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Allisa [31]
2 years ago
11

The length of the rectangle is 19 less than 3 times the width. If the width of the rectangle is 9 cm, what would the length of t

he rectangle be?
Mathematics
2 answers:
Delicious77 [7]2 years ago
5 0

Step-by-step explanation:

Given,

width = 9cm

so a/q length of the rectangle will be 19 - ( 9×3) = 19 - 27 = 8 cm

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pishuonlain [190]2 years ago
4 0

Answer: 8 cm

Step-by-step explanation:

Write out the equation described in the first sentence.

"Length is 19 less than..." means L = ... - 19

"Three times the width" means 3W

So, L = 3W - 19

Plug in value of W

L = 3(9) - 19 = 8 cm

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Consider the differential equation y'' − y' − 20y = 0. Verify that the functions e−4x and e5x form a fundamental set of solution
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y=c_1e^{-4x}+c_2e^{5x}

Step-by-step explanation:

Given differential equation is

y''-y'-20y =0

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\Rightarrow m(m-5)+4(m-5)=0

\Rightarrow (m-5)(m+4)=0

\Rightarrow m=-4,5

Therefore the complementary function is = c_1e^{-4x}+c_2e^{5x}

Therefore e^{-4x} and e^{5x} are fundamental solution of the given differential equation.

If y_1 and y_2 are the fundamental solution of differential equation, then

W(y_1,y_2)=\left|\begin{array}{cc}y_1&y_2\\y'_1&y'_2\end{array}\right|\neq 0

Then  y_1 and y_2 are linearly independent.

W(e^{-4x},e^{5x})=\left|\begin{array}{cc}e^{-4x}&e^{5x}\\-4e^{-4x}&5e^{5x}\end{array}\right|

                    =e^{-4x}.5e^{5x}-e^{5x}.(-4e^{-4x})

                    =5e^x+4e^x

                   =9e^x\neq 0

Therefore  e^{-4x} and e^{5x} are linearly independent, since W(e^{-4x},e^{5x})=9e^x\neq 0

Let the the particular solution of the differential equation is

y_p=v_1e^{-4x}+v_2e^{5x}

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and

\therefore v_2=\int \frac{y_1R(x)}{W(y_1,y_2)} dx

Here y_1= e^{-4x}, y_2=e^{5x},W(e^{-4x},e^{5x})=9e^x ,and  R(x)=0

\therefore v_1=\int \frac{-e^{5x}.0}{9e^x}dx

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and

\therefore v_2=\int \frac{e^{5x}.0}{9e^x}dx

       =0

The the P.I = 0

The general solution of the differential equation is

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7 0
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