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ladessa [460]
3 years ago
8

A carnival costs $10.50 to enter plus an additional $3.50 per ticket for rides and food.

Mathematics
1 answer:
Goryan [66]3 years ago
5 0

Answer:

\$80.50

Step-by-step explanation:

Let

n ----> represent the number of tickets purchased

y --->   the total cost for a visit to the carnival in dollars

we know that

The linear equation in slope intercept form is equal to

y=m(n)+b

where

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value

In this problem we have

The unit rate or slope is equal to

m=\$3.50\ per\ ticket

The y-intercept is equal to the cost for enter (value of y when the value of x is equal to zero)

b=\$10.50

substitute

y=3.50(n)+10.50

For n=20 tickets

substitute the value of n and solve for y

y=3.50(20)+10.50

y=\$80.50

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The derivative of this is computed as

\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=3\frac{d}{dx}\left(\left(4x^2+8\right)^5\right)\\\\\mathrm{Apply\:the\:chain\:rule}:\quad \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx}\\f=u^5,\:\:u=\left(4x^2+8\right)\\\\3\frac{d}{du}\left(u^5\right)\frac{d}{dx}\left(4x^2+8\right)\\\\3\cdot \:5\left(4x^2+8\right)^4\cdot \:8x\\\\120x\left(4x^2+8\right)^4

The derivative of the function is \frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4.

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