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NeTakaya
3 years ago
9

N is a positive integer. Explain why n(n-1) must be an even number.

Mathematics
1 answer:
Mandarinka [93]3 years ago
4 0
Let me assign n a number: 3 an easy value we can work with. If we substitute it into the equation we get:

3 * (3-1). According to BIDMAS/BODMAS, we must first work out the brackets and then multiple it by the 3.

Do 3-1 = 2, 2*3 = 6 which is an even number. If we try with an even number we also get an even number:

4-1 = 3, 3*4 = 12. Even if we try this with a number like 7, 9 or 10 - we will always get an even integer, this is because, whenever we multiple an even number with an even or odd number - we always get an even number. So when we take away 1 by an even number, and multiple it with an odd number, we get even. Same applies to when we take away an odd number by 1 to get an even number and then times it by an odd number - we always get even.
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The original price and percent paid of a 20% discount and a $14.40 sale price.
Vikentia [17]
Your answer is $18.00

Because 14.40 x 100/80 =$18

Hope this helps

Please please please like my comment
3 0
3 years ago
Calculate dy/dx when xy^3 + y =3x
Brilliant_brown [7]
You have to use implicit derivative

dy / dx = y'

xy^3+y=3x

y^3 + 3xy^2 y' + y' = 3

[3xy^2 + 1) y'= 3 - y^3

          3 - y^3
y' = -----------------   <-----------answer
         3xy^2 + 1

6 0
3 years ago
Does any body know math
olga nikolaevna [1]

Answer:

yes I do

Step-by-step explanation:

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4 0
2 years ago
You have been asked to design a rectangular box with a square base and an open top. The volume of the box must be 500cm3. Determ
babymother [125]

Answer:

x = 10 cm, y = 5 cm gives a minimum area of 300 cm^2.

Step-by-step explanation:

V= x^2y = 500

Surface area A = x^2 + 4xy.

From the first equation y = 500/x^2

So substituting for y in the equation for the surface area:

A = x^2 + 4x * 500/x^2

A = x^2 + 2000/x

Finding the derivative:

dA/dx = 2x - 2000x^-2

dA/dx = 2x - 2000/x^2

This = 0 for a minimum/maximum value of A, so

2x - 2000/x^2  = 0

2x^3 - 2000 = 0

x^3 = 2000/ 2 = 1000

x = 10

Second derivative is  2 + 4000/x^3

when x = 10  this is positive so x = 10 gives a minimum value of A.

So y =  500/x^2

= 500/100

= 5.

6 0
3 years ago
Which set of parametric equations represents the following function? y=/x+3?
Darina [25.2K]
The given equation is:

y= \sqrt{x+3}

We need to find which set of parametric equations, result in the equation given above. The correct answer is option A.

x=5t, y= \sqrt{5t+3}

From first equation, we can write t =x/5. Using this value in second equation, we get:

y= \sqrt{5( \frac{x}{5} )+3}  \\  \\ &#10;y= \sqrt{x+3}

Thus the set of equations in option A result in the given relation.
So, the answer to this question is option A
4 0
3 years ago
Read 2 more answers
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