What is x- and y- intercept of -7x + 2y= 14
1 answer:
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Answer:
Joint variation states that:
If z is directly proportional to x and inversely proportional to y,
i.e, ,
then the equation is in the form: where k is the constant of variation.
From the given information: The volume V of a gas varies inversely as the pressure P and directly as the temperature
i.,e ,
by definition of joint variation:
.....[1] where k is the constant of variation.
It is also given that a certain gas has a volume of 10 liters(L) , a temperature of 300 kelvins(K), and a pressure of 1.5 atmosphere(atm).
Substitute these given values in [1] to solve for k;
Simplify:
Divide by 200 both sides we have;
Now, if a gas has a temperature of 400 kelvins and a pressure of 5 atm.
To find the volume (V);
Now substitute the given data and value of k in [1] we have;
Therefore, the Volume of a gas is, 4 liters
The cost to produce n shirts is given as:
The cost function is a quadratic function with a positive leading coefficient, so the minimum value will be at the vertex of the function.
The vertex of a quadratic function can be calculated as:
a = coefficient of squared term = 0.4
b = coefficient of n term = -32
Using these values, we get:
This means, the cost will be minimized if 40 t shirts are produced.
The minimum cost can be found by calculating C at n=40
So, the minimum cost will be:
C(40) = 0.4(40)² - 32(40) + 650
C(40) = 10
Therefore, the minimum cost to produce a t shirt will be $10
The cost function is a quadratic function with a positive leading coefficient, so the minimum value will be at the vertex of the function.
The vertex of a quadratic function can be calculated as:
a = coefficient of squared term = 0.4
b = coefficient of n term = -32
Using these values, we get:
This means, the cost will be minimized if 40 t shirts are produced.
The minimum cost can be found by calculating C at n=40
So, the minimum cost will be:
C(40) = 0.4(40)² - 32(40) + 650
C(40) = 10
Therefore, the minimum cost to produce a t shirt will be $10