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Gemiola [76]
3 years ago
7

Calculate the average rate of change of the function f(x) = 3x2 over the interval 1 ≤ x ≤ 5.

Mathematics
1 answer:
RideAnS [48]3 years ago
5 0

Answer:

18

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

\frac{f(b)-f(a)}{b-a}

here [ a, b ] = [ 1, 5 ]

f(b) = f(5) = 3 × 5² = 75

f(a) = f(1) = 3 × 1² = 3, hence

average rate of change = \frac{75-3}{5-1} = \frac{72}{4} = 18

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Demand for a specific design of dinning sets has been fairly large in the past several years and Statewide Furnishings, Inc. usu
V125BC [204]

Answer:

1. a. 117.

2. $2,051.48

3. 592.82

4. 1472.01

5. d. 4116.11

6. d. 24

Step-by-step explanation:

Economic Order Quantity : \sqrt{\frac{2 * Annual Demand *ordering cost}{Holding cost per unit  }  ( \frac{Holding cost + Shortage Cost}{Shortage cost }) }

Economic order quantity is \sqrt{\frac{2 * 600 * 400}{50} (\frac{50 + 120}{120} )}

EOQ = 117

2. ordering cost :

( total demand / EOQ ) * Ordering cost

( 600 / 117 ) * 400 = $2051.28

3. Holding cost :

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3 0
3 years ago
A line goes through the points (8,9) and (-2,4).
Softa [21]
Part A:

Slope of line is given by vertical distance ÷ horizontal distance

Let (8, 9) be (x₁, y₂) and (-2, 4) be (x₂, y₂)
The vertical distance is y₂ - y₁ = 4 - 9 = -5
The horizontal distance is x₂ - x₁ = -2 - 8 = -10

slope of the line = -5 ÷ -10 = 0.5
---------------------------------------------------------------------------------------------------------------

Part B

The point-slope form is given by
(y - y₁) = m (x - x₁)

We have the gradient, m = 0.5
(x₁, y₁) = (8, 9) ⇒ You can also use the other coordinate (-2, 4)
Substitute these value into the form, we have

(y - 9) = 0.5 (x - 8)
----------------------------------------------------------------------------------------------------------------

Part C

The slope-intercept form is given by the equation
y = mx + c

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y - 9 = 0.5 (x - 8) ⇒ Multiplying out the bracket
y - 9 = 0.5x - 4
y = 0.5x - 4 + 9
y = 0.5x + 5 ⇒ This the slope-intercept form

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Answer:

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