Chapter 6.4, Problem 33PPS

(a)

To determine

To find: The value of given equation for $0\le x\le 10$ .

Answer to Problem 33PPS

The value of given equation for $0\le x\le 10$ are shown in table (1).

Explanation of Solution

Given information:

The givenequation of deflection is $d\left(x\right)=0\cdot 015x^2-0\cdot 0005x^3$ .

Calculation:

For the given equation the table is shown in table (1).

$x$	$d\left(x\right)$
$0$	$0$
$1$	$0\cdot 014$
$2$	$0\cdot 056$
$3$	$0\cdot 122$
$4$	$0\cdot 208$
$5$	$0\cdot 313$
$6$	$0\cdot 432$
$7$	$0\cdot 564$
$8$	$0\cdot 704$
$9$	$0\cdot 85$
$10$	$1$

Table (1)

Therefore,the value of given equation for $0\le x\le 10$ are shown in table (1).

(b)

To determine

To graph:For the given equation.

Explanation of Solution

Given information:

The given equation of deflection is $d\left(x\right)=0\cdot 015x^2-0\cdot 0005x^3$ .

Graph:

Using the table (1) from part (a).

The graph for the given equation is shown in figure (2).

  

Figure (2)

Interpretation:Graph for the equation $d\left(x\right)=0\cdot 015x^2-0\cdot 0005x^3$ is shown in figure (2).

(c)

To determine

To find: The behavior of the graph for $x$ increases.

Answer to Problem 33PPS

The deflection of the diving board increases as the diver gets further from the diving-board from $0$ to $1$ .

Explanation of Solution

Given information:

The given equation of deflection is $d\left(x\right)=0\cdot 015x^2-0\cdot 0005x^3$ .

Calculation:

From the graphshown in figure (2), the graph of the function for $x\in \left[0,10\right]$ . The graph suggest that the deflection of the diving board increases as the diver gets further from the diving-board from $0$ to $1$ .

Therefore, the deflection of the diving board increases as the diver gets further from the diving-board from $0$ to $1$ .

(d)

To determine

To find:Whether their trend continue indefinitely.

Answer to Problem 33PPS

The trend will not continue indefinitely.

Explanation of Solution

Given information:

The given equation of deflection is $d\left(x\right)=0\cdot 015x^2-0\cdot 0005x^3$ .

Calculation:

From the graph shown in figure (2), the deflection of the diving board increases as the diver gets further from the diving-board from $0$ to $1$ .As the value of $x$ cannot be greater than $10$ , so the trend will not continue indefinitely.

Therefore, the trend will not continue indefinitely.