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3 years ago

Find the equation of the line that is perpendicular to 3x-4y=5

Mathematics

1 answer:

Kaylis [27]3 years ago

7 0

Answer:

4x + 3y = 0

Step-by-step explanation:

A line perpendicular to one written in standard form can be found by swapping the x- and y-coefficients and negating one of them. Usually, you want the leading (x) coefficient to be positive, so here we can negate that one. This process give ...

4x + 3y = 0

The constant on the right can be chosen to make the line go through a desired point. Here, no point is specified, so we have set it to zero.

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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.

6 0

3 years ago

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dezoksy [38]

Answer:

$0.67x-2=0.43$

Step-by-step explanation:

2/3 = 0.6 repeating

3/7 = 0.42857

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3 years ago

Lyle graphs triangle ABC on coordinate axes. He performs two transformations on this figure that result in the congruent triangl

Shtirlitz [24]

Answer:

a rotation 90˚ clockwise and then a reflection across the y-axis

Step-by-step explanation:

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2 years ago

PLZ HELP ME:Evaluate: What is the value of the expression -5(3 + 4)?

almond37 [142]

Answer:

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Step-by-step explanation:

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3 years ago

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A container holds 6 quarts of lemonade. How much is this in cups?

sdas [7]

Well, 4 cups = 1 quart, so 4 *6= 24 cups in 6 quarts of lemonade.

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3 years ago

Find the equation of the line that is perpendicular to 3x-4y=5​

Find the equation of the line that is perpendicular to 3x-4y=5