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3 years ago

The ratio of boys to girls is 2 to 5 if they're 80 girls how many boys are there

1 answer:

4 0

There are 32 boys; if you set up a proportion of boys over girls like 2/5=x/80 and cross multiply you should get that x = 32 boys

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A bird was sitting 9 meters from the base of an oak tree and flew 10 meters to reach the top of the tree. How tall is the tree?

ArbitrLikvidat [17]

100=64-x^2
36=x^2
X=6 meters
:)

4 0

3 years ago

Which sign makes this number sentence true? |78| __ |-222|

sineoko [7]

The absolute value of 78 is < the absolute value of -222

6 0

3 years ago

Read 2 more answers

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

3 years ago

U(8, 9) and V(2, 5) are the endpoints of a line segment. What is the midpoint M of that line segment?

Pavel [41]

Answer:

The midpoint M is (5,7)

Step-by-step explanation:

$m = ( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )$

U(8,9)

V(2,5)

m = [(8+2)/2 , (9+5)/2]

= [(10/2) , (14/2)]

= (5,7)

(Correct me if i am wrong)

5 0

3 years ago

HELP PLEASE A cylinder and its dimensions are shown. Which equation can be used to find V, the volume of the cylinder in cubic c

blondinia [14]

Answer:

WRONG THE ANSWER IS ACUALLY C

Step-by-step explanation:

I know this because i decided to take th4e test use his answer and it was wrong telling me the right answer it's (c).

6 0

4 years ago