How many 12/4 are in 3

Find f(a), f(a+h), and 71. f(x) = 7x - 3 f(a+h)-f(a) h if h = 0. 72. f(x) = 5x²

Leni [432]

Answer:

$71. \ \ \ f(a) \ = \ 7a \ - \ 3; \ f(a+h) \ = \ 7a \ + \ 7h \ - \ 3; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 7$

$72. \ \ \ f(a) \ = \ 5a^{2}; \ f(a+h) \ = \ {5a}^{2} \ + \ 10ah \ + \ {5h}^{2}; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 10a \ + \ 5h$

Step-by-step explanation:

In single-variable calculus, the difference quotient is the expression

$\displaystyle\frac{f(x+h) \ - \ f(x)}{h}$ ,

which its name comes from the fact that it is the quotient of the difference of the evaluated values of the function by the difference of its corresponding input values (as shown in the figure below).

This expression looks similar to the method of evaluating the slope of a line. Indeed, the difference quotient provides the slope of a secant line (in blue) that passes through two coordinate points on a curve.

$m \ \ = \ \ \displaystyle\frac{\Delta y}{\Delta x} \ \ = \ \ \displaystyle\frac{rise}{run}$ .

Similarly, the difference quotient is a measure of the average rate of change of the function over an interval. When the limit of the difference quotient is taken as h approaches 0 gives the instantaneous rate of change (rate of change in an instant) or the derivative of the function.

Therefore,

$71. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{(7a \ + \ 7h \ - \ 3) \ - \ (7a \ - \ 3)}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{7h}{h} \\ \\ \-\hspace{4.25cm} = \ \ 7$

$72. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{{5(a \ + \ h)}^{2} \ - \ {5(a)}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{{5a}^{2} \ + \ 10ah \ + \ {5h}^{2} \ - \ {5a}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{h(10a \ + \ 5h)}{h} \\ \\ \-\hspace{4.25cm} = \ \ 10a \ + \ 5h$

4 0

2 years ago

A tuple is immutable. What does that mean?

Fantom [35]

Answer:

A tuple cannot be changed once it is created.

Step-by-step explanation:

4 0

3 years ago

Find the area of the following shape. (8 points) what is the answer?

Ivenika [448]

Answer:

72 square units

Step-by-step explanation:

Identify the height
Identify the length
Multiply those two together
That is your answer

H = 9 units

L = 8 units

A = H × L

A = 9 × 8

A = 72 square units

8 0

2 years ago

Mr. Smith traveled to a city 300 miles from his home to attend a meeting. Due to car trouble, his average speed returning was 6

Kryger [21]

Answer: The speed at which he traveled to the city is 69.8 mph

Step-by-step explanation:

Let x represent the speed at which he traveled to the city.

Mr. Smith traveled to a city 300 miles from his home to attend a meeting.

Time = distance/speed

Time taken to travel to the city is

300/x

Due to car trouble, his average speed on returning was 6 mph less than his speed going. This means that the speed at which he returned is (x - 6) mph. Time taken to return from the city is

300/(x - 6)

If the total time for the round trip was 9 hours, it means that

300/x + 300/(x - 6) = 9

Cross multiplying by x(x - 6), it becomes

300(x - 6) + 300x = 9x(x - 6)

300x - 1800 + 300x = 9x² - 54x

9x² - 54x - 300x - 300x - 1800 = 0

9x² - 654x -1800 = 0

Applying the general quadratic equation,

x = [- b ± √(b² - 4ac)]/2a

From the equation given,

a = 9

b = - 654

c = 1800

Therefore,

x = [- - 654 ± √(- 654² - 4 × 9 × 1800)]/2 × 9

x = [654 ± √(427716 - 64800)]/18

x = [654 ± √362916.4]/18

x = (654 + 602.4)/2 or x = (654 - 602.4)/18

x = 1256.4/18 or x = 51.6/18

x = 69.8mph or x = 2.9 mph

The speed at which he traveled to the city is 69.8 mph

By checking,

Time spent travelling to the city = 300/69.8 = 4.3 hours

Time spent returning =

300/(69.8 - 6) = 4.7 hours

4.3 + 4.7 = 9 hours

3 0

3 years ago

4a + c =17 A B C are consecutive numbers.

iris [78.8K]

A=3
B=4
C=5
Substitute 3 in for 'a' in the equation, and 5 in for 'c' in the equation to get 17.

6 0

2 years ago