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Paha777 [63]
3 years ago
8

A car driving on a straight track accelerates at a rate of 3.2 m/s2 for 14 s. If the initial velocity of the car was 5.1 m/s, an

d its initial position was 0 m, what is its final position?
Mathematics
1 answer:
liraira [26]3 years ago
6 0

Answer:

The data we have is:

The acceleration is 3.2 m/s^2 for 14 seconds

Initial velocity = 5.1 m/s

initial position = 0m

Then:

A(t) = 3.2m/s^2

To have the velocity, we integrate over time, and the constant of integration will be equal to the initial velocity.

V(t) = (3.2m/s^2)*t + 5.1 m/s

To have the position equation, we integrate again over time, and now the constant of integration will be the initial position (that is zero)

P(t) = (1/2)*(3.2 m/s^2)*t^2 + 5.1m/s*t

Now, the final position refers to the position when the car stops accelerating, this is at t = 14s.

P(14s) =   (1/2)*(3.2 m/s^2)*(14s)^2 + 5.1m/s*14s = 385m

So the final position is 385 meters ahead the initial position.

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Answer:

y = -2x + 3

Step-by-step explanation:

Let's just put the three points together.

(-1, 5) (-4, 11) (-7, 17)

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Plug in using (-1, 5) and (-4, 11)

11 - 5/-4 + 1 = 6/-3 (simplify)

-2 is the slope

Now plug in (-7, 17) in the equation to get b or the y-intercept)

y = mx + b

17 = -2(-7) + b

17 = 14 + b (subtract 14 on both sides)

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3 years ago
A public library has an aquarium in the shape of a rectangular prism. The base is 6 feet by 2.5 feet. The height is 4 feet. How
goldenfox [79]
6 * 2.5 = 15 That’s the area of the base

2.5 * 4 = 10
10 * 2 = 20
That’s the area of the 2 smaller sides

6 * 4 = 24
24 * 2 = 48
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Then you add all the dimensions together.

15+20+48 = 83.

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3 years ago
X2 - 6x + 9<br> help solve
Ulleksa [173]

Answer:

3

lazy approach was with a graphic plotting program, but you can also calculate it. with the pq-formula.

p = -6

q = 9

x = -p/2 +- sqrt( (p/2)² - q)

x = -(-6)/2 +- sqrt ( (-6/2)² - 9)

x = 3 +- sqrt(9-9)

x = 3 +- sqrt(0)

x = 3 +- 0

x = 3

4 0
3 years ago
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Solve each of the following quadratic equations<br><br> 3x=0.5x^2<br><br><br> 0=5x^2-2x+6
UNO [17]

<u>Question 1</u>

<u />3x=0.5x^{2}\\\\6x=x^{2} \\ \\ x^{2}-6x=0 \\ \\ x(x-6)=0 \\ \\ \boxed{x=0, 6}

<u>Question 2</u>

<u />0=5x^{2}-2x+6 \\ \\ x=\frac{2 \pm \sqrt{(-2)^{2}-4(5)(6)}}{2} \\ \\ x=\frac{2 \pm \sqrt{-116}}{10} \\ \\ x=\frac{2 \pm 2i\sqrt{29}}{10} \\ \\ \boxed{x=\frac{1 \pm i\sqrt{29}}{5}}

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y = -4x + 16
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