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3 years ago

Please complete the system of equations.

Mathematics

1 answer:

likoan [24]3 years ago

6 0

Answer:

Step-by-step explanation:

Eliminate the y terms by adding the equations together:

-10y+9x = -9

10y+5x = -5

——————-

14x = -14

x = -1

y = 0

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A flat circular plate has the shape of the region x squared plus y squared less than or equals 1.The plate, including the bound

rjkz [21]

Answer:

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!

4 0

2 years ago

Cual es la fraccion equivalente de 105/275

xxMikexx [17]

Answer:

21/55

Step-by-step explanation:

dividamos por 5

= 21/55

3 0

2 years ago

The information systems department of your firm has developed a new database program to store critical information on point of s

artcher [175]

Step-by-step explanation:

x'=53

σ=16

n=144

a) hypothesis

H0:µ=55

Ha:µ<55

This is a left tailed test

b) Test statistics

z=(x'-u)/(sigma/sqrt {n})

=(53-55)/(16/sqrt{144})

=-1.5

c)Pvalue at z=|-1.5|

pvalue= p(z>1.5)

=1-0.933193

=0.066807

=0.0668

<u>Decision</u>

since pvalue>alpha(0.05) fail to reject the null hypotheis.

<u>Conclusion</u>

There is not sufficient evidence to support the claim the new computer program has not reduce the time to retrieve the data.

d)since Pvalue>alpha(0.025),so fail to reject the null hypothesis.

No, change in conclusion.

4 0

3 years ago

A jewelry box is b2 inches long, 3c2 inches wide, and 2c1 inches tall. Which of the following are correct? Select ALL that apply

Mariulka [41]

9514 1404 393

Answer:

B, F

Step-by-step explanation:

The volume is the product of the dimensions:

V = LWH

V = (b^2)(3c^2)(2c^1) = (3·2)(b^2)(c^(2+1))

V = 6b^2·c^3 . . . . . matches B

For b=3 and c=2, the volume is ...

V = 6(3^2)(2^3) = 6(9)(8)

V = 432 . . . . cubic inches . . . . matches F

6 0

3 years ago

An 8-ounce bottle of lotion costs $4.50. Find the Unit Rate. hint: What is the cost per ounce?

natali 33 [55]

Answer:

approximately 56 cents

Step-by-step explanation:

4.5/8

4 0

3 years ago