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Anna [14]
3 years ago
7

A stray dog ate 6 of your muffins. That was four thirds of all of them. With how many did you you start?

Mathematics
1 answer:
Crazy boy [7]3 years ago
4 0

Answer:

Step-by-step explanation:

The total number of muffins was  

40

.

Explanation:

You can translate the important parts of the sentence from English to math (say that  

n

is the total number of muffins):

A stray dog ate  

6



6o f your muffins.

 

=



That was

3

10



3

10

×



of

 

n



all of them!

Now copy down the equation and solve for  

n

:

12

=

3

10

×

n

12

×

10

=

3

10

×

n

×

10

12

×

10

=

3

10

×

n

×

10

12

×

10

=

3

n

120

=

3

n

120

3

=

3

n

3

120

3

=

3

n

3

120

3

=

n

40

=

n

This means that the total number of muffins was  

40

(before the stray dog ate them).

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igomit [66]

Answer:

x=-cos(t)+2sin(t)

Step-by-step explanation:

The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:

A differential equation of the form:

a_n y^n +a_n_-_1y^{n-1}+...+a_1y'+a_oy=0

Will have a characteristic equation of the form:

a_n r^n +a_n_-_1r^{n-1}+...+a_1r+a_o=0

Where solutions r_1,r_2...,r_n are the roots from which the general solution can be found.

For real roots the solution is given by:

y(t)=c_1e^{r_1t} +c_2e^{r_2t}

For real repeated roots the solution is given by:

y(t)=c_1e^{rt} +c_2te^{rt}

For complex roots the solution is given by:

y(t)=c_1e^{\lambda t} cos(\mu t)+c_2e^{\lambda t} sin(\mu t)

Where:

r_1_,_2=\lambda \pm \mu i

Let's find the solution for x''+x=0 using the previous information:

The characteristic equation is:

r^{2} +1=0

So, the roots are given by:

r_1_,_2=0\pm \sqrt{-1} =\pm i

Therefore, the solution is:

x(t)=c_1cos(t)+c_2sin(t)

As you can see, is the same solution provided by the problem.

Moving on, let's find the derivative of x(t) in order to find the constants c_1 and c_2:

x'(t)=-c_1sin(t)+c_2cos(t)

Evaluating the initial conditions:

x(0)=-1\\\\-1=c_1cos(0)+c_2sin(0)\\\\-1=c_1

And

x'(0)=2\\\\2=-c_1sin(0)+c_2cos(0)\\\\2=c_2

Now we have found the value of the constants, the solution of the second-order IVP is:

x=-cos(t)+2sin(t)

3 0
3 years ago
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