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2 years ago

Please help with these questions (no links)

Mathematics

1 answer:

seraphim [82]2 years ago

3 0

If the cakes are circles,
3.14(4)2= 50.24
3.14(5)2= 78.5
78.5-50.24= 28.26

#1 is 28.26

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Using a portion of her savings as a down payment, Sarah bought a new car in order to commute to her new job, reducing her saving

vodomira [7]

Answer:

C. I and III

Step-by-step explanation:

5 0

3 years ago

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:

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,

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

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

The domain of definition of F is

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

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

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

8 0

2 years ago

The 4 fifth-grade classrooms have a total of 29 boxes of expo markers. If the boxes are

Vesnalui [34]

Answer: 7 Boxes

Step-by-step explanation:

There are 4 classrooms and 29 boxes of markers. So, you would divide 29 by 4 which is 7.25. Then, you need to round it because you don't have a quarter of a box. So, each classroom will get 7 boxes.

I hope that helps!

6 0

2 years ago

Read 2 more answers

Identify the equivalent expression for each of the expressions below (m1/3 m1/5)^0

Eva8 [605]

Answer:

Step-by-step explanation:

everything rise 0 power is 1.

8 0

3 years ago

Will the ball clear the crossbar of the goal post, which is 10 feer off the fround.

Allisa [31]

The problem gives you X, so replace X witht he given vaule and solve for y:

y = -0.1x^2 + 4X

X = 40

y = -0.1(40)^2 +4(40)

y = -0.1(1600) + 160

y = -160 + 160

y = 0

7 0

2 years ago