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3 years ago

(CHALLENGE QUESTION FOR ALL OF YOU):

Mathematics

2 answers:

NARA [144]3 years ago

5 0

Answer:

Euler's Identity

Euler's Identity is written simply as: e^(iπ) + 1 = 0, it comprises the five most important mathematical constants, and it is an equation that has been compared to a Shakespearean sonnet.

Step-by-step explanation:

aleksandrvk [35]3 years ago

4 0

Answer:

Calculus

Step-by-step explanation:

The fundamental theorem of calculus forms the backbone of the mathematical method known as calculus and links its two main ideas, the concept of the integral and the concept of the derivative.

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Part A: Create a third-degree polynomial in standard form. How do you know it is in standard form? (5 points)

Svetlanka [38]

Answer:

(See explanation for further details)

Step-by-step explanation:

a) Let consider the polynomial $p(x) = 5\cdot x^{3} +2\cdot x^{2} - 6 \cdot x +17$ . The polynomial is in standards when has the form $p(x) = \Sigma \limit_{i=0}^{n} \,a_{i}\cdot x^{i}$ , where $n$ is the order of the polynomial. The example has the following information:

$n = 3$ , $a_{0} = 17$ , $a_{1} = -6$ , $a_{2} = 2$ , $a_{3} = 5$ .

b) The closure property means that polynomials must be closed with respect to addition and multiplication, which is demonstrated hereafter:

Closure with respect to addition:

Let consider polynomials $p_{1}$ and $p_{2}$ such that:

$p_{1} = \Sigma \limits_{i=0}^{m} \,a_{i}\cdot x^{i}$ and $p_{2} = \Sigma \limits_{i=0}^{n}\,b_{i}\cdot x^{i}$ , where $m \geq n$

$p_{1}+p_{2} = \Sigma \limits_{i=0}^{n}\,(a_{i}+b_{i})\cdot x^{i} + \Sigma_{i=n+1}^{m}\,a_{i} \cdot x^{i}$

Hence, polynomials are closed with respect to addition.

Closure with respect to multiplication:

Let be $p_{1}$ a polynomial such that:

$p_{1} = \Sigma \limits_{i=0}^{m} \,a_{i}\cdot x^{i}$

And $\alpha$ an scalar. If the polynomial is multiplied by the scalar number, then:

$\alpha \cdot p_{1} = \alpha \cdot \Sigma \limits_{i = 0}^{m}\,a_{i}\cdot x^{i}$

Lastly, the following expression is constructed by distributive property:

$\alpha \cdot p_{1} = \Sigma \limits_{i=0}^{m}\,(\alpha\cdot a_{i})\cdot x^{i}$

Hence, polynomials are closed with respect to multiplication.

4 0

3 years ago

Which is an x-intercept of the continuous function in the table?

Airida [17]

we know that

The x-intercept is the value of the variable x when the value of the function is equal to zero

In the table we have

$(-1, 0)$ is a x-intercept, because

For $x=-1$ the value of the function is equal to zero

$(-6, 0)$ is a x-intercept, because

For $x=-6$ the value of the function is equal to zero

therefore

the answer is

the continuous function in the table has two x-intercepts

$(-1, 0)$

$(-6, 0)$

8 0

3 years ago

Read 2 more answers

Please and thank you

algol [13]

Answer:

the last one

Step-by-step explanation:

6 0

3 years ago

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Simplify 5m-2(6m-5)+2 a. -7m-8 b. -7m+12 c. 17m+12 d. 17m-8

fgiga [73]

The answer is B. -7m+12.

First distribute the -2 to 6m and -5.

5m-2(6m-5)+2

5m+(-2*6m)+(-2*-5)+2

5m+-12m+10+2

After that, combine the like terms.

5m+-12m+10+2

-5m+-12m=-7m

10+2=12

The simplified expression is -7m+12.

7 0

3 years ago

HELP

jenyasd209 [6]

Answer:

20 cyclists

Step-by-step explanation:

In 2007 only two bikes are there which mean only 20 cyclists participated and that is the least amount out of all years

5 0

3 years ago

Read 2 more answers