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hammer [34]
4 years ago
8

3x+y=9 3.2+y=9 6+y=9 what is the x

Mathematics
1 answer:
Nitella [24]4 years ago
5 0

<u>Answer:</u>

The value of x if y is 5.8 is 1.0667 or if y is 3, then x is 2.

<u>Solution:</u>

As given in the problem,

3x+y=9 ---------- (i)

3.2+y=9-------- (ii)

6+y=9------------ (iii)

From (ii) we get,

y = 9-3.2 = 5.8

From (iii) we get,

y = 9-6 = 3

As we can see y have two values,

Suppose y= 5.8, then x will be 3x+5.8=9 \Rightarrow x= \frac{9-5.8}{3} = 1.0667

or if y is 3, then x will be 3x+3=9 \Rightarrow x= \frac{9-3}{3} = 2

Therefore, the value of x if y is 5.8 is 1.0667 or if y is 3, then x is 2.

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4 years ago
Find the length of the curve x=e^t e^{-t},\;\;y=5-2t,\;\;0 \le t \le 3.
Oksana_A [137]
\begin{cases}x(t)=e^t+e^{-t}\\y(t)=5-2t\end{cases}\implies\begin{cases}x'(t)=e^t-e^{-t}\\y'(t)=-2\end{cases}

The length of the curve is given by the integral

\displaystyle\int_0^3\sqrt{(e^t-e^{-t})^2+(-2)^2}\,\mathrm dt

Expand and rewrite the integrand:

(e^t-e^{-t})^2+(-2)^2=e^{2t}+2+e^{-2t}
=e^{-2t}(e^{4t}+2e^{2t}+1)
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Now the integral is

\displaystyle\int_0^3\dfrac{e^{2t}+1}{e^t}\,\mathrm dt=\int_0^3(e^t+e^{-t})\,\mathrm dt
=2\displaystyle\int_0^3\cosh t\,\mathrm dt
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