Rectangle MNPQ is similar to rectangle RSTU. Given the information marked on the diagram, what is the perimeter of RSTU?
2 answers:
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Answer:
Step-by-step explanation:
First, let's determine which quadrant our angle θ lies in.
Remember ASTC, where:
Everything is positive in QI,
Only sine (and cosecant) is positive in QII,
Only tangent (and cotangent) is positive in QIII,
And only cosine (and secant) is positive in QIV.
Since our tangent is negative, and our cosine is positive, this means that our θ <em>must</em> be in QIV.
In QIV, sine is negative, tangent is negative, and cosine is positive.
With that, let's figure out the remaining trig ratios.
We know that:
Remember that tangent is the ratio of the opposite side to the adjacent side.
Let's figure out our hypotenuse using the Pythagorean Theorem:
Substitute 1 for a and 2 for b (we can ignore the negative since we're squaring anyways). This yields:
Square:
Add:
Take the square root:
So, our square root is √5.
So, our three sides are: Opposite=1, Adjacent=2, and Hypotenuse=√5.
Sine and Cosecant:
Remember that:
Substitute 1 for the opposite and √5 for the hypotenuse. This yields:
Rationalize:
And since our angle is in QIV, we add a negative:
Cosecant is simply the reciprocal of sine. So:
Cosine and Secant:
Remember that:
Substitute 2 for the adjacent and √5 for the hypotenuse. This yields:
Rationalize:
Since our angle is in QIV, cosine stays positive.
Secant is the reciprocal of cosine. So:
Tangent and Cotangent:
We were given that:
To find cotangent, flip:
And we're done!
<u>Answer:</u>
Michelle purchased 25 audio files in January. The percent increase is 60%
<u>Solution: </u>
Given Data:
Michelle purchases = 25 audio files in January
Again purchased = 40 audio files in February
We need to find the percent increase for the given data.
Step 1:
Use the formula for percent change ,
Step 2:
First we find the amount of change from the question.
Amount of change = 40 – 25
By subtracting, we get 15.
Step 3:
substitute the values in formula we get,
Formula percent change = = 0.6
Percent = 0.6 100 = 60 %.
Result:
Michelle purchased 25 audio files in January. And In February she purchased 40 audio files. Hence the percent increase is 60%.