Answer:

2.835
3.330
Step-by-step explanation:

Let the linear approximation be L(x) at a = 0. This is given by

is the derivative of
. To find this, we use the form
If
, then 
By doing this and applying chain rule for the power (which is a function of x), we have

Then

Also 
Hence 
For
,
and 
Using this in
,

For
,
and 
Using this in
,

Answer:
(a) The constant of proportionality is 0.25
(b) 1 apple = $0.25
(c) $3 = 12 apples
Step-by-step explanation:
Given

Solving (a): The constant of proportionality;
For an equation:

Where
k = constant of proportionality
By comparing:
to 

Hence, the constant of proportionality is 0.25
Solving (b): What information does
gives.
It represents the unit rate.
<em>So, it means that 1 apple costs $0.25</em>
<em></em>
Solving (c): Number of apples for $3.
This means that 
Substitute 3 for c in 

Make n the subject


Yep! It is an integer!
Any negative, positive number or 0 is an integer.
Hope it helps!
Answer:
He must study for at least 7.5 hours each week
Step-by-step explanation:
Here, we want to know the number of hours that Mr Smith must study each week
From the question, we are told that he must study a minimum of 60 hours total over the course of the 8 weeks
The number of hours he must study each week will be 60/8 = 7.5 minimum number of hours each week