All categories

4 years ago

If the graph f(x)= 9x^2+37x+41/3x+5 has an oblique asymptote at y=3x+k what is the value of k

Mathematics

2 answers:

ira [324]4 years ago

6 0

Answer:

$k=\frac{22}{3}$

Step-by-step explanation:

The oblique asymptote of

$f(x)=\frac{9x^2+37x+41}{3x+5}$ ,

We perform the long division as shown in the attachment.

The quotient is;

$3x+\frac{22}{3}$

Comparing to 3x+k

Hence the value of k is $\frac{22}{3}$

Archy [21]4 years ago

3 0

Answer:

$\frac{22}{3}$

Step-by-step explanation:

To find out oblique asymptote we divide the polynomials using long division

To find quotient divide the first term. then multiply the answer with 3x+5 and write it down. Subtract it from the top. Repeat the process till we get remainder.

$3x+\frac{22}{3}$

------------------------------

$3x+5$ $9x^2+37x+41$

$9x^2+15x$

-------------------------------------(Subtract)

$22x+41$

$22x+\frac{110}{3}$

------------------------------------(subtract)

$\frac{13}{3}$

Quotient is $3x+\frac{22}{3}$ that is our oblique asympotote

the value of k is 22/3

You might be interested in

Find the points on x^2+3(y-2)^2 = 27 which are closest to and farthest from the origin

maria [59]

$(-4.89, 3)$ and $(4.89, 3)$ are the farthest from the origin and $(0, -1)$ is the closest from the origin.

Let be a curve of the form $x^{2}+3\cdot (y-2)^{2} = 27$ . The distance with respect to origin is found by using the following Pythagorean identity:

$r = x^{2}+y^{2}$ (1)

Where $r$ is the square distance function.

We can modify (1) as following:

$r = [27-3\cdot (y-2)^{2}]+y^{2}$

$r = 27-3\cdot (y^{2}-4\cdot y +4)+y^{2}$

$r = 27-3\cdot y^{2}+12\cdot y -12 + y^{2}$

$r = -2\cdot y^{2}+12\cdot y+27$ (1b)

Now we apply the First and second derivative tests to determine the minimum and maximum distances from the origin:

First derivative test

$-4\cdot y +12 = 0$

$y = 3$

Second derivative test

$r'' = -4$

The y-component represents a maximum.

Now we graph the function with the ressource of a graphing tool, we find the following points:

Farthest points: $(-4.89, 3)$ , $(4.89, 3)$ .

Closest points: $(0, -1)$ .

$(-4.89, 3)$ and $(4.89, 3)$ are the farthest from the origin and $(0, -1)$ is the closest from the origin.

To learn more on ellipses, we kindly invite to check this verified question: brainly.com/question/19507943

6 0

3 years ago

HELPP ANYBODY KNOW THE ANSWERS TO THE BLANKS IN THE GRAPH?

Margaret [11]

Answer:

5,234

Step-by-step explanation:

4 0

3 years ago

A system of two linear equations in which the lines are identical is classified as __________.

Luba_88 [7]

Answer:

Step-by-step explanation:

c. consistent and dependent

3 0

3 years ago

Read 2 more answers

Can some one explain to me how I do it step by step to understand and with answer what is the area and perimeter and type please

frozen [14]

This is a square. because the lengths and the widths are equal. I mean, all four sides are equal.

the area of a square is the square of a side
${s}^{2} = {5.4}^{2} = 29.16$

and the perimeter of a square is a side multiplied by 4
$4s = 4 \times 5.4 = 21.6$

hope this helps

good luck

4 0

3 years ago

a rectangular fish pond fish pond is 21 square feet in area. if the owner can surround the pond with a 20-foot fence, what are t

Ksivusya [100]

The perimeter is 20 feet, half the perimeter Would be 10 feet.

Need 2 numbers when added together equal 10 and when multiplied together equal the area of 21.

3 and 7 The pond is 3 feet by 7 feet.

5 0

3 years ago

Read 2 more answers