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-Dominant- [34]
3 years ago
10

Please help me with these problems​

Mathematics
1 answer:
Zarrin [17]3 years ago
6 0

Answer:

The answer to your question is:

a) Letter B

b) Letter D

Step-by-step explanation:

a)   | x | + 3 < 10

Formula

               | x | < a      ⇒        - a < x < a

             

               | x | + 3 < 10

                | x |  < 10 - 3

               |x | < 7          solution             - 7 < x < 7

                                    or              -7 < x and  x < 7    Letter B

b) it must be letter D x < 4 and x < 1

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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
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mihalych1998 [28]

Answer:

15

Step-by-step explanation:

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R=8   P=7

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7 0
3 years ago
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zepelin [54]
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3 years ago
Can somebody help me do this, please
natta225 [31]

Step-by-step explanation:

For the triangle on the bottom right the missing angle is

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Answer:

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