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Lisa [10]
3 years ago
8

for her sculpture fetima cut 5 pieces of wire in the following lenghts 1.3m 4.2m 2.8m 5.9m 8.1m how much wirw did she use all al

ong
Mathematics
1 answer:
Stella [2.4K]3 years ago
3 0
1.3+4.2+2.8+5.9+8.1=?
3+2+8+9+1=23
carry the 2 over to the ones place
1+4+2+5+8=2=20
add the 2
22
drop the decimal
22.3m

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We have the coldest value of temperature T(\frac{3}{4},0) = -9/16. and the hottest value is T(-(3/4),\frac{\sqrt{7}}{4})=\frac{5}{16}.

Step-by-step explanation:

We need to take the derivative with respect of x and y, and equal to zero to find the local minimums.

The temperature equation is:

T(x,y)=x^{2}+2y^{2}-\frac{3}{2}x

Let's take the partials derivatives.

T_{x}(x,y)=2x-\frac{3}{2}=0

T_{y}(x,y)=4y=0

So, we can find the critical point (x,y) of T(x,y).

2x-\frac{3}{2}=0

x=\frac{3}{4}

4y=0

y=0

The critical point is (3/4,0) so the temperature at this point is: T(\frac{3}{4},0)=(\frac{3}{4})^{2}+2(0)^{2}-(\frac{3}{2})(\frac{3}{4})

T(\frac{3}{4},0)=-\frac{9}{16}    

Now, we need to evaluate the boundary condition.

x^{2}+y^{2}=1

We can solve this equation for y and evaluate this value in the temperature.

y=\pm \sqrt{1-x^{2}}

T(x,\sqrt{1-x^{2}})=x^{2}+2(1-x^{2})-\frac{3}{2}x  

T(x,\sqrt{1-x^{2}})=-x^{2}-\frac{3}{2}x+2

Now, let's find the critical point again, as we did above.

T_{x}(x,\sqrt{1-x^{2}})=-2x-\frac{3}{2}=0            

x=-\frac{3}{4}    

Evaluating T(x,y) at this point, we have:

T(-(3/4),\sqrt{1-(-3/4)^{2}})=-(-\frac{3}{4})^{2}-\frac{3}{2}(-\frac{3}{4})+2  

T(-(3/4),\frac{\sqrt{7}}{4})=\frac{5}{16}

Now, we can see that at point (3/4,0) we have the coldest value of temperature T(\frac{3}{4},0) = -9/16. On the other hand, at the point -(3/4),\frac{\sqrt{7}}{4}) we have the hottest value of temperature, it is T(-(3/4),\frac{\sqrt{7}}{4})=\frac{5}{16}.

I hope it helps you!

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2 years ago
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