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3 years ago

Calculate the area of the figure. Assume that all angles are right angles.

Mathematics

2 answers:

Setler [38]3 years ago

6 0

The best way to approach this is to assume that there are no spaces in the rectangle. Then subtract the space afterwards. From the image the total width of the solid rectangle is 200 with a height of 100. So we know that the total area is 20,000. Our next task is to fin the "areas" of the hollow parts of the rectagle and subtract from 20,000. We have 75 as height and 25 as width which results to 1875. Since there are 2 "spaces" the total area of the spaces is 3750. Subtracting from 20,000, the total area of this figure is 16 250.

Nookie1986 [14]3 years ago

3 0

Okay. So I find it easiest to calculate the full area as if the shape was a rectangle, then subtracting open space. We already know that length is 100, so now we just need to find width. 50 + 25 + 50 + 25 + 50 = 200. 200 x 100 =20,000. So now we just need to find the areas of open space and subtract. Both spaces have a length of 75 and a width of 25. 25 x 75 = 1875. There were 2 spaces, and 1875 x 2 = 3,750. 20,000 - 3,750 = 16,250.

The area of the figure is 16,250 feet.

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MARSVECTORCALC6 3.4.020. My Notes A rectangular box with no top is to have a surface area of 64 m2. Find the dimensions (in m) t

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

$wh = \lambda (w+2h)\\lh = \lambda (l+2h)\\lw = \lambda (2w+2l)$

Now, remember that you can multiply the first eqation, by "l" the second equation by "w" and the third one by "h" and you would get

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

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

$l^{2} + l^{2} + l^2 = 64 \\3l^{2} = 64 \\l = w = \frac{8\sqrt{3} }{3} \\h = \frac{8\sqrt{3} }{6}$

7 0

3 years ago

What Information is required

LenaWriter [7]

Answer:

BC=XY

Step-by-step explanation:

you know 2 angles. you need a side for ASA. BC and XY is the only one that would be included.

8 0

3 years ago

Read 2 more answers

Not very good at geometry

FromTheMoon [43]

It's B - 1/√3
because tan is opposite side over adjacent

6 0

3 years ago

Type your answer in the box.<br>Evaluate y3 – 2y (y – 5) + 13 when y = -3

kap26 [50]

Answer:

-62

Step-by-step explanation:

y³ – 2y (y – 5) + 13

when y = -3

y³ – 2y (y – 5) + 13

=(-3)³ – 2(-3) [ (-3) – 5] + 13 (by PEDMAS, evaluate parentheses first)

=(-27) + (6) (-8) + 13 (next do multiplication)

=(-27) + (-48) + 13

= -27 - 48 + 13

= -62

3 0

3 years ago

Solve the quadratic equation by completing the square.

ivolga24 [154]

X^2 - 10x + 15 = 0
x^2 - 10x = -15
x^2 - 10x + 25 = -15 + 25
(x - 5)^2 = 10 <====
x - 5 = (+-)sqrt 10
x = 5 (+-) sqrt 10

solutions are :
x = 5 + sqrt 10 and x = 5 - sqrt 10

6 0

3 years ago