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3 years ago

6

Write an equation relating width w and length l for rectangle with an area of 32 square inches.

2 answers:

kramer3 years ago

8 0

Answer:

Length(L) × Width(W) =32

V125BC [204]3 years ago

4 0

Answer:

$32 = wl$

Step-by-step explanation:

Since the formula for the area of a rectangle is <em>width</em><em> </em><em>times</em><em> </em><em>length</em><em>,</em><em> </em>we use this formula and set it equal to 32.

I am joyous to assist you anytime.

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Let φ(x, y) = arctan (y/x) .

Alexandra [31]

Answer:

a) $\large F(x,y)=(-\frac{y}{x^2+y^2},\frac{x}{x^2+y^2})$

b) $\large \mathbb{R}^2-\{(0,0)\}$

c) the points of the form (x, -x) for x≠0

Step-by-step explanation:

a)

If φ(x, y) = arctan (y/x), the vector field F = ∇φ would be

$\large F(x,y)=(\frac{\partial \phi}{\partial x},\frac{\partial \phi}{\partial y})$

On one hand we have,

$\large \frac{\partial \phi}{\partial x}=\frac{\partial arctan(y/x)}{\partial x}=\frac{-y/x^2}{1+(y/x)^2}=-\frac{y/x^2}{1+y^2/x^2}=\\\\=-\frac{y/x^2}{(x^2+y^2)/x^2}=-\frac{y}{x^2+y^2}$

On the other hand,

$\large \frac{\partial \phi}{\partial y}=\frac{\partial arctan(y/x)}{\partial y}=\frac{1/x}{1+(y/x)^2}=\frac{1/x}{1+y^2/x^2}=\\\\=\frac{1/x}{(x^2+y^2)/x^2}=\frac{x}{x^2+y^2}$

So

$\large F(x,y)=(-\frac{y}{x^2+y^2},\frac{x}{x^2+y^2})$

b)

The domain of definition of F is

$\large \mathbb{R}^2-\{(0,0)\}$

i.e., all the plane X-Y except the (0,0)

c)

Here we want to find all the points such that

$\large (-\frac{y}{x^2+y^2},\frac{x}{x^2+y^2})=(k,k)$

where k is a real number other than 0.

But this means

$\large -\frac{y}{x^2+y^2}=\frac{x}{x^2+y^2}\Rightarrow y=-x$

So, all the points in the line y = -x except (0,0) are parallel to the vector field F, that is, the points (x, -x) with x≠ 0

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3 years ago

A year has four seasons. What is the probability that a day chosen at random will be in the spring?

mestny [16]

Answer:

1/4; 25%

Step-by-step explanation:

if a year has four seasons we can say that there are 4 possibilities

spring appears once

this means that the probability that a day chosen at random will be in spring would be 1 out of 4

or 25%

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astraxan [27]

The answer is c, 6/9, because 0.75 equals 3/4 in fraction form, and 6/9 reduces to 2/3.

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emmainna [20.7K]

Answer:

A

Step-by-step explanation:

5 (-5 + n) = -3 - 6n

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Vsevolod [243]

Answer:

See explanation

Step-by-step explanation:

Step 1: Write equation

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