The simplest form of 18/45 is 2/5
I believe the answer would be -91 because if u solve both of the equations then the f(x) would be 7 and the g(x) would be -13 so it would be 7(-13) which equals -91.
Answer:
The correct answer is a. $2275.28; b. 17.04 years
Step-by-step explanation:
Principal to be invested is $2000
Interest rate (r) per year is 6.5 quarterly.
Interest is calculated compoundly.
a. Time (t) for the investment is given to be 2 years.
Amount after two years is = Principal × 
where the value of n is 4.
⇒ A = 2000 × 
⇒ A = $2275.28.
b. Now the value of A is given to be triple the principal = $ (3 × 2000).
Therefore we need to find the value of t.
⇒ 3 × 2000 = 2000 × 
⇒ ㏑ 3 = 4t × ㏑ ( 1.01625)
⇒ t = 17.04
Therefore it would take 17.04 years for the principal to triple.
Answer:
Differentiation will give you the gradient for the tangent at any point, and you use the product rule whenever a function can be thought of as two functions multiplied together.
If
f
(
x
)
=
g
(
x
)
×
h
(
x
)
then
f
'
(
x
)
=
g
'
(
x
)
h
(
x
)
+
g
(
x
)
h
'
(
x
)
so if
y
=
x
×
sin
x
then
d
y
d
x
=
1
×
sin
x
+
x
×
cos
x
=
sin
x
+
x
cos
x
We know that
x
=
π
2
, so the gradient is
m
=
sin
(
π
2
)
+
π
2
cos
(
π
2
)
=
1
+
π
2
×
0
=
1
Therefore, we can say that
y
=
m
x
+
c
y
=
(
1
)
x
+
c
y
=
x
+
c
So all we really need to find now is the value for
c
, the
y
intercept. We do this by working out a point
(
x
,
y
)
on the graph. We are already given that
x
=
π
2
, so
y
=
x
sin
x
=
π
2
sin
(
π
2
)
=
π
2
×
1
=
π
2
∴
(
x
,
y
)
=
(
π
2
,
π
2
)
Now we substitute this into the equation we already have for the tangent,
y
=
x
+
c
,
(
x
,
y
)
=
(
π
2
,
π
2
)
π
2
=
π
2
+
c
c
=
π
2
−
π
2
=
0
∴
y
=
x
+
c
=
x
+
(
0
)
=
x
which means the tangent to the curve
y
=
x
sin
x
at
(
π
2
,
π
2
)
is simply
y
=
x
.
