Answer:
The area after 9 years will be 1,234 km^2
Step-by-step explanation:
In this question, we are tasked with calculating what the area of a certain forest that decreases at a certain percentage would be after some years.
To answer this question, we shall be using an exponential approximation.
Now, to use this exponential approximation, we shall be needing a supporting exponential mathematical equation.
This can be written as;
A = I(1-r)^t
where A is the new area we are looking for
I is the initial area which is 1700 according to the question
r is the rate of decrease which is 3.5% = 3.5/100 = 0.035
t is time which is 9 years according to the question
We plug these values and have the following;
A = 1700(1-0.035)^9
A = 1700(0.965)^9
A = 1,233.66
This is 1,234 km^2 to the nearest square kilometer
Answer: In mathematics, the method of equating the coefficients is a way of solving a functional equation of two expressions such as polynomials for a number of unknown parameters. It relies on the fact that two expressions are identical precisely when corresponding coefficients are equal for each different type of term.
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Answer:
d=8km
Step-by-step explanation:
explanation is in the image above
Assume that the rule connecting height of the candle to time is a linear one. If you do, then we have to find the equation of this line, and then use this equation to predict the height of the candle after 11 hours.
Two points on this line are (6,17.4) and (23, 7.2). The slope is thus
7.2-17.4 -6
m = --------------- = ----------- or -3/5.
23-6 10
Find the equation of the line. I'm going to use the slope-intercept formula:
y = mx + b => 7.2 = (-3/5)(23) + b. Solving for b, b = 21.
Now we know that y = (-3/5)x + 21
Let x=11 to predict the height of the candle at that time.
y = (-3/5)(11) + 21 = 14.4 inches (answer)
Step-by-step explanation:
∫ dt / (cos²(t) ⁹√(1 + tan(t)))
If u = 1 + tan(t), then du = sec²(t) dt.
∫ du / ⁹√u
∫ u^(-1/9) du
9/8 u^(8/9) + C
9/8 (1 + tan(t))^(8/9) + C
