(d) The particle moves in the positive direction when its velocity has a positive sign. You know the particle is at rest when $t=0$ and $t=3$ , and because the velocity function is continuous, you need only check the sign of $v(t)$ for values on the intervals (0, 3) and (3, 6).

We have, for instance $v(1)\approx-0.91$ and $v(4)\approx0.91>0$ , which means the particle is moving the positive direction for $3$ , or the interval (3, 6).

(e) The total distance traveled is obtained by integrating the absolute value of the velocity function over the given interval:

$\displaystyle\int_0^6|v(t)|\,\mathrm dt=\int_0^3-v(t)\,\mathrm dt+\int_3^6v(t)\,\mathrm dt$

which follows from the definition of absolute value. In particular, if $x$ is negative, then $|x|=-x$ .

The total distance traveled is then 4 ft.

(g) Acceleration is the rate of change of velocity, so $a(t)$ is the derivative of $v(t)$ :

$a(t)=v'(t)=-\dfrac{\pi^2}9\cos\left(\dfrac{\pi t}3\right)$

Compute the acceleration at $t=4$ seconds:

$a(t)=\dfrac{\pi^2}{18}\dfrac{\rm ft}{\mathrm s^2}$

(In case you need to know, for part (i), the particle is speeding up when the acceleration is positive. So this is done the same way as part (d).)

6 0

3 years ago

Need help how do I do this, start it, and the steps please

Harman [31]

Let's solve this problem step-by-step.

STEP-BY-STEP SOLUTION:

Let's first write down the equation we are going to solve.

( 1 / 3 )h - 4 [ ( 2 / 3 )h - 3 ] = ( 2 / 3 )h - 6

To begin with, we will expand the brackets => [ ]

( 1 / 3 )h - ( 8 / 3 )h + 12 = ( 2 / 3 )h - 6

Next we will collect like terms by placing all the individual numbers on the right-side of the equation and the terms with ( h ) on the left-hand side of the equation so that we can begin making ( h ) the subject.

( 1 / 3 )h - ( 8 / 3 )h - ( 2 / 3 )h = - 6 - 12

Then we will simplify both the left-hand side and right-hand side of the equation to solve it for ( h ).

( - 9 / 3 )h = - 18

- 3h = - 18

h = - 18 / - 3

h = 18 / 3

h = 6

FINAL ANSWER:

Therefore, the answer is:

h = 6

Hope this helps! :)
Have a lovely day! <3

4 0

3 years ago

The function T(n) is defined below. Which of the following are equal to T(8)? Check all that apply.

Liula [17]

In function T(n), in which n = 8, plug in 8 for n

T(n) = 4n - 5
T(8) = 4(8) - 5

multiply 4 and 8

4(8) = 32

T(8) = 32 - 5

Simplify

T(8) = 27

27, or C) is your answer.

hope this helps

7 0

3 years ago

Read 2 more answers

Van Gogh’s painting Starry Night measures 92 cm long by 73 cm high. You buy two posters, each showing an enlargement of the pa

nirvana33 [79]

I think it's 138 Long by 109.5 more accurate .
92/73 = 1.26
120/100 = 1.2
138/109.5 =1.26
Hence 138 by 109.5 is more proportionate

3 0

3 years ago