What is the solution to the system of equations?

Mathematics

2 answers:

DaniilM [7]3 years ago

5 0

No solution would be the answer.

german3 years ago

3 0

ANSWER

The given system of equations has no solution.

EXPLANATION

We write the two equations in the slope-intercept form,

$y = mx + c$

The first equation is
$2x - y = 7$

We make y the subject to obtain,

$y = 2x - 7 - - (1)$

The second equation is already in slope intercept form.

$y = 2x + 3 - - (2)$

We can see that the two equations have the same slope but different y-intercept. This implies that, the two equations will never intersect. Therefore the system of equations has no solution.

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Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker sys

il63 [147K]

Answer:

a) $P(x)=-0.042x^2+530x-18000$

b) $P'(x)=-0.084x+530$

$P'(4000)=194$

$P'(9500)=-268$

Step-by-step explanation:

We know that Revenue is our total income and cost is our total cost. Thus, profit is what's left after cost is subtracted from Income (revenue). Thus, we can say:

P(x) = R(x) - C(x)

Finding Profit Function (P(x)):

$P(x) = R(x) - C(x)\\P(x) = -0.042x^2+800x-(270x+18000)\\P(x)=-0.042x^2+800x-270x-18000\\P(x)=-0.042x^2+530x-18000$

This is the profit function.

The marginal profit is the profit earned when ONE ADDITIONAL UNIT of the product is sold. This is basically the rate of change of profit per unit. We find this by finding the DERIVATIVE of the Profit Function.

Remember the power rule for differentiation shown below:

$\frac{d}{dx}(x^n)=nx^{n-1}$