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nydimaria [60]
3 years ago
12

In a pet store the number of birds is 10 less than twice the number of rabbits. if the pet store has 56 birds, how many rabbits

does it have?
Mathematics
2 answers:
mr Goodwill [35]3 years ago
8 0
B = 2r - 10
b = 56

56 = 2r - 10
56 + 10 = 2r
66 = 2r
66/2 = r
33 = r  <=== there are 33 rabbits
Gemiola [76]3 years ago
8 0

There are 56 birds. And there are 10 less than twice the number of rabbits

let rabbits = r

2r - 10 = 56

Note the equal sign. What you do to one side, you do to the other. Do the opposite of PEMDAS. Isolate the r.

add 10 to both sides

2r - 10 (+10) = 56 (+10)

2r = 66

Divide 2 from both sides

2r/2 = 66/2

r = 33

33 is your answer

hope this helps

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Answer with Step-by-step explanation:

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f(t)=10cos(3t)

A damping force is numerically equal to 1/2 the instantaneous velocity

\beta=\frac{1}{2}

Equation of motion :

m\frac{d^2x}{dt^2}=-kx-\beta \frac{dx}{dt}+f(t)

Using this equation

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\frac{1}{2}\frac{d^2x}{dt^2}+\frac{1}{2}\frac{dx}{dt}+6x=10cos(3t)

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Auxillary equation

m^2+m+12=0

m=\frac{-1\pm\sqrt{1-4(1)(12)}}{2}

m=\frac{-1\pmi\sqrt{47}}{2}

m_1=\frac{-1+i\sqrt{47}}{2}

m_2=\frac{-1-i\sqrt{47}}{2}

Complementary function

e^{\frac{-t}{2}}(c_1cos\frac{\sqrt{47}}{2}+c_2sin\frac{\sqrt{47}}{2})

To find the particular solution using undetermined coefficient method

x_p(t)=Acos(3t)+Bsin(3t)

x'_p(t)=-3Asin(3t)+3Bcos(3t)

x''_p(t)=-9Acos(3t)-9sin(3t)

This solution satisfied the equation therefore, substitute the values in the differential equation

-9Acos(3t)-9Bsin(3t)-3Asin(3t)+3Bcos(3t)+12(Acos(3t)+Bsin(3t))=20cos(3t)

(3B+3A)cos(3t)+(3B-3A)sin(3t)=20cso(3t)

Comparing on both sides

3B+3A=20

3B-3A=0

Adding both equation then, we get

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B=\frac{20}{6}=\frac{10}{3}

Substitute the value of B in any equation

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Particular solution, x_p(t)=\frac{10}{3}cos(3t)+\frac{10}{3}sin(3t)

Now, the general solution

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Substitute the values t=0 and x(0)=2

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