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3 years ago

Simplify (-3/5) ÷ (7/6). A. -7/10 B. -18/35 C. 18/35 D 7/10

Mathematics

1 answer:

docker41 [41]3 years ago

5 0

The answer would be B. You would need to keep the first fraction, change to multiplication, and flip the second fraction and multiply across.

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Find f'(x) and state the domain of f': f(x) = In (2x^2+1)

-Dominant- [34]

Answer:

$f'(x) = \frac{4x}{2x^2+1}$

Domain: All Real Numbers

General Formulas and Concepts:

Algebra I

Domain is the set of x-values that can be inputted into function f(x)

Calculus

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Chain Rule: $\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Derivative: $\frac{d}{dx} [ln(u)] = \frac{u'}{u}$

Step-by-step explanation:

Step 1: Define

f(x) = ln(2x² + 1)

Step 2: Differentiate

Derivative ln(u) [Chain Rule/Basic Power]: $f'(x) = \frac{1}{2x^2+1} \cdot 2 \cdot 2x^{2-1}$
Simplify: $f'(x) = \frac{1}{2x^2+1} \cdot 4x$
Multiply: $f'(x) = \frac{4x}{2x^2+1}$

Step 3: Domain

We know that we would have issues in the denominator when we have a rational expression. However, we can see that the denominator would never equal 0.

Therefore, our domain would be all real numbers.

We can also graph the differential function to analyze the domain.

5 0

3 years ago

Evaluate the following expression. 6^-1

Ugo [173]

Do you mean 1/6 as the evaluation?

8 0

3 years ago

Read 2 more answers

Find the product, using suitable properties:

Ray Of Light [21]

Answer: a) 6700 b) 2233

Step-by-step explanation:

$(-67)*(-99)+(-67)*(-1)=\\(-67)*((-99)+(-1))=\\(-67)*(-100)=\\6700$

$29*(80-3)=\\(30-1)*(80-3)=\\30*80+(-1)*80+(-3)*30+(-1)*(-3)=\\2400-80-90+3=\\2403-170=\\2233$

8 0

1 year ago

Suppose that a company needs 1, 200,000 items during a year and that preparation for each production run costs $500. Suppose als

MAVERICK [17]

Answer:

The number of items in each production run so that the total costs of production and storage are minimized is 8165 items/run

Step-by-step explanation:

We will use the following variables:

Q = Quantity being ordered

Q* = the optimal order Quantity: the result being sought

D = annual Demand for the item, over the year

P = unit Production cost

S = cost of setting up a production run, regardless of the number of units in the production run (fixed cost per production run)

H = annual cost to Hold one unit

It is important to note which variables are annualized, which are per-order and which are per-unit.

Using the variables, here are the components of the first equation

Total Cost, TC = PC + SC + HC

PC = P x D : Production Cost = unit Production cost times the annual Demand

SC = (D x S)/Q : Setting up Cost = annual Demand times cost per production setup, divided by the order Quantity (number of units)

HC = (H x Q)/2: Holding Cost = annual unit Holding cost times order Quantity (number of units), divided by 2 (because throughout the year, on average the warehouse is half full).

So TC = PC + SC + HC = (P x D) + ((D x S)/Q) + ((H x Q)/2) = PD + (DS/Q) + HQ/2

To obtain the optimal order quantity, Q* that minimizes TC, at the minimum TC, dTC/dQ = 0

dTC/dQ = (H/2) – (D x S)/(Q²) = 0

(H/2) – (D x S)/(Q²) = 0

Solving for Q, which is Q* at this point.

(Q*)² = 2DS/H

Q* = √(2DS/H)

D = annual demand for the item = 200000

S = cost of setting up a production run, regardless of the number of units in the production run (fixed cost per production run) = $500

H = annual cost to Hold one unit = $3

Q* = √(2×200000×500/3) = 8164.97 = 8165 items.

3 0

3 years ago

REALLY EASY POINTS - What are the values of a positive attitude?

faltersainse [42]

Answer:

3 values of postivity is Optimistim, Kindness, and an open mind/Growth mind set.

Step-by-step explanation:

8 0

2 years ago