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DaniilM [7]
3 years ago
5

Solve for x : x 3/2 = 6

Mathematics
1 answer:
ASHA 777 [7]3 years ago
6 0
I hope this helps you



2.x+3/2=6


2x+3=6.2


2x+3=12


2x=9


x=9/2
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Step-by-step explanation:

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3 years ago
Find ∂w/∂s and ∂w/∂t using the appropriate Chain Rule.
Vesnalui [34]

Answer:

<h3>The value of \frac{\partial w}{\partial s} is e^{3t}-18e^{2s+t}</h3><h3>The value of \frac{\partial w}{\partial t} is 3e^{3t}-9e^{2s+t}</h3><h3>The partial derivative at s=-5 and t=10 is \frac{\partial w}{\partial s} is e^{30}-18</h3><h3>The partial derivative at s=-5 and t=10 is \frac{\partial w}{\partial t}=3(e^{30}-3)</h3>

Step-by-step explanation:

Given that the Function point are w=y^3-9x^2y

x=e^s, y=e^t and s = -5, t = 10

<h3>To find \frac{\partial w}{\partial s} and \frac{\partial w}{\partial t}using the appropriate Chain Rule : </h3>

w=y^3-9x^2y  

Substitute the values of x and y in the above equation we get

w=(e^t)^3-9(e^s)^2(e^t)

w=e^{3t}-9e^{2s}.e^t

<h3>Now  partially differentiating w with respect to s by using chain rule we have </h3>

\frac{\partial w}{\partial ∂s}=e^{3t}-9(e^{2s}).2(e^t)

=e^{3t}-18e^{2s}.(e^t)

=e^{3t}-18e^{2s+t}

<h3>Therefore the value of \frac{\partial w}{\partial s} is e^{3t}-18e^{2s+t}</h3>

w=e^{3t}-9e^{2s}.e^t

<h3>Now  partially differentiating w with respect to t by using chain rule we have </h3>

\frac{\partial w}{\partial t}=e^{3t}.(3)-9e^{2s}(e^t).(1)

=3e^{3t}-9e^{2s+t}

<h3>Therefore the value of \frac{\partial w}{\partial t} is 3e^{3t}-9e^{2s+t}</h3>

Now put s-5 and t=10 to evaluate each partial derivative at the given values of s and t :

\frac{\partial w}{\partial s}=e^{3t}-18e^{2s+t}

=e^{3(10}-18e^{2(-5)+10}

=e^{30}-18e^{-10+10}

=e^{30}-18e^0

=e^{30}-18

<h3>Therefore the partial derivative at s=-5 and t=10 is \frac{\partial w}{\partial s} is e^{30}-18</h3>

\frac{\partial w}{\partial t}=3e^{3t}-9e^{2s+t}

=3e^{3(10)}-9e^{2(-5)+10}

=3e^{30}-9e{-10+10}

=3e^{30}-9e{0}

=3e^{30}-9

\frac{\partial w}{\partial t}=3(e^{30}-3)

<h3>Therefore the partial derivative at s=-5 and t=10 is \frac{\partial w}{\partial t}=3(e^{30}-3)</h3>
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3 years ago
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