42/9 in mixed fraction

The height (feet) of an object moving vertically is given by s= (-16t^2)+(208t)+(156), where t is in seconds.

OverLord2011 [107]

Answer:

The object's velocity at t = 7 is -16 ft/s

The maximum height is 832 ft and it occurs when $t=\frac{13}{2}$

Step-by-step explanation:

From the information given, the equation of motion of the object is

$s(t)= -16t^2+208t+156$

For any equation of motion s(t), the instantaneous velocity at time t is given by

$v(t)=\frac{ds}{dt}$

(a) To find the object's velocity at t = 7, you must:

$v(t)=\frac{d}{dt}(-16t^2+208t+156)\\\\v(t)=-\frac{d}{dt}\left(16t^2\right)+\frac{d}{dt}\left(208t\right)+\frac{d}{dt}\left(156\right)\\\\v(t)=-32t+208+0\\\\v(t)=-32t+208$

Next, we evaluate when t = 7

$v(7)=-32(7)+208=-224+208\\\\v(7)=-16$

The object's velocity at t = 7 is -16 ft/s

(b) To find the maximum of a function we always use the derivative of the function and we set it equal zero to find the critical points.

To find the maximum height and when it occurs, we set the velocity function equal to 0 and solve for t.

$-32t+208=0\\\\-32t+208-208=0-208\\\\-32t=-208\\\\\frac{-32t}{-32}=\frac{-208}{-32}\\\\t=\frac{13}{2}$

Next, we substitute this value into the equation of motion to find the maximum height

$s(\frac{13}{2})= -16(\frac{13}{2})^2+208(\frac{13}{2})+156\\\\s(\frac{13}{2})=-676+1352+156)=832$

The maximum height is 832 ft and it occurs when $t=\frac{13}{2}$

6 0

3 years ago

The spinner below is spun 10 times if the experimental probability of landing on a 3 is 1/2 then what is the difference between

AysviL [449]

Answer:

Difference between the experimental and the theoretical probability is 2/5 .

Step-by-step explanation:

Spinner is spun 10 times, and experimental probability of landing on a 3 is 1/2, i.e. out of 10 times spinner lands 5 times into 3.

Now, theoretical probability of landing on a 3 is 1/10.

∴ Difference between the experimental and the theoretical probability :

⇒ (1/2) - (1/10)

⇒ 2/5

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Plz help solve this math problem

a_sh-v [17]

Answer:

3 8/9

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Find the midpoint of the line segment joining the points (6,1) and (-2, -1).

tiny-mole [99]

Step-by-step explanation:

By the formula of slope, we have

$( \frac{y _{2} - y_{1} }{x _2 - x _{1} }) \\ ( \frac{ - 1 - 1}{ - 2 - 6} ) \\ ( \frac{ - 2}{ - 8} ) \\ ( \frac{1}{4} )$

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3 years ago

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