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3 years ago

In an axiomatic system which category do points, lines and planes belong to

Mathematics

2 answers:

snow_tiger [21]3 years ago

8 0

<h2>Answer:</h2>

The category in which points, lines and planes belong to is:

Undefined terms.

<h2>Step-by-step explanation:</h2>

An axiomatic system is a system that consist of the undefined terms and the collection of the statements or axioms or postulates that are related to these undefined terms.

As we know that in mathematics or geometry we know that there are three undefined terms--

1) Point -- It represent just a location.

2) Line-- It is a line that consist of all the points and extends infinitely in both the directions.

3) Plane-- It is a two-dimensional figure which extends infinitely.

tekilochka [14]3 years ago

4 0

Points, lines, and planes belong in to the axiomatic system of undefined terms. So undefined terms would be your answer.

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1. (5pts) Find the derivatives of the function using the definition of derivative.

andreyandreev [35.5K]

2.8.1

$f(x) = \dfrac4{\sqrt{3-x}}$

By definition of the derivative,

$f'(x) = \displaystyle \lim_{h\to0} \frac{f(x+h)-f(x)}{h}$

We have

$f(x+h) = \dfrac4{\sqrt{3-(x+h)}}$

and

$f(x+h)-f(x) = \dfrac4{\sqrt{3-(x+h)}} - \dfrac4{\sqrt{3-x}}$

Combine these fractions into one with a common denominator:

$f(x+h)-f(x) = \dfrac{4\sqrt{3-x} - 4\sqrt{3-(x+h)}}{\sqrt{3-x}\sqrt{3-(x+h)}}$

Rationalize the numerator by multiplying uniformly by the conjugate of the numerator, and simplify the result:

$f(x+h) - f(x) = \dfrac{\left(4\sqrt{3-x} - 4\sqrt{3-(x+h)}\right)\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{\left(4\sqrt{3-x}\right)^2 - \left(4\sqrt{3-(x+h)}\right)^2}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{16(3-x) - 16(3-(x+h))}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{16h}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)}$

Now divide this by <em>h</em> and take the limit as <em>h</em> approaches 0 :

$\dfrac{f(x+h)-f(x)}h = \dfrac{16}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ \displaystyle \lim_{h\to0}\frac{f(x+h)-f(x)}h = \dfrac{16}{\sqrt{3-x}\sqrt{3-x}\left(4\sqrt{3-x} + 4\sqrt{3-x}\right)} \\\\ \implies f'(x) = \dfrac{16}{4\left(\sqrt{3-x}\right)^3} = \boxed{\dfrac4{(3-x)^{3/2}}}$

3.1.1.

$f(x) = 4x^5 - \dfrac1{4x^2} + \sqrt[3]{x} - \pi^2 + 10e^3$

Differentiate one term at a time:

• power rule

$\left(4x^5\right)' = 4\left(x^5\right)' = 4\cdot5x^4 = 20x^4$

$\left(\dfrac1{4x^2}\right)' = \dfrac14\left(x^{-2}\right)' = \dfrac14\cdot-2x^{-3} = -\dfrac1{2x^3}$

$\left(\sqrt[3]{x}\right)' = \left(x^{1/3}\right)' = \dfrac13 x^{-2/3} = \dfrac1{3x^{2/3}}$

The last two terms are constant, so their derivatives are both zero.

So you end up with

$f'(x) = \boxed{20x^4 + \dfrac1{2x^3} + \dfrac1{3x^{2/3}}}$

8 0

2 years ago

Which ratio is equivalent to 9/36

balandron [24]

Answer:

1/4

Step-by-step explanation:

Step 1: Find the GCF. List out the factors of the numerator and the denominator. 1, 3, 9 are the factors of 9, while 1, 2, 3, 4, 6, 9, 12, 18, and 36 are the factors of 36. 9 is a common factor of both of them, so the GCF is 9.

Step 2: Divide the numerator and denominator by 9 (the GCF). 9/9 is 1. 36/9 is 4. This means that our fraction is 1/4. The fraction is in simplest form.

5 0

3 years ago

I need to know the answer

Nesterboy [21]

Answer in the attachment.

3 0

3 years ago

Please help me on this math I have been trying to solve it but I can't please please help me!!!!!!

ludmilkaskok [199]

Answer:The first table would be a proportional relationship.

Step-by-step explanation:

It's the only table with a constant, which is required in a proportional relationship. The constant would be 1300 which you can find by divided the two numbers in each row.

7 0

2 years ago

Ms. Mor ris has 35 tests to grade this weekend. Mrs. Cook has 80% more tests than that to grade this weekend. How many tests doe

Serga [27]

Answer:

Mrs. Cook has to grade 63 tests.

Step-by-step explanation:

In order to find the answer, first you have to calculate 80% of the number of tests Ms. Morris has:

35*80%= 28

Then, you have to add the number that represents 80% to the number of tests Ms. Morris has to grade:

35+28=63

According to this, the answer is that Mrs. Cook has to grade 63 tests.

8 0

2 years ago