$f(x)=-x^3+2\\\\\dfrac{f(a+h)-f(a)}{h}\\\\f(a+h)\to\text{substitute x = a + h}\\f(a)\to\text{substitute x = a}\\\\\dfrac{f(a+h)-f(a)}{h}=\dfrac{-(a+h)^3+2-(-a^3+2)}{h}\\\\\text{use}\ (x+y)^3=x^3+3x^2y+3xy^2+y^3\\\\=\dfrac{-(a^3+3a^2h+3ah^2+h^3)+2-(-a^3)-2}{h}\\\\=\dfrac{-a^3-3a^2h-3ah^2-h^3+2+a^3-2}{h}\\\\\text{combine like terms}$

$=\dfrac{(-a^3+a^3)-3a^2h-3ah^2-h^3+(2-2)}{h}\\\\=\dfrac{-3a^2h-3ah^2-h^3}{h}\\\\=\dfrac{h(-3a^2-3ah-h^2)}{h}\\\\=-3a^2-3ah-h^2$

6 0

2 years ago

Divide the following polynomials, then place the answer in the proper location on the grid. Write answer in descending powers of

irina1246 [14]

Let's rewrite the expression correctly:
(12x3 - 11x2 + 22x - 5) / (4x -1)
Dividing the expression between (4x -1) we have:
3x2 - 2x + 5
We can check the result:
(3x2 - 2x + 5) * (4x-1)
= 12x3 - 8x2 + 20x - 3x2 + 2x - 5
= 12x3 - 11x2 + 22x - 5
Division OK.
Answer:
The result of the division is:
3x2 - 2x + 5

5 0

3 years ago

A grocer buys food from three suppliers. The suppliers deliver every 5 days, 6 days, and 7 days. All three came today. In how ma

AlekseyPX

Answer:

210

Step-by-step explanation:

For getting this answer we need to find the minimum common multiplier, this is, the smaller number that is multiple of all 5, 6 and 7.

For example, 30 is multiple of both 5 and 6, son in 30 days two suppliers will come, but not the third, as 30 is not a multiple of 7.

Let's try with the next multiple of 5 and 6, this is 60, but is not a multiple of 7.

The next is 90, but again not multiple of 7. Niether are the next: 120, 150, 180.

But when we arrive to 210 we see that, as we are going from multiples of 5 and 6, and 210/7=30, 210 is also multiple of 7.

So, the answer is 210.

5 0

2 years ago