Write 77/20 as a terminating decimal

Mathematics

1 answer:

ahrayia [7]3 years ago

8 0

77/20 = 3.85 <== terminating decimal

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Use the definition of continuity and the properties of limit to show that the function f(x)=x sqrtx/ (x-6)^2 is continuous at x=

jasenka [17]

Answer:

The function $\\ f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}$ is continuous at x = 36.

Step-by-step explanation:

We need to follow the following steps:

The function is:

$\\ f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}$

The function is continuous at point x=36 if:

The function $\\ f(x)$ exists at x=36.
The limit on both sides of 36 exists.
The value of the function at x=36 is the same as the value of the limit of the function at x = 36.

Therefore:

The value of the function at x = 36 is:

$\\ f(36) = \frac{36*\sqrt{36}}{(36-6)^{2}}$

$\\ f(36) = \frac{36*6}{900} = \frac{6}{25}$

The limit of the $\\ f(x)$ is the same at both sides of x=36, that is, the evaluation of the limit for values coming below x = 36, or 33, 34, 35.5, 35.9, 35.99999 is the same that the limit for values coming above x = 36, or 38, 37, 36.5, 36.1, 36.01, 36.001, 36.0001, etc.

For this case:

$\\ lim_{x \to 36} f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}$

$\\ \lim_{x \to 36} f(x) = \frac{6}{25}$

Since

$\\ f(36) = \frac{6}{25}$

And

$\\ \lim_{x \to 36} f(x) = \frac{6}{25}$

Then, the function $\\ f(x) = \frac{x*\sqrt{x}}{(x-6)^{2}}$ is continuous at x = 36.

8 0

3 years ago

A box contains 5 plain pencils and 7 pens. A second box contains 3 color pencils and 3 crayons. One item from each box is chosen

Andru [333]

Multiply the two desired probabilities to find the answer.

5/12 is the probability for the plain pencil since there are 5 pencils out of 12 total items.

1/2 is the probability for the colored pencil since there are 3 colored pencils out of 6 total items. 3/6 simplifies to 1/2.

5/12*1/2= 5/24

Final answer: 5/24

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3 years ago

I would greatly appreciate it if you helped me out

g100num [7]

Answer:no correlation

5 0

3 years ago

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PLEASE HELP! While shopping, Kyla found a dress that she would like to purchase, but it costs $52.25 more than she has. Kyla cha

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I don’t have a double number line but she would have to spend 9.5 (9 1/2) hours babysitting to earn enough money to buy the dress

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