1) What is the shape of the graph of the following parametric equations?
1 answer:
Answer:
The shape of the graph of the parametric equations given is:
- <u>B. ellipse</u>.
Step-by-step explanation:
By inserting each of the equations given in a graphing calculator (Annex 1), it can be identified that both the first and second equations have an elliptical or ellipse shape, which is characterized by being periodic in the two directions in which it runs. Thus, the equation x = 3 cos t runs with elliptical motion on the Y-axis of the Cartesian plane, while the equation y = 2 without t + 1 runs with elliptical motion on the X-axis.
You might be interested in
First we must understand how to write a logarithmic function:
In the equation above, b is the base, x is the exponent, and a is the answer. These same variables can be rearranged to be expressed as an exponential equation as followed:
Next, we need to understand basic logarithm rules.
1. When a value is raised to a power, we can move the exponent to the front of the logarithm. Example:
log(a^2) = 2log(a)
2. When two variables are multiplied together, we can add the logarithms of the individual variables together. Example:
log(ab) = log(a) + log(b)
3. When a variable is divided by another variable, we can subtract the logarithms of the individual variables. Example:
log(a/b) = log(a) - log(b)
Now we can use these rules to solve the problem.
![log(r)=log( \sqrt[3]{ \frac{A^2B}{C} } )](https://tex.z-dn.net/?f=log%28r%29%3Dlog%28%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7BA%5E2B%7D%7BC%7D%20%7D%20%29)
We can rewrite the cube root as:
Now we can move the one-third to the front:
Now we can split up the logarithm:
Finally, we can move the exponent to the front of the log of A:
Distribute the one-third to get the answer:
The answer is (4).
In the equation above, b is the base, x is the exponent, and a is the answer. These same variables can be rearranged to be expressed as an exponential equation as followed:
Next, we need to understand basic logarithm rules.
1. When a value is raised to a power, we can move the exponent to the front of the logarithm. Example:
log(a^2) = 2log(a)
2. When two variables are multiplied together, we can add the logarithms of the individual variables together. Example:
log(ab) = log(a) + log(b)
3. When a variable is divided by another variable, we can subtract the logarithms of the individual variables. Example:
log(a/b) = log(a) - log(b)
Now we can use these rules to solve the problem.
We can rewrite the cube root as:
Now we can move the one-third to the front:
Now we can split up the logarithm:
Finally, we can move the exponent to the front of the log of A:
Distribute the one-third to get the answer:
The answer is (4).