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2 years ago

Can someone help me with this? its a relatively simple problem for extra credit in algebra 1.

Mathematics

1 answer:

suter [353]2 years ago

4 0

(2x^2+3x+4)(x^3+4x^2+3x)(x+4)

First use the distributive property for the first two:

(2x^5+8x^4+6x^3+3x^4+12x^3+9^2+4x^3+16x^2+12x)(x+4)

And then combine like terms:

(2x^5+11x^4+22x^3+25x^2+12x)(x+4)

Continue use the distributive property:

(2x^6+11x^5+22x^4+25x^3+12x^2+8x^5+44x^4+88x^3+100x^2+48x)

Continue combine like terms:

(2x^6+19x^5+66x^4+113x^3+112x^2+48x)
And that is your final answer.

Hope that help:)

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Prove:<br> a/(b+c)+b/(a+c)+c/(a+b)<2

faust18 [17]

Answer:

Step-by-step explanation:

a/(b+c) < 2a/(a+b+c)

b/(a+c) < 2b/(a+b+c)

c/(a+b) <2c/ (a+b+c)

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2 years ago

F=(2xy +z³)i + x³j + 3xz²k find a scalar potential and work done in moving an object in the field from (1,-2,1) to (3,1,4)

Alex73 [517]

Step-by-step explanation:

Given:

$\textbf{F} = (2xy + z^3)\hat{\textbf{i}} + x^3\hat{\textbf{j}} + 3xz^2\hat{\textbf{k}}$

This field will have a scalar potential $\varphi$ if it satisfies the condition $\nabla \times \textbf{F}=0$ . While the first x- and y- components of $\nabla \times \textbf{F}$ are satisfied, the z-component doesn't.

$(\nabla \times \textbf{F})_z = \left(\dfrac{\partial F_y}{\partial x} - \dfrac{\partial F_x}{\partial y} \right)$

$\:\:\:\:\:\:\:\:\: = 3x^2 - 2x \ne 0$

Therefore the field is nonconservative so it has no scalar potential. We can still calculate the work done by defining the position vector $\vec{\textbf{r}}$ as

$\vec{\textbf{r}} = x \hat{\textbf{i}} + y \hat{\textbf{j}} + z \hat{\textbf{k}}$

and its differential is

$\textbf{d} \vec{\textbf{r}} = dx \hat{\textbf{i}} + dy \hat{\textbf{j}} + dz \hat{\textbf{k}}$

The work done then is given by

$\displaystyle \oint_c \vec{\textbf{F}} • \textbf{d} \vec{\textbf{r}} = \int ((2xy + z^3)\hat{\textbf{i}} + x^3\hat{\textbf{j}} + 3xz^2\hat{\textbf{k}}) • (dx \hat{\textbf{i}} + dy \hat{\textbf{j}} + dz \hat{\textbf{k}})$

$\displaystyle = (x^2y + xz^3) + x^3y + xz^3|_{(1, -2, 1)}^{(3, 1, 4)}$

$= 422$

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