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tangare [24]
3 years ago
6

In a pen with rabbits and chickens someone counted 25 heads and 80 legs a rabbit has four legs and each chicken has 2 legs, how

many chickens and rabbits are there?
Mathematics
2 answers:
Basile [38]3 years ago
7 0
Let "rabbits" be represented by the variable "x"
and "chickens" be represented by the variable "y"

then in total we have 25 animals
so  x + y = 25
-> y = -x + 25
and since a rabbit has four legs and a chicken has two legs
and there are 80 legs in total
4x + 2y = 80
-> 2x + y = 40
-> y = -2x + 40

[I had solved for y for each equation]
and since we are looking for when  y = y
-x + 25 = -2x + 40   [we can solve for x from here]
x + 25 = 40     [added 2x to both sides]
x = 15  [subtracted 25 from both sides]

then we can plug this back into
y = -x + 25
to get  y = -15 + 25 = 10

therefore there are 15 Rabbits and 10 Chickens
Komok [63]3 years ago
6 0
I just kind of sat here playing with numbers i dont really know a shortcut but the answer is 10 chickens and 15 rabbits 
10*2= 20 each chicken has two legs so thats 10 heads 20 legs
15*4=60 each rabbit has four legs so thats 15 heads 60 legs
15+10=25 heads
20+60=60 legs
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3 years ago
Solve the following differential equation: (2x+5y)dx+(5x−4y)dy=0 *Hint: they are exact<br><br> C=.
Tpy6a [65]

Answer with Step-by-step explanation:

The given differential equation is

(2x+5y)dx+(5x-4y)dy=0

Now the above differential equation can be re-written as

P(x,y)dx+Q(x,y)dy=0

Checking for exactness we should have

\frac{\partial P}{\partial y}=\frac{\partial Q}{\partial x}

\frac{\partial P}{\partial y}=\frac{\partial (2x+5y)}{\partial y}=5

\frac{\partial Q}{\partial x}=\frac{\partial (5x-4y)}{\partial x}=5

As we see that the 2 values are equal thus we conclude that the given differential equation is exact

The solution of exact differential equation is given by

u(x,y)=\int P(x,y)dx+\phi(y)\\\\u(x,y)=\int (2x+5y)dx+\phi (y)\\\\u(x,y)=x^2+5xy+\phi (y)

The value of \phi (y) can be obtained by differentiating u(x,y) partially with respect to 'y' and equating the result with P(x,y)

\frac{\partial u}{\partial y}=\frac{\partial (x^2+5xy+\phi (y)))}{\partial y}=Q(x,y))\\\\5y+\phi '(y)=(5x-4y)\\\\\phi '(y)=5x-9y\\\\\int\phi '(y)\partial y=\int (5x-9y)\partial y\\\\\phi (y)=5xy-\frac{9y^2}{2}\\\\\therefore u(x,y)=x^2+10xy-\frac{9y^2}{2}+c

5 0
3 years ago
Are the figures below similar? Why or why not? Determine whether the triangles shown in the image are similar.
Vika [28.1K]

Answer:

B) no, because the corresponding angles are not congruent

Step-by-step explanation:

Similar triangles must have proportional sides, as well as congruent corresponding angles. In this instance, we can see that the angles are not <em>congruent</em>, and so there is no need to solve for proportion.

~

3 0
3 years ago
Read 2 more answers
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