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3 years ago

If a and b are positive, then a-b is positive identify the conclusion of the statement

Mathematics

2 answers:

ale4655 [162]3 years ago

7 0

Answer:

a-b is positive 100% correct

Elanso [62]3 years ago

6 0

Answer:

The statement is wrong. a-b can be positive but not always.

Step-by-step explanation:

There can be three possible situations that are:

Now taking first condition, the result will be positive because a smaller integer is subtracted from a greater one. Such as 5-2=3

In second condition, the result will be negative because a greater integer is subtracted from smaller one. Such as 2-5= -3

In the third condition, the result will always be zero because both the integers will cancel each other. Such as 5-5=0

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QUESTION 3 [10 MARKS] A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the nu

Harman [31]

Answer:

(a)Revenue function, $R(x)=580x-x^2$

Marginal Revenue function, R'(x)=580-2x

(b)Fixed cost =900 .

Marginal Cost Function=300+50x

(c)Profit, $P(x)=-35x^2+280x-900$

(d)x=4

Step-by-step explanation:

Part A

Price Function $= 580 - 10x$

The revenue function

$R(x)=x\cdot (580-10x)\\R(x)=580x-x^2$

The marginal revenue function

$\dfrac{dR}{dx}= \dfrac{d}{dx}(R(x))=\dfrac{d}{dx}(580x-x^2)=580-2x\\R'(x)=580-2x$

Part B

(Fixed Cost)

The total cost function of the company is given by $c=(30+5x)^2$

We expand the expression

$(30+5x)^2=(30+5x)(30+5x)=900+300x+25x^2$

Therefore, the fixed cost is 900 .

Marginal Cost Function

If $c=900+300x+25x^2$

Marginal Cost Function, $\frac{dc}{dx}= (900+300x+25x^2)'=300+50x$

Part C

Profit Function

Profit=Revenue -Total cost

$580x-10x^2-(900+300x+25x^2)\\580x-10x^2-900-300x-25x^2\\$Profit,P(x)=-35x^2+280x-900$

Part D

To maximize profit, we find the derivative of the profit function, equate it to zero and solve for x.

$P(x)=-35x^2+280x-900\\P'(x)=-70x+280\\-70x+280=0\\-70x=-280\\$Divide both sides by -70\\x=4$

The number of cakes that maximizes profit is 4.

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3 years ago

Which value is the solution to the equation -8 = 6 - 7x? A. -7 B. - 2 C. 2 D. 5

r-ruslan [8.4K]

Step-by-step explanation:

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