A model of a boat is 4 inches wide and 12 inches high. If the actual boat is 12 feet wide, what is the height?

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

1 year ago

Which of the following tables shows a rate greater than 1 kilometer per hour

LenKa [72]

Answer:

it is C

Step-by-step explanation:

4 0

2 years ago

tony buy 3 packages of gum. each package has 5 packs of gum.each pack of gumhas 10 pieces in it how many pieces of gum are in al

marin [14]

1 pack has 5 seperate packs, each with 10 pieces
=>50 pieces
50*3=150 pieces of gum

5 0

3 years ago

If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalen

alexandr1967 [171]

The new equation after the expression equivalent to x from the first equation is substituted into the second equation is: $2(-4y-9)+5y=-6$

Step-by-step explanation:

We will solve the initial steps for substitution method for finding the correct answer

Given equations are:

$x+4y = -9\ \ \ \ Eqn1\\2x+5y=-6\ \ \ Eqn2$

From equation one

$x+4y = -9\\x+4y-4y = -9-4y\\x = -4y-9$

Putting x = -4y-9 in equation 2

$2(-4y-9)+5y=-6$

Hence,

The new equation after the expression equivalent to x from the first equation is substituted into the second equation is: $2(-4y-9)+5y=-6$

Keywords: Linear equations, variables

Learn more about linear equations at:

#LearnwithBrainly

6 0

3 years ago

For A brainlist ** explain

IrinaVladis [17]

Answer:

So interval notation is with ( and [ where ( is exclusive and [ is inclusive.

Like (1,2) is between 1 and 2 exclusive. [1,2] is between 1 and 2 inclusive. (1,2] is between 1 and 2, 1 exclusive 2 inclusive.

at the point (6,0) you see that the graph goes from above 0 to below 0 (from positive to negative)

The values are positive when x is less than 6 and negative when x is greater than 6.

so the positive interval is

(-infinity, 6)

and with inifinity you always use exclusive

It's that because everything from all the way to the left (-infinity) to 6, is above the x-axis, which means it's positive

using this logic can you do the negative interval?

5 0

2 years ago