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En un polinomio P(x,y), homogéneo y completo en "x" e "y", la suma de los grados absolutos de todos sus términos es 420. ¿Cuál e

Mandarinka [93]

Answer:

the degree of homogeneity is 20.

Step-by-step explanation:

In a polynomial P (x, y), homogeneous and complete in "x" and "y", the sum of the absolute degrees of all its terms is 420. What is its degree of homogeneity?

A homogeneous polynomial is one in which all monomials have the same degree.

This is an example of a homogeneous polynomial of degree 4 (the degree of all monomials is 4):

x ^ 4 + 3x ^ 3y + 2x ^ 2y ^ 2 + xy ^ 3 + 8y ^ 4.

As you can see, the sum of the exponents of the variables x, y in each monomial is 4.

And the number of terms is 5, that is, it is the degree of homogeneity plus 1.

In relation to the sum of the absolute degrees of all monomials or terms it will be: 4 + 4 + 4 + 4 + 4 = 4 * 5 = 20.

In general, you can say that the sum of the absolute degrees in a homogeneous polynomial will be the degree of each monomial by the number of terms = degree * (degree + 1)

Calling n, the degree of our polynomial, it must be fulfilled:

n (n + 1) = 420

=> n ^ 2 + n = 420

=> n ^ 2 + n - 420 = 0

Factoring:

(n + 21) (n - 20) = 0

=> n = -21 and n = 20.

Only the positive value makes sense, therefore n = 20.

In other words, the polynomial is of the form (excluding the coefficients):

x ^ 20 + x ^ 19 y + x ^ 18 y ^ 2 + x ^ 17 y ^ 3 + .... x ^ 3 y ^ 17 + x ^ 2y ^ 18 + xy ^ 19 + y ^ 20

That polynomial has 21 terms.

So the sum of the degrees will be 20 * 21 = 420, as required in the statement.

Therefore, the degree of homogeneity is 20.

8 0

3 years ago

What is the value of b? 75 100 90 80

Vladimir [108]

Hello from MrBillDoesMath!

Answer:

80

Discussion:

Per the attachment, arc AB spans 110 degrees and arc BC spans 90 degrees (as that is the measure of the central angle subtending it). Hence arc ABC spans 110 + 90 = 200 degrees. As a circle has 360 degrees the smaller arc CA spans 360 - 200 = 160 degrees. But angle"b" is a tangent chord angle so its measure equals 1/2 the arc spanned, that is 1/2 ( 160 ) = 80 degrees

Thank you,

MrB

4 0

3 years ago

Evaluate the algebraic expressions, and put their values in order from least (1) to greatest (4), for a = 2 and b = 5. 1.50 − b2

Aneli [31]

Is it possible to add a picture to this

8 0

3 years ago

An Electrician charges $30 for a service call plus $75 per hour of service. If he charged 210 how many hours did he work?

valkas [14]

Answer:

2.4 hours Electrician works.

Step-by-step explanation:

Let us assume that the number of hours Electrician works be x.

As given

An Electrician charges $30 for a service call plus $75 per hour of service.

If Electrician charged $210.

Than the equation becomes

30 + 75x = 210

75x = 210 - 30

75x = 180

$x =\frac{180}{75}$

x =2.4 hours

Therefore 2.4 hours Electrician works.

8 0

4 years ago

A decimal is never a rational number True False

inysia [295]

Answer:

true happy to help

Step-by-step explanation:

8 0

3 years ago

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