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4 years ago

Complete the paragraph proof to prove the statement.

Mathematics

1 answer:

Aleonysh [2.5K]4 years ago

7 0

Answer:

1. angle DEF

2. definition of congruent angles

3. the measure of angle GHI

Step-by-step explanation:

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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

If 30% of the students in your class like basketball, how many students are in your class if 6 students like

7nadin3 [17]

You need 20 students in the class

3 0

4 years ago

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Which expression is equivalent to 9-2? -81 -18

Ilia_Sergeevich [38]

Are those the only answer choices?

5 0

3 years ago

Look at the figure above: If the measure of <MNL is 43°, find the measures of the following angles. Be sure to justify each m

zimovet [89]

Answer:

NP = 43

LNO = 137

MNP = 137

Step-by-step explanation:

MNL is a vertical angle to PNO, therefore they are equal

MNL = PNO

MNL = 43 = PNO

MNL and LNO are supplementary angles. They add to 180 degrees

MNL + LNO = 180

43+LNO = 180

Subtract 180 from each side

43-43 +LNO = 180-43

LNO = 137

LNO and MNP are vertical angles. Vertical angles are equal

LNO = MNP

137=MNP

3 0

3 years ago

This is too much for me if you know please answer

SOVA2 [1]

Answer:

-4x + y + 6z

Step-by-step explanation:

Combine like terms (Terms with the same variable):

(2x + 5y - z) + (-6x - 4y + 7z)

Add straight across:

2x - 6x = -4x

5y - 4y = y

-z + 7z = 7z - z = 6z

-4x + y + 6z is your answer.

8 0

3 years ago

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