This doesn't make sense ask another
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
.
Answer:
The distance between them after 1 hour and 30 minutes will be of 63.64 miles.
Step-by-step explanation:
This question can be solved using the Pythagorean Theorem.
Both cars travel at a constant speed of 30 miles per hour. So, after 1 hour and 30 minutes, which is 1 and a half hour, they will have traveled 30*1.5 = 45 miles.
The distance between them is the hypotenuse of a right triangle, in which the sides are 45. So
The distance between them after 1 hour and 30 minutes will be of 63.64 miles.
Answer:
Its proportional
Step-by-step explanation:
15×1 hour is 15
15×2 hours is 30 and so on
