If the graph f(x)= 9x^2+36x+41/3x+5 has an oblique asymptote at y=3x+k what is the value of k

Mathematics

2 answers:

Galina-37 [17]3 years ago

7 0

Answer:

Step-by-step explanation:

Gelneren [198K]3 years ago

5 0

Answer:

<u><em>The value of k is 7.</em></u>

Explanation:

To find the<em> oblique asymptote</em> of a rational function you divide the numerator by the denominator and take the quotient (not the remainder).

Such quotient (without the remainder) is the equation of the line that is the oblique asymptote of the rational function.

The rational function is:

$\frac{9x^2+36x+41}{3x+5}$

You can see the long division in the picture attached. The quotient is 3x + 7.

Hence, by comparison with y = 3x + k, k = 7.

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5 0

3 years ago

The rabbit population of Springfield, Ohio was 144,000 in 2016. It is expected to decrease by about 7.2% per year. Use an expone

ehidna [41]

Answer:

The estimated Rabbit population by the year 2036 is 32,309 rabbits

Step-by-step explanation:

In this question, we are expected to use the exponential decay function to estimate population of rabbits in a certain year.

An exponential decay function refers to an equation that estimates the value of a parameter(dependent parameter) at a certain value of the independent parameter given that the independent parameter decreases at a certain constant rate.

Firstly, what we need to do is to write the decay function. To do this, we shall be representing the population by variable P, the rate by r , the number of years by t and the initial population by I

Mathematically, we have the decay function as;

P = I(1-r)^t

From the question, we identify these values as;

P = 144,000 : r = 7.2% = 7.2/100 = 0.072, I = 144,00 and t = 2036-2016 = 20 years

Let's plug these values;

P = 144,000(1-0.072)^20

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3 years ago

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