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forsale [732]
3 years ago
10

The daily production cost, C, for x units is modeled by the equation: C = 200 – 7x + 0.345x2 Explain how to find the domain and

range of C
Mathematics
1 answer:
scZoUnD [109]3 years ago
6 0
Domain is the sex of x values that are feasible. this is all of the positive integer values + 0, in case you only consider that can produce whole units.

range is the set of possible results for c(x), possible costs.

you can derive this from the fact that c(x) is a parabole and you can draw it, for which you can find the vertex of the parabola, the roots, the y intercept, the shape. also limit the costs to be positive.

you can substitute some values for x to help you, for example.

x y
0 200
1 200 - 7 + 0.345 = 193.345
2 200 - 14 + .345(4) = 187.38
3 200 - 21 + .345(9) = 182.105

the function does not have real roots, then the costs never decrease to 0.

the function starts at c(x) = 200, decreases until the vertex, (x = 10, c = 164.5) and starts to increase

then the range goes to 164.5 to infinity, limited to the solution for x = positive integers.
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Last question please
MatroZZZ [7]

Let's try an make a formula to make things easy.

_________________________________________________

Look at Andrew's pattern, it goes up 6 every time. Lets look at the 6 times table

6 times table:           6, 12, 18, 24, ...

____________________________________

First think, how would you work out the <u>7</u>th term in the <u>6</u>th times table?

You would do <u>6</u> times <u>7</u>.

So the formula for the 6th times table is:

6n     (where n is the term you want to find out)

_______________________________________

So to get the 9th term in the 6 times table, you would replace the n with 9, like so:

9th term in 6 times table = 6 x 9 = 54

______________________________________

Now lets compare the 6 times table to Andrew's pattern:

6 times table:           6, 12, 18, 24,

Andrew's pattern:     3, 9, 15, 21,

_____________________________________

If you look, you can see that Andrew's pattern is the 6 times table minus 3!

So what would be the formula for Andrew pattern?

---> it would be:  6n - 3   (since it's the 6 times table but minus 3)

_____________________________________

We can use this formula to easily work out the 20th term in Andrew's pattern!:

20th term = 6 x 20 - 3 = 120 - 3 = <u>117</u>    (remember, replace the n with 20)

______________________________________

Now let's make a formula for Ben's pattern!

Ben's pattern goes up in 5s, so lets compare it to the 5 times table:

5 times table:       5, 10, 15, 20

Ben's pattern:       3, 8, 13, 18,

The formula for the 5 times table is 5n, and Ben's pattern is the 5 times table but minus 2.

So the formula for Ben's pattern is: 5n - 2

__________________________________

<u>Now swap out the n for 20</u>  (to get the 20th term):

20th term = 5 x 20 - 2 = 100 - 2 = <u>98</u>

_________________________________________

So Andrew's 20th term is <u>117</u>, and Ben's 20th term is <u>98</u>.

All we do now is subtract them to find the difference:

117 - 98 = <u>19</u>

- - - - - - - - - - - - - - - - - - - - - - - - -

Answer:

Ben's 20th term is smaller by 19!

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5 0
3 years ago
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