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Kruka [31]
3 years ago
8

A cube has an edge of 2 feet. The edge is increasing at the rate of 5 feet per minute. Express the volume of the cube as a funct

ion of m, the number of minutes elapsed.
Mathematics
1 answer:
Agata [3.3K]3 years ago
4 0

Answer:

V(m) = (2 + 5m)^3

Step-by-step explanation:

Given

Solid Shape = Cube

Edge = 2 feet

Increment = 5 feet per minute

Required

Determine volume as a function of minute

From the question, we have that the edge of the cube increases in a minute by 5 feet

<em>This implies that,the edge will increase by 5m feet in m minutes;</em>

Hence,

New\ Edge = 2 + 5m

Volume of a cube is calculated as thus;

Volume = Edge^3

Substitute 2 + 5m for Edge

Volume = (2 + 5m)^3

Represent Volume as a function of m

V(m) = (2 + 5m)^3

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Answer:

x = -5

Step-by-step explanation:

Since these two triangles are similar, the ratio between the corresponding lengths of each triangle will be the same.

This means the ratio between one side of each triangle (e.g. AD and DC) will be the same as the ratio between a different side of each triangle (e.g. BE and BC).

So, to create an equation for the sides which contain the unknown 'x', we must first find the ratio between the two sides by using a different set of sides.

On the right side we are given 9 for AD, and 18 for DC.

9/18 = 0.5

This means that the extra length of the larger triangle from the smaller one (AD) is half the length of the smaller triangle (DC). We can use this to make an equation for x:

If AD/DC = 0.5, then BE/EC will also = 0.5

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Therefore:

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x+23=0.5(x+41)

Now we multiply out the brackets and move the terms to different sides:

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