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:
9
Step-by-step explanation:
<h3>
Answer:</h3>
f(x) = -(x -2)² +3
<h3>
Step-by-step explanation:</h3>
We can fill in the vertex (h, k) values immediately in the vertex form ...
... f(x) = a(x -h)² +k
To find the value of a, we solve the equation for a at some point other than the vertex. The given point is (0, -1), so we can use that:
... -1 = a(0 -2)² +3
... -4 = 4a . . . . . . . . . subtract 3, simplify
... -1 = a . . . . . . . . . . . divide by 4
Now, we know the function is ...
... f(x) = -(x -2)² +3
Answer:
Step-by-step explanation:
We can rewrite the equation as
Notice that we have 
in both the numerator and the denominator, so it looks like we can divide it out. However, what if is 
? Then we would have 
, which is undefined. So although it looks like the numerator and denominator can be simplified, the resulting function we would get from simplification would not have the same behavior as this one (since such a function would be defined for 
, but this one is not).
A point of discontinuity refers to a particular point which is included in the simplified function, but which is not included in the original one. In this case, the point which is not included in the unsimplified function is at . In the simplified version of the function, if we plug in , we get
So the point is our only point of discontinuity.
It's also important to distinguish between specific points of discontinuity and vertical asymptotes. This function also has a vertical asymptote at 
(since it causes the denominator to be 0), but the difference in behavior is that in the case of the asymptote, only the denominator becomes 0 for a specific value of 
Answer:
43.5
Step-by-step explanation:
First
1218 divided by 2
= 609
Second
609 divided by 14 is =43.5
43.5 is the answer
