(1/3+1/2)-(5/6-3/4)=
1/3+1/2-5/6+3/4=
4/12+6/12-10/12+9/12=
10/12-1/12=
9/12=
3/4
The area of the rectangle is changing at
0.75 sq.cm/min
Let
x
and
y
be the base and height of the rectangle.
x
=
0.5
cm is constant :. dx/dt=0#. Area of the rectangle
is
A
=
x
⋅
y
. Differentiating both sides we get
d
A
d
t
=
d
x
d
t
⋅
y
+
d
y
d
t
⋅
x
;
y
=
1.5
,
d
y
d
t
=
1.5
cm /min.
∴
d
A
d
t
=
0
⋅
1.5
+
1.5
⋅
0.5
=
0.75
sq.cm/min.
The area of the rectangle is changing at
0.75
sq.cm/min
Answer:
2 ( Option A )
Step-by-step explanation:
The given integral to us is ,
Here 5 is a constant so it can come out . So that,
Now we can write √x as ,
Simplify ,
By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,
On simplifying we will get ,

Before we calculate we can use some common sence thinknig to narrow down the choices. We know that Robert is gonig DOWN the hill, so it doesnt make sence that he woudl have a positive rate of change (i.e. the number feet up the hill he is is decreasing, not increasing) So right away, A & B are clearly wrong.
If we look at the last two (C & D) we can see that if -460 were right after 10 minutes he would have walked down 4,600 feet. This is WAY more that the total height of the hill and so can't be correct.
So C must be correct.
We can check this with some simple math:
Answer:
D. 720cm squared is the answer