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3 years ago

Circle P is divided into four central angles by the diameters AC and BD.

Mathematics

1 answer:

Vanyuwa [196]3 years ago

8 0

Answer:

m∠CPD = 129.75°

Step-by-step explanation:

m∠APD + m∠APB = 180 since the angles are supplementary

x + 1 + 3x - 18 = 180

4x - 17 = 180

4x = 197

x = 49.25

m∠APB = 3(49.25) - 18 = 129.75

m∠APB = m∠CPD because the angles are vertical angles

m∠CPD = 129.75°

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3 years ago

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Answer:

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Step-by-step explanation:

Given the data:

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3 years ago

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Answer:

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3 years ago

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2 years ago

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ioda

Answer:

We would have

$l =w =\frac{8\sqrt{3}}{3} \\h = \frac{8\sqrt{3}}{6}$

where " l " is length, " w" is width and "h" is height.

Step-by-step explanation:

Step 1

Remember that

Surface area for a box with no top = $lw+2lh+2wh = 64$

where " l " is length, " w" is width and "h" is height.

Step 2.

Remember as well that

Volume of the box = $l*w*h$

Step 3

We can now use lagrange multipliers. Lets say,

$F(l,w,h) = lwh$

and

$g(l,w,h) = lw+2lh+2wh = 64$

By the lagrange multipliers method we know that

$\nabla F = \lambda \nabla g$

Step 4

Remember that

$\nabla F = (wh,lh,lw)$

and

$\nabla g = (w+2h,l+2h , 2w+2l)$

So basically you will have the system of equations

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Then you would get

$l\lambda (w+2h) = w\lambda (l+2h) = h\lambda (2w+2l)$

You can get rid of $\lambda$ from these equations and you would get

$lw+2lh = lw+2wh = 2wh+2lh$

And from those equations you would get

$l = w =2h$

Now remember the original equation

$lw+2lh+2wh = 64$

If we plug in what we just got, we would have

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3 years ago