<h2>
Part 1.</h2>
Answer: 
The limit of the difference quotient is simply the derivative, so we can express this as follows:
So our function is:
Taking the derivative, we have:
So the correct option is:
<h2>Part 2.</h2>
Answer: 
The equation of the line that passes through the same point can be found as:
Where 
, so we need to find 
. Plug in that x-value in the function we have:
And the slope is:
Then, the equation of the line is:
<h2 /><h2>Part 3.</h2>
Answer: Shown below
As you can see below, the graph of the function of 
is continuous. This is so because we have plotted a polynomial function whose domain is the set of all real numbers. So the function is defined at the point 
, so the derivative exists at this point, hence we can calculate a tangent line there. In conclusion, we get the graph shown below. The blue line is the tangent line while the red curve is the graph of
Answer: to be honest im kinda confused also.
Step-by-step explanation:
131+-5 is equal to 126
To make it less confusing it’s just 131-5
a = amount (in oz) of solution A
b = amount of solution B
The scientist wants a mixture of 110 oz, so
a + b = 110
Solution A consists of 65% salt, so each ounce of solution A contributes 0.65 oz of salt; similarly, each ounce of B contributes 0.9 oz. The mixture is supposed to consist of 75% salt, which amounts to 0.75 * (110 oz) = 82.5 oz of salt. So
0.65 a + 0.9 b = 82.5
Solve for a and b:
b = 110 - a
0.65 a + 0.9 (110 - a) = 82.5
0.65 a + 99 - 0.9 a = 82.5
0.25 a = 16.5
a = 66 ==> b = 44
Answer:
The system 150x+400y=1950 and x = y+2 could be used to determine the number of small boxes and large boxes ordered where x represents the number of small boxes and y represent the number of large boxes.
Step-by-step explanation:
Given,
Number of nails in small box = 150 nails
Number of nails in large box = 400 nails
Total nails in ordered boxes = 1950 nails
Let,
x be the number of small boxes ordered.
y be the number of large boxes ordered.
According to given statement;
150x+400y=1950 Eqn 1
The contractor bought 2 more small boxes than large boxes
x = y+2 Eqn 2
The system 150x+400y=1950 and x = y+2 could be used to determine the number of small boxes and large boxes ordered where x represents the number of small boxes and y represent the number of large boxes.
Step-by-step explanation:
