Find the conjugate of 2 - 5i and then calculate the product of the given complex number and its conjugate. (1 point)
2 answers:
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Answer:
401
Step-by-step explanation:
1. Approach
To solve this problem, one first has to think about the given figure in a certain way. In the figure, one can see that it is a circle attached on either side of a rectangle. To find the perimeter of the figure, one has to find the circumference of the circle and then add two sides of the rectangle to the answer
2. Circumference of the circle
The formula to find the circumference of a circle is;
(pi) or
(pi)
~ diameter times the value (pi)
Normally to find the circumference of a semicircle, one would have to divide this formula by 2, but since in this case, one has to add two congruent semicircles, so therefore, the effect of dividing the equation by two, only to multiply by two again cancels, and hence, there is no need to divide by 2.
Substitute in the values;
(78)(pi)
~ 245
3. Find the perimeter of the entire object
Now, one has to add the two additional sides of the figure, to the circumferences of the semicircles to get the final answer;
78 + 78 + 245
= 401
Answer: 1/10 miles/hour
To find how fast a snail moves in miles per hour, we can find the unit rate using a proportion.
<h2>Unit Rate</h2>The unit rate is the amount per one unit. In this problem, the unit is for one hour. One way to find the unit rate is by using a proportion.
<h2>Proportions</h2>Proportions look like two fractions set equal to each other with a missing variable to solve.
<h3>State our variables</h3>let <em>x</em> be the number of miles per hour
<h3>Write a proportion</h3>The first fraction has a number for the numerator (top) and denominator (bottom), because the question gives us the information. The second fraction has a missing value, <em>x</em>, that we are solving for. We can write <em>x</em> in the numerator.
We can solve by finding the scale factor. The scale factor is the number we can multiply the numerator by to find <em>x</em>.
<h3>Find the scale factor</h3>Start with the proportion.
To find the scale factor,
- Take the denominator from the fraction with a variable:
- Take the denominator from the fraction that has no variable:
- Divide step 1 by step 2 and solve:
Our scale factor is <u>3</u>.
<h3>Solve for x</h3>We can find <em>x</em> by multiplying the numerator in the first fraction by the scale factor. This is because <em>x</em> is also in the numerator.
Simplify 3/30 by dividing the fraction by 3.
x = 1/10
∴ a snail moves 1/10 miles per hour.
Learn another way to solve proportions here: brainly.com/question/18437927
