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Llana [10]
3 years ago
15

Velocity of a Car The velocity of a car (in feet per second) t sec after starting from rest is given by the function f(t) = 11 t

(0 ≤ t ≤ 30). Find the car's position, s(t), at any time t. Assume that s(0) = 0. s(t) =
Mathematics
1 answer:
pochemuha3 years ago
6 0

Answer:

<h2>s(t) = 11t²/2 </h2>

Step-by-step explanation:

Velocity is defined as the rate of change in displacement of a body. It is expressed mathematically as v = change in displacement/time

v(t) = ds(t)/dt

ds(t) = v(t)dt

integrating both sides;

s(t) =  \int\limits v(t)dt

Given the velocity function f(t) = 11t, the car's position (displacement) is expressed as s(t) = \int\limits 11t\ dt

s(t) = 11t²/2 + C

at the initial point, s(0) = 0 i.e when t = 0, s(t) = 0. The resulting equation becomes;

0 = 11(0)²/2+ C

0 = 0+C

C = 0

To find the car's position, s(t), we will substitute C = 0 into the equayion above;

s(t) = 11t²/2 + 0

s(t) = 11t²/2

Hence s(t) = 11t²/2  is the required position of the car in terms of t.

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You can set up a proportion:
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Using the distance formula, calculate how far Tre threw the ball. (4 points: 2 points for setup, 1 for calculation, 1 for the an
sergij07 [2.7K]

Answer:

D = 63.717

Step-by-step explanation:

The details that complete the question are:

(x_1,y_1) = (0,42.78)

and

(x_2,y_1)=(90,42.78)

Required

Determine how far the ball travelled

Distance is calculated using:

D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Substitute values for x's and y's

D = \sqrt{(42.78 - 0)^2+(42.78-90)^2}

D = \sqrt{42.78^2+(-47.22)^2

D = \sqrt{1830.1284+2229.7284

D = \sqrt{4059.8568

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<em>Hence, the ball travelled a distance of 63.717 units</em>

6 0
3 years ago
Find the missing angles for every point here
dimulka [17.4K]

In order to find the missing angles, we can see that vertically opposite angles and corresponding angles are equal.

46° + 82° + No. 4 = 180°

No. 4 = 180° - 128° = 52°

Therefore: No. 4 = No. 1 = 52° (vertically opposite angles)

<h3>What is angle?</h3>

In geometry, an angle is actually known to be the figure that is created by two rays that actually meet at an end point that is common to the both rays. It is represented by the symbol: ∠.

So, we can see that:

Line a || Line b and Line c || Line d

46° = 7 (corresponding angles)

So, 46° + 82° + No. 4 = 180°

Thus, No. 4 = 180° - 128° = 52°

Therefore:

No. 4 = No. 1 = 52° (vertically opposite angles)

No. 2 = 180° - 52° = 128° (angles on a straight line)

No. 2 = No. 3 = 128° (vertically opposite angles)

No. 7 = No. 6 = 46° (vertically opposite angles)

No. 8 = 180° - 46° = 134° (angles on a straight line)

No. 8 = No. 5 = 134° (vertically opposite angles).

82° = No. 11 (vertically opposite angles)

No. 9 = 180° - 82° = 98° (angles on a straight line)

No. 9 = No. 10 = 98° (vertically opposite angles)

No. 9 = No. 15 = 98° (alternate angles)

No. 13 = No. 15 = 98° (vertically opposite angles)

No. 12 = No. 14 = 82° (vertically opposite angles)

46°= No. 17 (vertically opposite angles)

No. 18 = 180° - 46° = 134° (angles at a point)

No. 18 = No. 16 = 134° (vertically opposite angles)

No. 19 = 180° - (46° + 82°) = 52° (sum of angles in a triangle)

No. 19 = No. 22 = 52° (vertically opposite angles)

No. 20 = 180° - 52° = 128° (angles on a straight line).

No. 20 = No. 21 = 128° (vertically opposite angles)

No. 25 = No. 2 = 128° (corresponding angles)

No. 25 = No. 24 = 128° (vertically opposite angles)

No. 23 = No. 26° (vertically opposite angles).

So, all the angles are:

1= 52°

2= 128°

3= 128°

4= 52°

5= 134°

6= 46°

7= 46°

8=134°

9= 98°

10= 98°

11= 82°

12= 82°

13= 98°

14= 82°

15= 98°

16= 134°

17= 46°

18= 134°

19= 52°

20= 128°

21= 128°

22= 52°

23= 52°

24= 128°

25= 128°

26= 52°

Learn more about angles on brainly.com/question/26167358

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