Find the value of a3 + 3b2 when a = 2 and b = -2

Mathematics

1 answer:

FrozenT [24]3 years ago

5 0

Given:

a = 2 and b = -2.

To find:

The value of $a^3+3b^2$ .

Solution:

We need to find the value of expression $a^3+3b^2$ at a = 2 and b = -2.

Substituting a = 2 and b=-2 in $a^3+3b^2$ , we get

$(2)^3+3(-2)^2$

$=8+3(4)$

$=8+12$

$=20$

Therefore, the value of expression $a^3+3b^2$ at a = 2 and b = -2 is 20.

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Vitek1552 [10]

All the answers to the given parts are mentioned below -

<h3>What is the general equation of a Straight line? How it represents a proportional relationship?</h3>

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

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We have a cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one-half gallon of water is needed, and for every 6 scoops of mix, one and one-half gallons of water are needed.

We can write the proportional relationship as -

y = kx

Now, from the given information, we can write -

2 scoops need 0.5 gallon of water

6 scoops need 1.5 gallon of water

So -

k = 2/0.5

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k = 2 x 2 = 4

Equations that represents the relationship can be written as -

y = 4x + c

Now, 2 scoops need 0.5 gallon of water.