Answer: 38 pages per night
Step-by-step explanation:
Tori used to read an average of 40 pages per night but now she is going at a rate that is 5% slower.
To find the number of pages she is reading now, first find 5% of 40 pages:
= 5% * 40
= 2
Then subtract this figure from 40:
= 40 - 2
= 38 pages per night
<em>By deducting 5% from the reading quantity, the person is reading at 5% less. </em>
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:
Step-by-step explanation:
Guess and Check:
$80.00*15=$1,200
$165.00*10=$1,650
$1,200+$1,650=$2,850.
15 of the pairs of shoes are Jordans, while 10 of the pairs are Adidas.
Answer: x = 9
Explanation: 180 - (84 + 33) = 63, 63 - 9 = 54, 54/6 = 9
