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3 years ago

For the graphed exponential equation, calculate the average rate of change from x = -3 to x = 0

Mathematics

1 answer:

Dimas [21]3 years ago

3 0

The answer to the question is D.

3,2 was your first point and it dropped to -5,0.

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Need help with my homework

Volgvan

Answer:

$\displaystyle y=\frac{16-9x^3}{2x^3 - 3}$

$\displaystyle y=-\frac{56}{13}$

Step-by-step explanation:

<u>Equation Solving</u>

We are given the equation:

$\displaystyle x=\sqrt[3]{\frac{3y+16}{2y+9}}$

To make y as a subject, we need to isolate y, that is, leaving it alone in the left side of the equation, and an expression with no y's to the right side.

We have to make it in steps like follows.

Cube both sides:

$\displaystyle x^3=\left(\sqrt[3]{\frac{3y+16}{2y+9}}\right)^3$

Simplify the radical with the cube:

$\displaystyle x^3=\frac{3y+16}{2y+9}$

Multiply by 2y+9

$\displaystyle x^3(2y+9)=\frac{3y+16}{2y+9}(2y+9)$

Simplify:

$\displaystyle x^3(2y+9)=3y+16$

Operate the parentheses:

$\displaystyle x^3(2y)+x^3(9)=3y+16$

$\displaystyle 2x^3y+9x^3=3y+16$

Subtract 3y and $9x^3$ :

$\displaystyle 2x^3y - 3y=16-9x^3$

Factor y out of the left side:

$\displaystyle y(2x^3 - 3)=16-9x^3$

Divide by $2x^3 - 3$ :

$\mathbf{\displaystyle y=\frac{16-9x^3}{2x^3 - 3}}$

ii) To find y when x=2, substitute:

$\displaystyle y=\frac{16-9\cdot 2^3}{2\cdot 2^3 - 3}$

$\displaystyle y=\frac{16-9\cdot 8}{2\cdot 8 - 3}$

$\displaystyle y=\frac{16-72}{16- 3}$

$\displaystyle y=\frac{-56}{13}$

$\mathbf{\displaystyle y=-\frac{56}{13}}$

8 0

2 years ago

(48. PERSEVERE Wha

katrin2010 [14]

Answer: 4

Step-by-step explanation:

We know that a plane is 2 dimensional surface that extends infinitely far.

The number of points required to define a plane = 3

Here , we have 4 points A, B, C, and D.

So, the number of possible combinations of 3 points to make a plane from 4 points = $C(4,3)$

$=4$ [ $C(n,n-1)=n$ ]

Hence, the greatest number of planes determined using any three of the points A, B, C, and D if no three points are collinear = 4.

6 0

3 years ago

Evaluate the expression,<br> if x = 9, y = 14, and z = 6.<br> x• y - z^2

alex41 [277]

The answer is 90. Hope this helps

7 0

2 years ago

Read 2 more answers

Square root of 45 with radicals

slavikrds [6]

√(45)
√(9×5)
√(3×3×5)
3√5

6 0

3 years ago

Read 2 more answers

Kate wants to divide 20,000 peso savings between her 2 cousins. If she divides it in the ratio 2:3 between Maria and Ana, respec

lara [203]

Maria: 2x

Ana: 3x

2x + 3x = 20000

5x = 20000

x = 20000/5

x = 400

Maria: 2x

2× 400

8000

Anna: 3x

3 × 400

12000

8 0

2 years ago