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2 years ago

What is the rate of change in the equation y=8x+6?

Mathematics

1 answer:

schepotkina [342]2 years ago

6 0

The rate of change is the number next to the x when in this form. Therefore the rate of change is 8

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F(x) = 3x + x3

____ [38]

Answer:

Please check the explanation.

Step-by-step explanation:

Given

f(x) = 3x + x³

Taking differentiate

$\frac{d}{dx}\left(3x+x^3\right)$

$\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'$

$=\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(x^3\right)$

solving

$\frac{d}{dx}\left(3x\right)$

$\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'$

$=3\frac{d}{dx}\left(x\right)$

$\mathrm{Apply\:the\:common\:derivative}:\quad \frac{d}{dx}\left(x\right)=1$

$=3\cdot \:1$

$=3$

now solving

$\frac{d}{dx}\left(x^3\right)$

$\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}$

$=3x^{3-1}$

$=3x^2$

Thus, the expression becomes

$\frac{d}{dx}\left(3x+x^3\right)=\frac{d}{dx}\left(3x\right)+\frac{d}{dx}\left(x^3\right)$

$=3+3x^2$

Thus,

f'(x) = 3 + 3x²

Given that f'(x) = 15

substituting the value f'(x) = 15 in f'(x) = 3 + 3x²

f'(x) = 3 + 3x²

15 = 3 + 3x²

switch sides

3 + 3x² = 15

3x² = 15-3

3x² = 12

Divide both sides by 3

x² = 4

$\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

$x=\sqrt{4},\:x=-\sqrt{4}$

$x=2,\:x=-2$

Thus, the value of x will be:

$x=2,\:x=-2$

5 0

2 years ago

HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Evgen [1.6K]

Answer:

3.3 and 5

Step-by-step explanation:

Suppplement angle is totaling both of angle to 180 degree

8 0

2 years ago

Match each expression with the equivalent expanded expression.

adelina 88 [10]

Answer:

Question

Match each expression with the equivalent expanded expression.

0.5 (2x + 3)

- 10x - 3

1/3 ( 9 +81)

8x - 4

-5 (2x + 3/5)

-2x + 3

2 (4x-2)

x + 1.5

-3 (2/3x - 1)

Answer:

Step-by-step explanation:

Step-by-step explanation:

Question

Match each expression with the equivalent expanded expression.

0.5 (2x + 3)

- 10x - 3

1/3 ( 9 +81)

8x - 4

-5 (2x + 3/5)

-2x + 3

2 (4x-2)

x + 1.5

-3 (2/3x - 1)

Answer:

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

what is the solution to this system of equations (Use the elimination method by multiplying the first equation by 3.) 2x+y=20 6x

user100 [1]

Answer:

(7, 6)

Step-by-step explanation:

multiply first eq. by 3 to get 6x - 3y = 60

now do

6x + 3y = 60

- 6x - 5y = 12

--------------------

8y = 48

solve for y: y = 6

with this y value, plug it in to the first equation (easier to solve) and get 2x + 6 = 20

solve for x and get x = 7

so ans is (7, 6)

5 0

2 years ago

Can you help me with this.

Ugo [173]

Answer:

1. x = 2

y = 1

2. x = 3 or 6 (Mistake or typo in problem)

3. y = 13

4. x = 7

y = 15

5. x = 4

Step-by-step explanation:

1. 6x - 3 = x + 7, 5x = 10, x = 2

3y + 2 = y + 4, 2y = 2, y = 1

2. There is most likely a typo. Either 8x = 24 and x = 3 or 2x + 10 = 3x + 4 and x = 6

3. 5y -3 = 2y + 36, 3y = 39, y = 13

4. 8y + 11 + 3y + 4 = 180, 11y + 15 = 180, 11y = 165, y = 15

7x = 3y + 4 = 49, x = 7

5. 7x - 10 = 4x + 2, 3x = 12, x = 4

5 0

2 years ago

Read 2 more answers