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Pie
3 years ago
11

A car is being driven at a rate of 40 ft/sec when the brakes are applied. The car decelerates at a constant rate of 10 ft/sec2.

Calculate how far the car travels in the time it takes to stop. Round your answer to one decimal place.
Mathematics
1 answer:
IRISSAK [1]3 years ago
4 0

Answer:

80 feet

Step-by-step explanation:

Given:

Initial speed of the car (v_0) = 40 ft/sec

Deceleration of the car (\frac{dv}{dt}) = -10 ft/sec²

Final speed of the car (v_x) = 0 ft/sec

Let the distance traveled by the car be 'x' at any time 't'. Let 'v' be the velocity at any time 't'.

Now, deceleration means rate of decrease of velocity.

So, \frac{dv}{dt}=-10\ ft/sec^2

Negative sign means the velocity is decreasing with time.

Now, \frac{dv}{dt}=\frac{dv}{dx}(\frac{dx}{dt}) using chain rule of differentiation. Therefore,

\frac{dv}{dx}\cdot\frac{dx}{dt}= -10\\\\But\ \frac{dx}{dt}=v.\ So,\\\\v\frac{dv}{dx}=-10\\\\vdv=-10dx

Integrating both sides under the limit 40 to 0 for 'v' and 0 to 'x' for 'x'. This gives,

\int\limits^0_{40} {v} \, dv=\int\limits^x_0 {-10} \, dx\\\\\left [ \frac{v^2}{2} \right ]_{40}^{0}=-10x\\\\-10x=\frac{0}{2}-\frac{1600}{2}\\\\10x=800\\\\x=\frac{800}{10}=80\ ft

Therefore, the car travels a distance of 80 feet before stopping.

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How can you tell if a discontinuity of a limit is removable or not removable?
azamat

A discontinuity is present if any of ...

  • the limit doesn't exist
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If the one of these that is the cause of discontinuity is the last one and defining the function will make this issue go away, then the discontinuity is removable.

8 0
3 years ago
Instructions
exis [7]

Answer:

Note Due Date Interest due at Maturity

1 Mar 6 $500

2 Apr 23 $360

3 July 20 $840

4 Sept 6 $945

5 Nov 29 $270

6 Dec 30 $300

Step-by-step explanation:

Calculation to Determine the due date and the amount of interest due at maturity for Flush Mate Co.

Using this formula to Calculate for the amount of interest due at maturity.

Interest due at Maturity= [Face amount * Numbers of days to maturity / 360 * Interest rate]

Note, Due Date,  Face Amount, No of days to maturity,  Interest rate, Interest due at Maturity

1 Mar 6 80,000× 45/360 ×5% =$500

2 Apr 23 24,000 × 60/360 ×9% =$360

3 July 20 42,000×120/360 ×6% =$840

4 Sept 6 54,000× 90/360 ×7% =$945

5 Nov 29 27,000× 60/360 ×6% =$270

6 Dec 30 72,000× 30/360 ×5% =$300

Therefore  the due date  and the amount of interest due at maturity for Flush Mate Co are:

Note Due Date Interest due at Maturity

1 Mar 6 $500

2 Apr 23 $360

3 July 20 $840

4 Sept 6 $945

5 Nov 29 $270

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4 0
3 years ago
Use the table to find the COORDINATES of the image ​
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Answer:

Q = ( -3 , 6 ) .... R = ( -1 , 8 )  ...... S = ( -5 , 7 )

Step-by-step explanation:

Q = ( 1 + ( -4 ) , 4 + 2 ) = ( -3 , 6 )

R = ( 3 + ( -4 ) , 6 + 2 ) = ( -1 , 8 )

S = ( -1 + ( -4 ) , 5 + 2 ) = ( -5 , 7 )

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2 years ago
Victoria’s printer can print 8.804 in one minute if Victoria’s prints page for 0.903 minutes, about how many pages will she have
SVETLANKA909090 [29]

Victoria’s printer can print 8.804 in one minute if Victoria’s prints page for 0.903 minutes,

We apply unitary method

In one minute the number of pages printed is 8.804. we need to find the number of pages for 0.903 minutes

1 minute = 8.804 pages

0.903 minutes = ? pages

We multiply 8.804 by 0.903

8.804 * 0.903 = 7.95

Number of pages printed = 7.95 pages


8 0
3 years ago
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