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3 years ago

Determine the end behavior of each rational function below. f(x) = 7x5 − 3x + 1 / 4x3 + 2

Mathematics

1 answer:

Svetllana [295]3 years ago

8 0

Answer:

When x ⇒ +∞ and x ⇒ -∞, f(x) ⇒ +∞

Step-by-step explanation:

Hi there!

First, let´s write the function:

f(x) = (7x⁵ - 3x +1) / (4x³ + 2)

When x ⇒ +∞

f(x) ⇒ (7x⁵ - 3x) / 4x³ because (7x⁵ - 3x)>>>1 and 4x³>>>2 we can neglect those constants.

f(x) ⇒7x⁵/4x³ - 3x/4x³

f(x) ⇒ 1.75x² - 0.75/x² (0.75/x² ⇒ 0 because a number divided by a very big number is approximately zero). Then:

f(x) ⇒ 1.75x² ⇒ +∞

When x ⇒ -∞

f(x) ⇒ 1.75x² = +∞ (because x² is always positive)

Then, when x ⇒ +∞ and x ⇒ -∞, f(x) ⇒ +∞

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What should we multiply the top equation by in order for both equations to have like coefficients?

ASHA 777 [7]

Answer:

Multiply by 2

Step-by-step explanation:

If we multiply 2x-6y=26 by 2, we get 4x-12y=52 and the x's cancel out, making it easier to solve for y, using the elimination process.

Hope this makes sense!

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3 years ago

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Gemiola [76]

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3 years ago

At Yo-Yo Yogurt, the scale says that Sara has 8 ounces of vanilla yogurt in her cup. Her father’s yogurt weighs 11 ounces. How m

saveliy_v [14]

Answer: $1 \frac{3}{16}\ lb$

Step-by-step explanation:

You know that Sara has 8 ounces of vanilla yogurt in her cup and her father’s yogurt weighs 11 ounces. Then, the total ounces of frozen yogurt they buy altogether is:

$total_{(ounces)}=8\ oz+11\ oz\\\\total_{(ounces)}=19\ oz$

The next step is to make the conversion from ounces to pounds.

You need to remember that:

$1\ lb=16\ oz$

Therefore:

$total_{(pounds)}=(19\ oz)(\frac{1\ lb}{16\ oz})=\frac{19}{16}\ lb$

This result expressed as a mixed number, is:

$total_{(pounds)}=1\frac{3}{16}\ lb$

8 0

3 years ago

Helppppp plsss solve for x

pogonyaev

The two triangles we can see in the diagram are similar, which means that their measurements are proportional. Line MN on the larger triangle MNP is 71.5ft long, and its corresponding line, MA, on the smaller triangle is 71.5-22= 49.5ft long. This means that the scale factor from the bigger to the smaller triangle is 71.5/49.5=13/9.
If line MP on the bigger rectangle is 97.5ft long, then its corresponding line, MB, must be 97.5÷13/9=67.5 ft long.
Therefore, x=67.5 ft

8 0

3 years ago

Read 2 more answers

A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each

Nataly_w [17]

Answer:

12 small boxes

8 large boxes

Step-by-step explanation:

let x be the number of small boxes shipped

let y be the number of large boxes shipped

This means:

the total number of boxes is 20, so

x + y = 20

the number of 50 pound boxes is x and the number of 100 pound boxes is y and together there are 1400 pounds, so

50x + 100y = 1400

Then, solve

First, simplify the equation 50x + 100y = 1400 by dividing both sides by 50

x + 2y = 28

Now, subtract the two equations:

x + 2y = 28

- (x + y = 20)

y = 8

Now plug this into the equation x + y = 20

x + 8 = 20

x = 12

So the number of small boxes is 12 and the number of large boxes is 8.

Here's a graph:

7 0

3 years ago