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3 years ago

Exercise 6.2

Mathematics

1 answer:

Ronch [10]3 years ago

6 0

9514 1404 393

Answer:

average cost = 7x -5 +100/x
marginal cost = 14x -5

Step-by-step explanation:

The average cost is the total cost divided by the number of units produced:

average cost = C/x = 100/x -5 +7x

The marginal cost is the derivative of the total cost function.

marginal cost = -5 +14x

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The sum of two consecutive negative integers is -171. What is the number closest to zero?

Anton [14]

Consecutive numbers are always 1 away from each other
3,4

so consecutive is represented by
x and x+1
so sum is -171
x+x+1=-171
add like terms
2x+1=-171
subtract 1 from both sides
2x=-172
divide both sides by 2
x=-86
subustitute
x+1=otehr number
x+1=-86+1=-85
answer is -85 and -86

6 0

3 years ago

Use a linear approximation (or differentials) to estimate the given number. (Round your answer to five decimal places.) 3 217

Soloha48 [4]

Answer:

$f(216) \approx 6.0093$

Step-by-step explanation:

Given

$\sqrt[3]{217}$

Required

Solve

Linear approximated as:

$f(x + \triangle x) \approx f(x) +\triangle x \cdot f'(x)$

Take:

$x = 216; \triangle x= 1$

So:

$f(x) = \sqrt[3]{x}$

Substitute 216 for x

$f(x) = \sqrt[3]{216}$

$f(x) = 6$

So, we have:

$f(x + \triangle x) \approx f(x) +\triangle x \cdot f'(x)$

$f(215 + 1) \approx 6 +1 \cdot f'(x)$

$f(216) \approx 6 +1 \cdot f'(x)$

To calculate f'(x);

We have:

$f(x) = \sqrt[3]{x}$

Rewrite as:

$f(x) = x^\frac{1}{3}$

Differentiate

$f'(x) = \frac{1}{3}x^{\frac{1}{3} - 1}$

Split

$f'(x) = \frac{1}{3} \cdot \frac{x^\frac{1}{3}}{x}$

$f'(x) = \frac{x^\frac{1}{3}}{3x}$

Substitute 216 for x

$f'(216) = \frac{216^\frac{1}{3}}{3*216}$

$f'(216) = \frac{6}{648}$

$f'(216) = \frac{3}{324}$

So:

$f(216) \approx 6 +1 \cdot f'(x)$

$f(216) \approx 6 +1 \cdot \frac{3}{324}$

$f(216) \approx 6 + \frac{3}{324}$

$f(216) \approx 6 + 0.0093$

$f(216) \approx 6.0093$

6 0

3 years ago

Are there always the same number of prime numbers between 2 consecutive multiples of 10? Explain.

11111nata11111 [884]

Zenhhffv hgfcvbbbgggg

3 0

3 years ago

Read 2 more answers

The volume of a cube is 27 cubic inches. What is the length of one edge of the cube?

hjlf

The volume for any cube is length x width x height,
so in this case because all side of cube is the same, let it be y.
y x y x y = 27
y = 3
so each side will be 3 inches

3 0

3 years ago

Helpppppp pleaseeee me helpppp

Readme [11.4K]

Answer:

$10 + $10 + $1 + 25¢ + 5¢

$20 + $1 + 25¢ + 5¢

Step-by-step explanation:

Each one must pay $21.30

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3 years ago