Answer:
The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches
Step-by-step explanation:
We have that:
Let the dimension of the paper be x and y;
Such that:
So:
Substitute 128 for Area
Make x the subject
When 1 inch margin is at top and bottom
The length becomes:
When 2 inch margin is at both sides
The width becomes:
The New Area (A) is then calculated as:
Substitute 
for x
Open Brackets
Collect Like Terms
To calculate the smallest possible value of y, we have to apply calculus.
Different A with respect to y
Set
This gives:
Collect Like Terms
Multiply through by 
Divide through by 2
Take square roots of both sides
Recall that:
Recall that the new dimensions are:
So:
To double-check;
Differentiate A'
The above value is:
This means that the calculated values are at minimum.
<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>
Answer:
The anwers is D
Step-by-step explanation:
Answer:
Step-by-step explanation:
Response Variable: Miles per gallon
Predictor Variables: Weight, Horsepower
The multiple regression equation would be: M = aW + bH + c
where M = miles per gallon
a = slope of the graph of W on M OR rate of change in M due to change in W
W = weight
b = slope of the graph of H on M OR rate of change in M due to change in H
H = horsepower
c = intercept of M on the y-axis OR constant variable
How might the car rental company use this model?
The car rental company might use the regression model to determine the following:
- Effect of weight (of car) on miles run per gallon (of premium motor spirit)
- Effect of horsepower on miles per gallon; etc.
The resultant velocity of the plane is the sum of the two velocity vectors which are perpendicular to each other. See the attached figure.
The magnitude of the resultant velocity is
.
The approximate value of the actual velocity of the plane is 
. Correct choice is (D).
