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nata0808 [166]
2 years ago
8

Show questions

Mathematics
1 answer:
cupoosta [38]2 years ago
7 0

Answer:

The cost is a fixed $2, plus $3.25 for any additional hour.

Then if you rent it for x hours, the cost is:

c(x) = $2 + $3.25*x

Is this situation continuous or discrete?

Yes, it is discrete, because x is "the number of hours"

so if you rent it for 1.30 hours, they will say "ok, this is equivalent to two hours".

This means that while the values of x are continuous, the possible costs are:

{$2, $2 + $3.25, $2 + 2*$3.25, ....}

Which is a discrete set.

Then the sign for 1 to 5 hours will be:

1 hour ---------- $2 + $3.25 = $5.25

2 hours -------- $2 + 2*$3.25 = $8.50

3 hours--------- $2 + 3*$3.25 = $11.75

4 hours--------- $2 + 4*$3.25 =  $15

5 hours -------- $2 + 5*$3.25 = $18.25

In the other park the cost is only $4 for each hour (no fixed cost) then the total cost for x hours is:

c(x) = $4*x

Now, which option is better?

If we look at the costs for different numbers of hours for this other equation, we have:

1 hour ----- $4

2 hours ---- 2*$4 = $8

3 hours ----- 3*$4 = $12

4 hours ------ 4*$4 = $16

Then: if you want to skate 2 hours or less, Skate City is cheaper, if you want to skate more than that, kate Days is cheaper.

This happens because the first one has a smaller slope, meaning that is larger at first, but as x grows the price does not grow as much as in Skate City

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Step-by-step explanation:

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3 years ago
If f(x) = 2x^4, then f'(3) =
valkas [14]

To find f'(3) (f prime of 3), you must find f' first.  f' is the derivative of the function f(x).

Finding the derivative of f(x) = 2x⁴ requires the use of the power rule.

The power rule for derivatives is \frac{d}{dx} [x^{n} ] =nx^{n-1}.  In other words, you bring the exponent forward and multiply it by the coefficient of the term, and then you subtract 1 from the original exponent.

f'(x) = \frac{d}{dx}(2x⁴)

f'(x) = 2(4)x³

f'(x) = 8x³

Now, to find f'(3), plug 3 into your derivative.

f'(3) = 8(3)³

f'(3) = 216

<h3>Answer:</h3>

f'(3) = 216

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