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4 years ago

5(2x-8) in distributive property

Mathematics

1 answer:

babunello [35]4 years ago

3 0

Answer:

10x-40

Step-by-step explanation:

5 times 2x minus 40 works because of the distributive property

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Find the second derivative at the point (1,2), given the function below. y^2-2=2x^3

vagabundo [1.1K]

Solution:

Given:

$y^2-2=2x^3$

Lets First Differentiate the given equation with respect to x

$\frac{d}{dx} ( y^2 - 2 ) = \frac{d}{dx} 2x^3$

$2y \cdot \frac{dy}{dx} - 0 = 6x^2$

$\frac{dy}{dx} = \frac{6x^2}{2y}$

$\frac{dy}{dx} = \frac{3x^2}{y}$ -----------------------(1)

this can be rewritten as

$\frac{dy}{dx} =3x^2y^{-1}$

Now differentiating again with respect to x

$\frac{d^2y}{dx^2} =6x^2y^{-1} + 3x^2 \cdot (-y^{-2}) \cdot \frac{dx}{dy}$

Now substituting (1) we get

$\frac{d^2y}{dx^2} =6x^2y^{-1} + 3x^2 \cdot (-y^{-2}) \cdot \frac{3x^2}{y}$

$\frac{d^2y}{dx^2} = \frac{6x^2}{y} + ( \frac{3x^2}{y^2}) \cdot \frac{3x^2}{y}$

$\frac{d^2y}{dx^2} = \frac{6x^2}{y} + ( \frac{9x^4}{y^3})$

At(1,2) $\frac{d^2y}{dx^2} = \frac{6(1)^2}{2} + ( \frac{9(1)^4}{(2)^3})$

$\frac{d^2y}{dx^2} = \frac{6}{2} + ( \frac{9}{8})$

$\frac{d^2y}{dx^2} = 3 + 1.125$

$\frac{d^2y}{dx^2} = 4.125$

5 0

4 years ago

A company determined that for each $1 increase in the price of their product, the

zaharov [31]

Answer:

To have maximum profit, the price must be increased by 5,

Step-by-step explanation:

Given that the price increase function is:

f(x) = -2x² + 20x + 150,

For maximum profit, then f(x) = 0.

Putting f(x) = 0, we have

-2x² + 20x + 150 = 0

x² - 10x - 75 = 0

(x + 5)(x - 15) = 0

x = -5

x = 15

Again, differentiating f(x) and equating to zero, we have

-4x + 20 = 0

4x = 20

x = 20/4

= 5

To have maximum profit, the price must be increased by 5,

5 0

4 years ago

Read 2 more answers

I only need the answers to 8 an 9

musickatia [10]

Answer:

#8: distance is 3 units

#9: distance is 1 unit

Step-by-step explanation:

for #8 the x values are the same and there's a 3 unit difference between the y value

for #9 the y values are the same and there's a 1 unit difference between the x values

hope this helps chu :3

8 0

3 years ago

Read 2 more answers

Li is running a race around the school track he runs 0.327 kilometer during the first half of the race.What is the distance that

Nady [450]

Its far real far I tell you what

5 0

4 years ago

Translate and solve: 47% of 312 is what number? Round to the nearest tenth.

Svetradugi [14.3K]

Answer:

146.6

Step-by-step explanation:

0.47 * 312=146.64 when rounded to the nearest tenth that = 146.6

8 0

3 years ago