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raketka [301]
3 years ago
5

Suppose a baby food company has determined that its total revenue R for its food is given by R = − x ^3 + 102 x ^2 + 1575 x wher

e R is measured in dollars and x is the number of units (in thousands) produced. What production level will yield a maximum revenue?
Mathematics
1 answer:
cricket20 [7]3 years ago
7 0

Answer:

75 thousand

Step-by-step explanation:

R = -x³ + 102x² + 1575x

To maximize R, find dR/dx and set to 0:

dR/dx = -3x² + 204x + 1575

0 = -3x² + 204x + 1575

0 = x² − 68x − 525

0 = (x + 7) (x − 75)

x = -7 or 75

Since x can't be negative, x = 75.

Therefore, the revenue is a maximum when 75 thousand units are produced.

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2)<br> A circle has a radius of 8 cm. What is its circumference?<br> 8 cm
egoroff_w [7]

Answer

16π cm ≈ 50.2655 cm

Step-by-step explanation

To find the circumference of a circle, we can use the equation C = 2πr.

C stands for the circumference while r stands for the radius. We can see that there is a proportional positive linear relationship between radius and circumference for all circles, and that to find circumference when we have a radius value, we multiply the radius value by 2π.

The value of π, also called pi, is a constant and is the ratio of a circle's circumference to its diameter (the diameter is twice the radius, hence the 2 in the equation). Note that π is a constant and applies to all circles because all circles are similar.

Since we know the value of r, or the radius, given as 8 cm in the question, we can plug this value into the equation C = 2πr from earlier.

C = 2πr (plug in 8 cm for the radius)

C = 2π * 8

C = 16π cm

Since the radius is in units of cm (centimeters), the circumference is also in units of cm (centimeters).

16π cm is the exact value of the circumference. However, if we want this circumference in decimal form, we would multiply 16 by the decimal form of π which is approximately 3.1416. Note that π actually has an infinite amount of decimals and that this 3.1416 is actually a rounded π value

C = 16π

C ≈ 16 * 3.1416

C ≈ 50.2655 cm rounded to four decimal places

6 0
3 years ago
Simplify 30x-140-(x-4)
balu736 [363]

Answer:

x = 4.7

Step-by-step explanation:

30x - 140 -(x - 4)

Multiply the -1 into (x - 4)

30x - 140 - x + 4

Add/subtract

29x - 136 = 0

      +136

29x = 136

\frac{29x}{29} = \frac{136}{29}

x = 4.689655172413793

8 0
3 years ago
Ben has 3 times as many guppies as goldfish if he has a total of 20 fish how many guppies does have?
kondor19780726 [428]
Guppies: u
Goldfish: o

3 times as many guppies as goldfish
3*o = u   (there are more guppies than goldfish)

o + u = 20
o = 20 - u

Substitute in (20 - u)  for o in the first equation and solve:
3* (20 - u) = u
60 - 3u = u
60 = 4u
u  = 15

He has 15 guppies. Then substitute in the number of guppies into either equation to find the number of goldfish:
o + u = 20
o + (15) = 20
o = 5

Hope this helps! :)

4 0
3 years ago
How many equilateral triangles with sides of 4 can fit into a larger triangle with sides of 2012
igomit [66]
The base measures 2012 if you divide that by four you get 503 trianles on the bottom and on the sides and each one gets one smaller until you get to one so 503+502+501,.... or 252+251(504) so the answer is 126,756 triangles in total because 1+503=504  2+502=504... when you get to 252 you just add that to itself so that is the odd one out
6 0
3 years ago
What is the square root of 100
tino4ka555 [31]
I believe that the answer to the equation is 10
8 0
2 years ago
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