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2 years ago

The table shows three unique functions.

Mathematics

1 answer:

Lady_Fox [76]2 years ago

4 0

The true statements about the functions are:

g(x) has the maximum greatest value.
h(x) has a range of all negative numbers.

<h3>How to determine the true statements?</h3>

The complete question is in the attached image

From the image, we have:

g(x) has the greatest maximum value of 7 1/2
All the values of h(x) are negative
All the values of f(x) are positive

This means that the true statements about the functions are g(x) has the maximum greatest value and h(x) has a range of all negative numbers.

Read more about domain and range at:

brainly.com/question/17019835

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A division of Ditton Industries manufactures the Futura model microwave oven. The daily cost (in dollars) of producing these mic

Fofino [41]

Answer:

The actual cost incurred in manufacturing:

the 111st oven is $114.07
the 221st oven is 122.71
the 311st oven is $140.59

The marginal cost when x = 110, 220, and 310 is

$C'(110)=\$114.06$

$C'(220)=\$122.64$

$C'(310)=\$140.46$

Step-by-step explanation:

We know that the daily cost function of producing microwave ovens is given by

$C(x)=0.0002x^3 - 0.06x^2 + 120x + 5000$

(a) The actual cost incurred in manufacturing the 111st oven is the difference between the total cost incurred in manufacturing the first 111 ovens and the total cost of manufacturing the first 110 ovens:

$C(111)-C(110)=[0.0002(111)^3 - 0.06(111)^2 + 120(111) + 5000]-[0.0002(110)^3 - 0.06(110)^2 + 120(110) + 5000]\\\\C(111)-C(110)=17854.27-17740.2\\\\C(111)-C(110)=114.07$

For the 221st

$C(221)-C(220)=[0.0002(221)^3 - 0.06(221)^2 + 120(221) + 5000]-[0.0002(220)^3 - 0.06(220)^2 + 120(220) + 5000]\\\\C(221)-C(220)=30748.31-30625.6\\\\C(221)-C(220)=122.71$

For the 311st

$C(311)-C(310)=[0.0002(311)^3 - 0.06(311)^2 + 120(311) + 5000]-[0.0002(310)^3 - 0.06(310)^2 + 120(310) + 5000]\\\\C(311)-C(310)=42532.79-42392.2\\\\C(311)-C(310)=140.59$

(b) If C(x) is a total cost function, then the marginal cost function is defined to be its derivative C'(x).

We need to find the derivative of the total cost function:

$\frac{d}{dx}C(x)=\frac{d}{dx}(0.0002x^3 - 0.06x^2 + 120x + 5000)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\\frac{d}{dx}C(x)=\frac{d}{dx}\left(0.0002x^3\right)-\frac{d}{dx}\left(0.06x^2\right)+\frac{d}{dx}\left(120x\right)+\frac{d}{dx}\left(5000\right)\\\\C'(x)=0.0006x^2-0.12x+120$

The marginal cost when x = 110, 220, and 310 is given by

$C'(110)=0.0006(110)^2-0.12(110)+120\\C'(110)=114.06$

$C'(220)=0.0006(220)^2-0.12(220)+120\\C'(220)=122.64$

$C'(310)=0.0006(310)^2-0.12(310)+120\\C'(310)=140.46$

6 0

3 years ago

What is the solution to the system of equations?

sukhopar [10]

Answer:

(x, y) = (-3, -6)

Step-by-step explanation:

The second equation can be used to write an expression for y:

... -5x -21 = y . . . . . . . add y-21 to both sides

This expression can be substituted for y in the first equation:

... 6 = -4x +(-5x -21)

... 27 = -9x . . . . . add 21, collect terms

... -3 = x . . . . . . . divide by -9

Using this value of x in the expression for y, we find ...

... -5(-3) -21 = y = -6

The solution is x = -3, y = -6.

8 0

3 years ago

Find the complete factorization of the expression. 32xy − 56xyz A) 8xy(4 − 7z) B) −8xy(4 + 7z) C) xy(32 − 56z) D) 8(4xy − 7xyz)

Sav [38]

The answer is A. Greatest common factor is 8xy because of the gcf and wat the equation has in common, xy. Then you are here- 8xy(?-?). Now, you have to find what's in the parenthesis. So, what number multiplied by 8xy gives you 32, you already have your variables, is 4. 8xy(4-?). Then what number multiplied by 8xy gives you -56z? It's -7z. So u r done. 8xy(4-7z).

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4 years ago

Please help!!!

lisov135 [29]

Answer:

f(0) = 3

.....

.................................

4 0

3 years ago

viva [34]

Please read "Step-by-step" if you're having trouble

Answer:

x²(1- $\frac{1}{4}$ $\pi$ )

Step-by-step explanation:

Each side of the cookie dough is x long, since there is no given number, the diameter of the plate is also x, its as long as the square is wide, making the radius 1/2x.

The area of the cookie dough is x², the area of the plate is 1/4 $\pi$ x².

You have the equation x²- $\frac{1}{4}$ $\pi$ x²the equation has a Greatest Common Factor of x² so your factored equation is x²(1- $\frac{1}{4}$ $\pi$ )

8 0

3 years ago