20
To make a profit of at least 100:
P(
x) ≥ 100 =⇒ 4
x − 20 ≥ 100
Now,
4
x − 20 ≥ 100
[Add 20 to both sides]
4
x ≥ 120
[Divide throughout by
4]
x
≥ 30
Therefore, the club should make at least 30 T-shirts to make a
profit of at least 100 $.
3

Q 6.
Answer
The velocity (
v) of sound in air is given by
v=20 √273+ t
where,
t is
the
temperature
of air in ◦C.
The temperature corresponding to a velocity of 329 m/s can be
determined by graphing the function in the following way:
1. Plot the equation: v=20 √273+ t, with
v as the vertical axis and
t as the horizontal axis.
2.
v = 329 represents a horizontal line on the graph, plot it
3. Both the curves intersect at a point. This point has a velocity
of 329 and a temperature
t which corresponds to this velocity
The graph below shows the plot for
v =
f(
t),
v = 329 and the
point of intersection.
4