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Gelneren [198K]
3 years ago
5

What is the formula for a^3-b^3??

Mathematics
2 answers:
grandymaker [24]3 years ago
6 0

Answer:

\boxed{\mathrm{view \ explanation}}

Step-by-step explanation:

The difference of two cubes formula is given as:

a^3-b^3 =(a-b)(a^2 +ab+b^2)

artcher [175]3 years ago
4 0

Step-by-step explanation:

{(a - b)}^{3}  =  {(a - b)}^{2} (a - b)

{a}^{3}  -  3{a}^{2} b + 3a {b}^{2}  -  {b}^{3} =  {(a - b)}^{2} (a - b)

{a}^{3}  -  {b}^{3}  + 3ab(a - b)=  {(a - b)}^{2} (a - b)

{a}^{3}  -  {b}^{3}=  {(a - b)}^{2} (a - b) + 3ab(a - b)

{a}^{3}  - {b}^{3}  = (a - b)(( {a}^{2}  - 2ab +  {b}^{2} ) - 3ab)

{a}^{3}  -  {b}^{3}  = (a - b)( {a}^{2}  +  ab + {b}^{2} )

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PLEASE HELP! find (1,2) obtained by translating 2 units down followed by a rotation of 180 counterclockwise.
N76 [4]

Answer:

Please check the explanation.

Step-by-step explanation:

Translating two units down means we need to subtract two units from the y-coordinate. i.e

(x, y) → (x, y-2)

We are given that the original point is (1, 2), and we have to find the image of (2, 4) obtained by translating 2 units down followed by a rotation of 180 counterclockwise.

                                                FOR (1, 2)

Given

  • P(1, 2)

First translation: Translating two units down

(x, y) → (x, y-2)

P(1, 2) → P'(1, 2-2) → P'(1, 0)

Second transformation: Rotation of 180 counterclockwise.

Rotation of 180 counterclockwise will make both 'x' and 'y' coordinates negative. i.e

(x, y) → (-x, -y)

Thus, after second transformation

P'(1, 0) → (-1, 0)

Thus, the image of (1, 2) obtained by translating 2 units down followed by a rotation of 180 counterclockwise will be: (-1, 0)

                                                    FOR (2, 4)

Given

  • P(2, 4)

First translation: Translating two units down

(x, y) → (x, y-2)

P(2, 4) → P'(2, 4-2) → P'(2, 2)

Second transformation: Rotation of 180 counterclockwise.

Rotation of 180 counterclockwise will make both 'x' and 'y' coordinates negative. i.e

(x, y) → (-x, -y)

Thus, after the second transformation

P'(2, 2) → (-2, -2)

Thus, the image of (2, 4) obtained by translating 2 units down followed by a rotation of 180 counterclockwise will be: (-2, -2)                                        

6 0
3 years ago
Which values of k are solutions to the inequality StartAbsoluteValue negative k minus 2 EndAbsoluteValue less-than 18? Check all
Stella [2.4K]

Answer:

You could just replace all the given possible values of k in the inequality and see which ones are solutions, but let's solve this in a more interesting way:

First, remember how the absolute value works:

IxI = x if x ≥ 0

IxI = -x if x ≤ 0

Then if we have something like:

IxI < B

We can rewrite this as

-B < x < B

Now let's answer the question, here we have the inequality:

I-k -2I < 18

Then we can rewrite this as:

-18 < (-k - 2) < 18

Now let's isolate k:

first, we can add 2 in the 3 parts of the inequality:

-18 + 2 < -k - 2 + 2 < 18 + 2

-16 < -k < 20

Now we can multiply all sides by -1, remember that this also changes the direction of the signs, then:

-1*-16 > -1*-k > -1*20

16 > k > -20

Then k can be any value between these two limits.

So the correct options (from the given ones) are:

k = -16

k = -8

k = 0

6 0
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