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3 years ago

What does AB congruent symbol CD mean? AB and CD here have lines over them How is it different than AB=CD?

Mathematics

1 answer:

masha68 [24]3 years ago

4 0

Answer:

Suppose that we have two line segments, AB and CD. We know that they have the same length.

I know that AB¯¯¯¯¯¯¯¯=CD¯¯¯¯¯¯¯¯ means AB is identical to CD (aka. They are the same lines), and also that AB¯¯¯¯¯¯¯¯≅CD¯¯¯¯¯¯¯¯ means that AB and CD have the same size, but what does AB=CD mean?

Step-by-step explanation:

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A container in the shape of a square-based prism has a volume of 2744 cm'. What dimensions give the

Vinvika [58]

Answer:

The dimensions that give the minimum surface area are:

Length = 14cm

width = 14cm

height = 14cm

And the minimum surface is:

S = 1,176 cm^2

Step-by-step explanation:

A regular rectangular prism has the measures: length L, width W and height H.

The volume of this prism is:

V = L*W*H

The surface of this prism is:

S = 2*(L*W + H*L + H*W)

If the base of the prism is a square, then we have L = W

Then the equations become:

V = L*L*H = L^2*H

S = 2*(L^2 + 2*H*L)

We know that the volume of the figure is 2744 cm^3

Then:

V = 2744 cm^3 = H*(L^2)

In this equation, we can isolate H.

H = (2744 cm^3)/(L^2)

Now we can replace this on the surface equation:

S = 2*(L^2 + 2*L* (2744 cm^3)/(L^2))

S = 2*L^2 + 4(2744 cm^3)/L

Now we want to minimize the surface area, then we need to find the zeros of the first derivative of S.

S' = 2*(2*L) - 4*(2744 cm^3)/L^2

This is equal to zero when:

0 = 2*(2*L) - 4*(2744 cm^3)/L^2

0 = 4*L*L^2 - 4*(2744 cm^3)

4*(2744 cm^3) = 4*L^3

2744 cm^3 = L^3

∛(2744 cm^3) = L = 14cm

Then the length of the base that minimizes the surface is L = 14.

Then we have:

H = (2744 cm^3)/(L^2) = (2744 cm^3)/(14cm)^2 = 14cm

Then the surface is:

S = 2*(L^2 + 2*L*H) = 2*( (14cm)^2 + 2*(14cm)*(14cm)) = 1,176 cm^2

8 0

2 years ago

When graphing 5x-3y>30 do we shade above or below?

Hatshy [7]

Answer:

below

Step-by-step explanation:

5x - 3y > 30

-3y > -5x + 30 divide by negative switches the inequality

y < 5/3x - 10 y is less than 5/3x - 10 so shade below the line

8 0

2 years ago

Read 2 more answers

if A and B together can do a piece of work in 10 days and B along can do it in 15 days, how many part of the work does A complet

anzhelika [568]

Answer:

1/5

Step-by-step explanation:

Well work can be defined as: $work = rate \ *\ time$

where rate=amount of work that can be done in one unit of time

let a = rate of work A does in a day

let b = rate of work B does in a day

this means that: $10a + 10b=1$ where work=1 and it just means the entire job has been completed.

Since b can do it alone in 15 days, this means that: $15b=1$

If we divide by 15 here, we get the equation: $b=\frac{1}{15}$

We can now use this definition to substitute it into the first equation we made.

$10a + 10(\frac{1}{15}) = 1$

Multiply the 10 and 1/15

$10a+\frac{2}{3}=1$

subtract 2/3 from both sides

$10a=\frac{1}{3}$

Now divide both sides by 10

$a=\frac{1}{30}$

Now multiply this by 6, since we a represents the amount of work that can be done in a day, we want to find how many parts of the work can be done by a in 6 days

$6a=\frac{6}{30}$