<em>Answer:</em>
<em>There would be 173,535 lionfish after 6 years.</em>
<em>Step-by-step explanation:</em>
<em>Since lionfish are considered an invasive species, with an annual growth rate of 67%, ya scientist estimates there are 8,000 lionfish in a certain bay after the first year, A) to write the explicit equation for f (n) that represents the number of lionfish in the bay after n years; B) determine how many lionfish will be in the bay after 6 years; and C) if scientists remove 1,200 fish per year from the bay after the first year, determine what is the recursive equation for f (n); the following calculations must be performed:</em>
<em></em>
<em>A)</em>
<em>8000 x 1.67 ^ n = f </em>
<em>B)</em>
<em>8000 x 1.67 ^ 6 = X</em>
<em>8000 x 21.691961596369 = X</em>
<em>173,535.692770952 = X </em>
<em>C)</em>
<em>(8000 - 1200 x 1 ^ n) x 1.67 ^ n = f</em>
<em>Therefore, there would be 173,535 lionfish after 6 years.</em>
If tan0=-3/4 and 0 is in quadrant IV, cos20= (33/25, -17/25, 32/25, 7/25, 24/25?) and tan20= (24/7, -24/7, 7/25, -7/25, 13/7, -1
Oksana_A [137]
Answer:
- cos(2θ) = 7/25
- tan(2θ) = -24/7
Step-by-step explanation:
Sometimes, it is easiest to let a calculator do the work. (See below)
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The magnitude of the tangent is less than 1, so the reference angle will be less than 45°. Then double the angle will be less than 90°, so will remain in the 4th quadrant, where the cosine is positive and the tangent is negative.
You can also use the identities ...
cos(2θ) = (1 -tan(θ)²)/(1 +tan(θ)²)
cos(2θ) = (1 -(-3/4)²)/(1 +(-3/4)²) = ((16-9)/16)/((16+9)/16)
cos(2θ) = 7/25
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tan(2θ) = 2tan(θ)/(1 -tan(θ)²) = 2(-3/4)/((16-9/16) = (-6/4)(16/7)
tan(2θ) = -24/7
100/17 = 5.88 meters per second
13x - y = 19
-y = - 13x + 19
y = 13x + 19
