An artist makes a scale drawing of a parallelogram-shaped sculpture. The scale is 10 cm on the drawing for every 8 meters on the
sculpture. What is the area of the scale drawing? Show your work.
1 answer:
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Let's call the lengths of our two types of sides <em />
and 
.
The two sides will that our 1.3 inches bigger than the third side will be have length x, and the length of the other side will be known as y. Thus,
.
Considering this, we can add our sides together and set this value equal to 8, given the information in the problem:
Now, let's solve for y.
Now, we are not done yet. We must determine the true lengths of all of our sides. Using the equation we found earlier, the length of the two bigger sides is
inches and the length of our smaller side is simply 
inches.
To verify, we can add these sides together and check that they equal 8:
3.1 + 3.1 + 1.8 = 8 ✔
The two sides will that our 1.3 inches bigger than the third side will be have length x, and the length of the other side will be known as y. Thus,
Considering this, we can add our sides together and set this value equal to 8, given the information in the problem:
Now, let's solve for y.
Now, we are not done yet. We must determine the true lengths of all of our sides. Using the equation we found earlier, the length of the two bigger sides is
To verify, we can add these sides together and check that they equal 8:
3.1 + 3.1 + 1.8 = 8 ✔
We have the following equation:
If we graph this equation we realize that in fact this is an ellipse with major axis matching the y-axis. So we can recognize these characteristics:
1. Center of the ellipse:
The midpoint C<span> of the line segment joining the foci is called the </span>center<span> of the ellipse. So in this exercise this point is as follows:
</span>
2. Length of major axis:
The line through the foci is called the major axis<span>, so in the figure if you go from -5, at the y-coordinate, and walk through this major axis to the coordinate 1, the distance you run is the length of the major axis, that is:</span>
3. Length of minor axis:
The line perpendicular to the foci through the center is called the minor axis. So in the figure if you go from -2, at the x-coordinate, and walk through this minor axis to the coordinate 2, the distance you run is the length of the minor axis, that is:
4. Foci:
Let's find c as follows:
Then the foci are:
If we graph this equation we realize that in fact this is an ellipse with major axis matching the y-axis. So we can recognize these characteristics:
1. Center of the ellipse:
The midpoint C<span> of the line segment joining the foci is called the </span>center<span> of the ellipse. So in this exercise this point is as follows:
</span>
2. Length of major axis:
The line through the foci is called the major axis<span>, so in the figure if you go from -5, at the y-coordinate, and walk through this major axis to the coordinate 1, the distance you run is the length of the major axis, that is:</span>
3. Length of minor axis:
The line perpendicular to the foci through the center is called the minor axis. So in the figure if you go from -2, at the x-coordinate, and walk through this minor axis to the coordinate 2, the distance you run is the length of the minor axis, that is:
4. Foci:
Let's find c as follows:
Then the foci are:
Answer:
Step-by-step explanation:
The first case is a special case of the second one, so we will solve the question for the second case first.
Consider . Using the properties of derivatives and the derivatives of trigonometric functions we get that
We have the equation . Note that since
then we have the equation
,
which implies that . Then,
Note that in this case, the value of k doesn't depend on the values of A and B. So, it applies to every value of A and B. The first case is included, since it is the case in which A=0 and B=1.