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3 years ago

15

Robert and his coworkers brought 11 work trucks to a service station for oil changes. While there they also put 6 gallons of gas

into each vehicle. The cost of gas was $3.52 a gallon. The total bill was $694.32. What was the cost of an oil change for 1 truck?

1 answer:

Free_Kalibri [48]3 years ago

7 0

Answer:

The cost of an oil change for 1 truck was $42

Step-by-step explanation:

Let

x -----> the cost of an oil change for 1 truck

y -----> the cost of gas for 1 truck

z ----> the total bill

we know that

$z=11[x+y]$

we have

$z=\$694.32$

$y=(6)(3.52)=\$21.12$

substitute and solve for x

$694.32=11[x+21.12]$

$x=(694.32/11)-21.12$

$x=\$42$

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A graphing calculator is recommended. A function is given. g(x) = x4 − 5x3 − 14x2 (a) Find all the local maximum and minimum val

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Answer:

The local maximum and minimum values are:

Local maximum

$g(0) = 0$

Local minima

$g(5.118) = -350.90$

$g(-1.368) = -9.90$

Step-by-step explanation:

Let be $g(x) = x^{4}-5\cdot x^{3}-14\cdot x^{2}$ . The determination of maxima and minima is done by using the First and Second Derivatives of the Function (First and Second Derivative Tests). First, the function can be rewritten algebraically as follows:

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First derivative

$g'(x) = 2\cdot x \cdot (x^{2}-5\cdot x -14) + x^{2}\cdot (2\cdot x -5)$

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$g'(x) = x\cdot (4\cdot x^{2}-15\cdot x -28)$

Second derivative

$g''(x) = 12\cdot x^{2}-30\cdot x -28$

Now, let equalize the first derivative to solve and solve the resulting equation:

$x\cdot (4\cdot x^{2}-15\cdot x -28) = 0$

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$x\cdot (x-5.118)\cdot (x+1.368) = 0$

The critical points are 0, 5.118 and -1.368.

Each critical point is evaluated at the second derivative expression:

x = 0

$g''(0) = 12\cdot (0)^{2}-30\cdot (0) -28$

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This value leads to a local maximum.

x = 5.118

$g''(5.118) = 12\cdot (5.118)^{2}-30\cdot (5.118) -28$

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x = -1.368

$g''(-1.368) = 12\cdot (-1.368)^{2}-30\cdot (-1.368) -28$

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This value leads to a local minimum.

Therefore, the local maximum and minimum values are:

Local maximum

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Local minima

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$g(5.118) = -350.90$

$g(-1.368) = (-1.368)^{4}-5\cdot (-1.368)^{3}-14\cdot (-1.368)^{2}$

$g(-1.368) = -9.90$

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