Hello :
f'(7) = the slope of the tangent line : let A(7,4) B(0,3)
the slope is : (YB - YA)/(XB -XA)= (3-4)/(0-7) = -1/-7 = 1/7=f'(7)
the equation of the tangent line is :
y-3 = 1/7 (x-0)
y = (1/7)x+3
the line tangent and the graph of : f passes through the point A(7, 4)
x= 7 y=4 so : f(7) =4

4 0

3 years ago

1. Adam has 2.6 gallons of red paint, 2.35 gallons of white paint, and 2 5/8 gallons of blue paint. If he wants to use up the ca

Korvikt [17]

1. Blue

2. 18 units

3. 3 students

4. 36.75 lbs

7 0

3 years ago

The price of a European tour includes stopovers at five cities to be selected from 15 cities. In how many ways can a traveler pl

xeze [42]

Answer:

The traveler can plan such a tour in 3003 ways.

Step-by-step explanation:

The order that the cities are chosen is not important, since it is chosen by the company and not by the traveler. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this problem, we have that:

Combinations of 5 cities from a set of 15. So

$C_{15,5} = \frac{15!}{5!10!} = 3003$

The traveler can plan such a tour in 3003 ways.

4 0

3 years ago