the width of a rectangle is x centimetres and its length is (x+ 2) cm. Write down an expression for the perimeter of the rectang
2 answers:
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Answer:
P=2A+B where:
A= # of pounds of American blend and
B= # of pounds of British blend
Step-by-step explanation:
This is a linear programming problem. In order to solve it we need to determine how we are going to use the provided data and we need to keep in mind what we need to maximize (or minimize depending on the problem)
So, the problem states that "The goal of Fine Coffees, Inc. Is to maximize profits." This last sentence will tell us what the objective function will be. The objective function must model the desired value we want to maximize. So the objective function should represent the profits of selling the two tipes of cofee blends.
So this is the data the problem gives us:
"He can only get 300 pounts of Colombian beans per week and 200 pounts of Dominican beans per week." This part or the problem is talking about the amount of coffee beans he can get depending on its type. This will help us find the restrictions for our linear programming problem, so they are not necessary to state the objective function. Next it states:
"Each pount of American blend cofee requires 12 oz of Colombian beans and 4 oz. of Dominican beans, while a pound of British blend coffee uses 8 oz of each type of bean." Again, this data will help us find the restrictions for our linear programming problem, since they will tell us how much coffe we can manufacture, so they are not needed to find the objective function.
The next part states: "Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound." Now, we are interested in this part since it's talking about profits, which is what we need to maximize.
We set A to be the number of pounds of American blend and B to be the number of pounds of British blend. So the profit for American blend is found by using the following equation:
And the profit for the British blend is found by using the following equation:
so the total profit is found by adding the two given profits, so we get:
or
which can be simplified to:
P=2A+B
which is our objective function.
The acceleration of the particle is given by the formula mentioned below:
Differentiate the position vector with respect to t.
Differentiate both sides of the obtained equation with respect to t.
Substitute t=2 in the above equation to obtain the acceleration of the particle at 2 seconds.
The initial position is obtained at t=0. Substitute t=0 in the given position function.
The perpendicular bisector theorem gives the statements that ensures
that and
are perpendicular.
The two statements if true that guarantee is perpendicular to line
are;
Reasons:
The given diagram is the construction of the line perpendicular to line
.
Required:
The two statements that guarantee that is perpendicular to line
.
Solution:
From the point <em>C</em> arcs <em>E</em> and <em>D</em> are drawn to cross line , therefore;
arcs drawn from the same radius.
is perpendicular to line
, given.
Therefore;
by perpendicular bisector theorem.
Learn more about the perpendicular bisector theorem here: