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3 years ago

How many centimeters are there in 1 yard if there are 2.54 centimeters per inch show your work?

2 answers:

4 0

There are 36 inches in a yard and 2.54 centimeters per inch.
2.54•36= 91.44 centimeters
There are 91.44 cm in a yard.
Hope this helps.

Mariulka [41]3 years ago

3 0

Good morning from Canada! :D

What we know:
-there are 2.54cm per inch
-there is 1 yard
-1 yard=36 inches

Basically, this question is asking us to make simple conversions from centimeters to inches, based on how many centimeters there are in a yard.
All we need to do to find the number of centimeters is to multiply 36 (the number of inches per year) by 2.54 (the number of centimeters in an inch).

36×2.54=91.44cm

Therefore there are 91.44cm in 1 yard.

Hope this helps!

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Solve y'' + 10y' + 25y = 0, y(0) = -2, y'(0) = 11 y(t) = Preview

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Answer: The required solution is

$y=(-2+t)e^{-5t}.$

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$y^{\prime\prime}+10y^\prime+25y=0,~~~~~~~y(0)=-2,~~y^\prime(0)=11~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Let us consider that

$y=e^{mt}$ be an auxiliary solution of equation (i).

Then, we have

$y^prime=me^{mt},~~~~~y^{\prime\prime}=m^2e^{mt}.$

Substituting these values in equation (i), we get

$m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.$

So, the general solution of the given equation is

$y(t)=(A+Bt)e^{-5t}.$

Differentiating with respect to t, we get

$y^\prime(t)=-5e^{-5t}(A+Bt)+Be^{-5t}.$

According to the given conditions, we have

$y(0)=-2\\\\\Rightarrow A=-2$

and

$y^\prime(0)=11\\\\\Rightarrow -5(A+B\times0)+B=11\\\\\Rightarrow -5A+B=11\\\\\Rightarrow (-5)\times(-2)+B=11\\\\\Rightarrow 10+B=11\\\\\Rightarrow B=11-10\\\\\Rightarrow B=1.$