Mathematics, 07.04.2020 01:10 nadarius2017

2x2y + 8x3 – xy2 – 2x3 + 3xy2 + 6y3

Answers: 2

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Answers

Answer from: Queey

2 x y^2 + 6 y^3 + 4 y + 18

Step-by-step explanation:

2×2 y + 8×3 - x y^2 - 2×3 + 3 x y^2 + 6 y^3

Result:

2 x y^2 + 6 y^3 + 4 y + 18

3D plot:

3D plot

Contour plot:

Contour plot

Alternate forms:

2 (x y^2 + 3 y^3 + 2 y + 9)

2 (y (y (x + 3 y) + 2) + 9)

y (y (2 x + 6 y) + 4) + 18

Real roots:

x≈-9.24225, y≈-0.797732

x≈-9.24225, y≈1.93924

Roots:

y = (-2 x^3 + 9 sqrt(3) sqrt(36 x^3 - 4 x^2 - 972 x + 19779) + 54 x - 2187)^(1/3)/(9 2^(1/3)) - (2^(1/3) (18 - x^2))/(9 (-2 x^3 + 9 sqrt(3) sqrt(36 x^3 - 4 x^2 - 972 x + 19779) + 54 x - 2187)^(1/3)) - x/9

y = -((1 - i sqrt(3)) (-2 x^3 + 9 sqrt(3) sqrt(36 x^3 - 4 x^2 - 972 x + 19779) + 54 x - 2187)^(1/3))/(18 2^(1/3)) + ((1 + i sqrt(3)) (18 - x^2))/(9 2^(2/3) (-2 x^3 + 9 sqrt(3) sqrt(36 x^3 - 4 x^2 - 972 x + 19779) + 54 x - 2187)^(1/3)) - x/9

y = -((1 + i sqrt(3)) (-2 x^3 + 9 sqrt(3) sqrt(36 x^3 - 4 x^2 - 972 x + 19779) + 54 x - 2187)^(1/3))/(18 2^(1/3)) + ((1 - i sqrt(3)) (18 - x^2))/(9 2^(2/3) (-2 x^3 + 9 sqrt(3) sqrt(36 x^3 - 4 x^2 - 972 x + 19779) + 54 x - 2187)^(1/3)) - x/9

Polynomial discriminant:

Δ_y = -16 (36 x^3 - 4 x^2 - 972 x + 19779)

Integer roots:

x = -14, y = 1

x = -4, y = -1

Properties as a function:

Domain

R^2

Range

R (all real numbers)

Roots for the variable y:

Partial derivatives:

d/dx(2 x y^2 + 6 y^3 + 4 y + 18) = 2 y^2

d/dy(2 x y^2 + 6 y^3 + 4 y + 18) = 4 x y + 18 y^2 + 4

Indefinite integral:

integral(18 + 4 y + 2 x y^2 + 6 y^3) dx = x^2 y^2 + 6 x y^3 + 4 x y + 18 x + constant

Definite integral over a disk of radius R:

integral integral_(x^2 + y^2<R^2)(2 x y^2 + 6 y^3 + 4 y + 18) dx dy = 18 π R^2

Definite integral over a square of edge length 2 L:

integral_(-L)^L integral_(-L)^L (18 + 4 y + 2 x y^2 + 6 y^3) dy dx = 72 L^2

Related Queries:

Answer from: Quest

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall is needed to match the record of 40 inches is given by

$40-37.6\\\\=2.4\ inches$

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.

Answer from: Quest

pay attention in your classes and concentrate the best thing you can do to raise your test scores is to pay attention when you're supposed to be learning the material: in class!

take good notes.

do your homework.

use mnemonics and other tricks.

do practice tests.

note: the best i know.

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