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BARSIC [14]
3 years ago
9

Please..............

Mathematics
1 answer:
Sidana [21]3 years ago
7 0

Answer:

3n

Step-by-step explanation:

the output is 3 times the input

three times n equals 3n

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Find f(a), f(a+h), and<br> 71. f(x) = 7x - 3<br> f(a+h)-f(a)<br> h<br> if h = 0.<br> 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 <em>h</em> 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
X<br> I ㅗ<br> ]<br> Factor: -2/3<br> out of -3X<br> - 12
sesenic [268]

Answer:what is this

Step-by-step explanation:

bruh

3 0
3 years ago
Question 1 (1 point)
alisha [4.7K]

Answer:

See below

Step-by-step explanation:

1) x=2-1

x=1

2) (x+1)(x+1)=2(x+1)

3) 10x-20 -11 = 4+3x

10x-3x=20+11+4

7x=35

x=5

5 0
3 years ago
A box of chocolates contains 12.5% caramels. There are 5 caramels in the box. How many pieces of chocolate are in the box?
Butoxors [25]

Answer:

8% C = 4      1% C = 4 ÷ 8 =0.5      100% C = 0.5 × 100 = 50

5 0
3 years ago
Read 2 more answers
Mr. Burk traveled 240 miles last weekend. His average rate of speed for the trip was 70 miles per hour. Since he did not stop, a
Yuki888 [10]

Answer:

about 3 1/2 hours long

Step-by-step explanation:

70 goes into 240 evenly 3 times, and 70×3 equals 210. that leaves 30 miles remaining. since he is moving at an average rate of 70mph, 3/7 would be the remaining time. to decimal that equals a total of about 3 hours and 25 minutes, which, rounded up, equals 3 and 1 half hours.

5 0
3 years ago
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