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marin [14]
3 years ago
8

Find all the critical points of the function

TexFormula1" title=" f(x)= (x+1)/(x-3) " alt=" f(x)= (x+1)/(x-3) " align="absmiddle" class="latex-formula"> and determine the intervals in which the function is increasing and in which it is decreasing?

Mathematics
1 answer:
yulyashka [42]3 years ago
5 0

The function

... y = 1/x

has derivative

... y' = -1/x²

which has no zeros. It is undefined at x=0, the only critical point. The derivative is negative for all values of x, so the function is decreasing everywhere in its domain.

Your function

... y = (x+1)/(x-3)

can be written as

... y = 1 +4/(x-3)

which is a version of y = 1/x that has been vertically scaled by a factor of 4, then shifted 1 unit up and 3 units to the right. Shifting the function to the right means x=3 is excluded from the domain (and the interval on which the function is decreasing).

The critical point is x=3.

The function is decreasing on (-∞, 3) ∪ (3, ∞), increasing nowhere.

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What is the measure of x?
UkoKoshka [18]

Answer:

x=4

Step-by-step explanation:

(whole secant) x (external part) = (tangent)^2

(x+5) *x = 6^2

x^2 +5x = 36

Subtract 36 from each side

x^2 +5x - 36 = 0

Factor

( x-4) (x+9) = 0

Using the zero product property

x-4 = 0  x+9 =0

x = 4  x=-9

Cannot be negative since that is negative length

x=4

7 0
3 years ago
If the heights of a population of men are approximately Normally distributed, and the middle 99.7% have heights between 5'0" and
kirza4 [7]

Answer:

4 inches

Step-by-step explanation:

the middle number is 6 and the distance from 99.7 from the middle is 3 standard deviations. 12/3 =4

5 0
2 years ago
Three scatterplots are shown, along with their best-fit lines and correlation coefficients, r1, r2, and r3. Choose the correct s
ira [324]

Answer:

C) r3 < r2 < r1

Step-by-step explanation:

8 0
3 years ago
Brad says that if a second number is 125% of the first number, then the first number must be 75% of the second number. Is he cor
olga55 [171]

Answer: He is not correct.

Steps:

Let x1 and x2 be the first and second number, respectively.

x_2 = \frac{5}{4}x_1\\\frac{4}{5}x_2 =x_1

In words, if the second is 125%, or 5/4 of the first number (first equation),

then the first is 4/5 of the second, which is 0.8 or 80%.

8 0
3 years ago
To create a giant gemstone, sara first made two identical square pyramids that each had a base area of 100 square inches. Then s
inysia [295]

Answer:

8 inches.

Step-by-step explanation:

From the statement we have that they first made two identical square pyramids, each with a base area of 100 square inches.

Ab = s ^ 2 = 100

Therefore each side would be:

s = (100) ^ (1/2)

s = 10

So, side of the square base = 10 inches

Then they tell us that they glued the bases of the pyramids together to form the precious stone. The surface area of the gemstone is 520 square inches, so for a single pyramid it would be:

Ap = 520/2 = 260

For an area of the square pyramid we have the following equation:

Ap = 2 * x * s + s ^ 2

Where x is the height of each triangular surface and s is the side of the square base

Replacing we have:

260 = 2 * x * 10 + 10 ^ 2

20 * x + 100 = 260

20 * x = 160

x = 160/20

x = 8

Therefore, the value of x is 8 inches.

5 0
3 years ago
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