I think it’s gonna be all real numbers except 13
Answer:
bucket of water = 50.397 lbs
Step-by-step explanation:
Pi(r^2)(h) = volume
3.14(6^2)(12) = 1356.48 in^3 = volume of bucket
one ft^3 = 12 x 12 x 12 = 1728 in^3
1356.48/1728 = 0.785 ft^3 (volume of bucket)
0.785(64.2) = 50.397 lbs
1 4/5 + 1/5 + 2/7 =
1 28/35 + 7/35 + 10/35 =
1 45/35 = 2 35/45 =
2.78 gallons rounded to the nearest hundredth
The volume of a cube is the length of one side cubed, therefore the side length of the cube is the cubed root of the volume. Using a calculator to find the cubed root, you find that it is 0.4 meters, or answer C.
Therefore the solution is 0.4 meters; answer C.
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
.
