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Mathematics

1 answer:

Kazeer [188]3 years ago

7 0

Remember that a rational function will have an oblique asymptote if the degree of the polynomial in the numerator is higher than the degree of the polynomial in the denominator. Since the degree of the numerator of our rational function is 2, and the degree of its numerator is 1, our function will have an oblique asymptote. To find it, we are going to use long division:
$\frac{2x^{2} +5x+6}{x-1} = 2x+3$ with a remainder of 3.
The quotient of the division will be the terms of the linear equation that represents the oblique asympote of our function; notice that you don't need to use the remainder at all:

Equation of the oblique asymptote:
$y=2x+3$

We can conclude that the correct answer is <span>C) y = 2x + 3.</span>

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Which of the following is the graph of y = sin(0.5x)?

Alexeev081 [22]

You did not include the graphs, but I can explain how the graph is and so you can recognize it.

1) for x = 0, y = sin(0) = 0, so the origin (0,0) is part of the graph.

2) The range of the function is the interval [-1, 1]. This is, y is from -1 to 1, and the graph oscilates (is a wave) between those minimum and maximum.

3) The periodicity, P, of the function is such that 0.5P = 2π = > P = 4π

That means that the values repeat every 4π interval (which is the same that 720°)

4) The zeroes of the function are 2π * n, where n is any whole number (negative, zero or positive).

That means that the function crosses the x-axis at

..., -6π, -4π, 2π, 0, 2π, 4π , 6π, ...

5) It is an odd function (which means that f(x) = sin(0.5x) = - f(-x) = - sin(-0.5x).

Now you have plenty information to identify the graph.

I also include a graph of the function in the attached pdf file.

Download pdf

5 0

3 years ago

Read 2 more answers

A pet store sells angle fish for $6 each and clown fish for $4 each. If the pet store sold fish for $36, how many of each type d

artcher [175]

There are four possibilities...but first does the problem tell you how many total fish were sold?

If not the possible combinations are:

0 angel and 9 clownfish
2 angel and 6 clownfish
4 angel and 3 clownfish
6 angel and 0 clownfish

3 0

3 years ago

Jill has a collection of bugs. Her collection contains butterflies and tarantulas. She has 47 bugs and counts 320 total legs. (N

prisoha [69]

Answer:

The solution to this system of equations is:

B = 28
T = 19

Step-by-step explanation:

We are given that Jill has 47 bugs and counts a total 320 legs.

We can concur that by adding the total number of butterflies and the total number of tarantulas, we will get 47 bugs.

$\text{tarantulas + butterflies} = 47$

We are also told that T is tarantulas and B is butterflies.

$T + B = 47$

Then, we also know that butterflies have 6 legs and tarantulas have 8 legs. So, for every tarantula, we get a multiple of 8 and for butterflies, we get a multiple of 6. This gives us a new equation:

$6B + 8T = 320$

Now, we can set up a system of equation.

$\displaystyle \left \{ {{B + T = 47} \atop {6B + 8T = 320}} \right.$

Using the first equation, we can solve for B.

$\displaystyle B + T = 47\\\\B + T - T = 47 - T\\\\B = 47 - T$

Then, we can substitute this value of B into the second equation and solve for T.

$\displaystyle 6(47-T)+8T=320\\\\282 - 6T + 8T = 320\\\\282 + 2T = 320\\\\2T + 282 = 320\\\\2T + 282 - 282 = 320 -282\\\\2T = 38\\\\\frac{2T}{2}=\frac{38}{2}\\\\T = 19$