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Anestetic [448]
2 years ago
5

A body moves s metres in a time t seconds so that s = t3 – 3t2 + 8. Find:

Mathematics
1 answer:
Lady bird [3.3K]2 years ago
7 0

Using derivatives, it is found that:

i) v(t) = 3t^2 - 6t

ii) 9 m/s.

iii) a(t) = 6t - 6

iv) 6 m/s².

v) 1 second.

<h3>What is the role of derivatives in the relation between acceleration, velocity and position?</h3>
  • The velocity is the derivative of the position.
  • The acceleration is the derivative of the velocity.

In this problem, the position is:

s(t) = t^3 - 3t^2 + 8

item i:

Velocity is the <u>derivative of the position</u>, hence:

v(t) = 3t^2 - 6t

Item ii:

v(3) = 3(3)^2 - 6(3) = 27 - 18 = 9

The speed is of 9 m/s.

Item iii:

Derivative of the velocity, hence:

a(t) = 6t - 6

Item iv:

a(2) = 6(2) - 6 = 6

The acceleration is of 6 m/s².

Item v:

t for which a(t) = 0, hence:

6t - 6 = 0

6t = 6

t = \frac{6}{6}

t = 1

Hence 1 second.

You can learn more about derivatives at brainly.com/question/14800626

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Questions are in the picture
gtnhenbr [62]

The closest point is (3.5, 1.9) and the distance is 1.96 units

<h3>How to determine the point and the distance?</h3>

The coordinate is given as:

(4, 0)

The equation of the function is

y = √x

The distance between two points is calculated using

d = √(x2 - x1)^2 + (y2 - y1)^2

So, we have the following points

(x1, y1) = (4, 0) and (x2, y2) = (x, 0)

This gives

d = √(x - 4)^2 + (√x - 0)^2

Evaluate the difference

d = √(x - 4)^2 + (√x)^2

Evaluate the exponent

d = √x^2 - 8x + 16 + x

Evaluate the like terms

d = √x^2 - 7x + 16

Next, we differentiate using a graphing calculator

d' = (2x - 7)/[2√(x^2 - 7x + 16)]

Set to 0

(2x - 7)/[2√(x^2 - 7x + 16)] = 0

Cross multiply

2x - 7 = 0

Add 7 to both sides

2x = 7

Divide by 2

x = 3.5

So, we have:

Substitute x = 3.5 in y = √x

y = √3.5

Evaluate

y = 1.9

So, the point is (3.5, 1.9)

The distance is then calculated as:

d = √(x2 - x1)^2 + (y2 - y1)^2

This gives

d = √(3.5 - 4)^2 + (1.9 - 0)^2

Evaluate

d = 1.96

Hence, the closest point is (3.5, 1.9) and the distance is 1.96 units

Read more about distance at:

brainly.com/question/23848540

#SPJ1

3 0
1 year ago
Due to weather mark walk to school day of the 20 days in february what would be the fraction representation for the number of da
nekit [7.7K]

Tbe question doesn't state the number of days he walked to school out of 20 school days in the

Month of February.

Answer:

Kindly check explanation

Step-by-step explanation:

To. Obtain the fractional representayion for the number of days he walked to school ;

Let the number of days he walked to school = 10 (this is an hypothesized value)

Number of school days in February = 20

Fraction = 10 /20 = 0.5

The percentage of times walked to school : multiply the fraction obtained above by 100%

0.5 * 100% = 50%

Just put the desired value and proceed uSing the steps described above.

8 0
3 years ago
THE FUNCTION! f(x) = x^2+4 is defined over the interval (-2,2). If the interval is dived into n equal parts what is the height o
Svetradugi [14.3K]

Answer:

-2+k.5/n

Step-by-step explanation:

nsnsndksksnskksnsksnsnksnwkbsbssksj sosnanskzbwkssbkwwnkwsnwosbsndosnkssneosnenkssbkssnnkbwjwoswnks

3 0
2 years ago
Use I = PRT to solve.
Mice21 [21]

Answer:

Time T = 15 year

Step-by-step explanation:

Given:

Interest I = $270,000

Principal P = $150,000

Rate R = 12% = 0.12

Find:

Time T

Computation:

I = PRT

270,000 = (150,000)(0.12)(T)

270,000 = (18,000)(T)

Time T = 15 year

4 0
2 years ago
List the steps to solve the following equation: 5x - 6 = 44 then solve x
Dafna1 [17]

Answer:

1. Add 6 to both sides, cause that is the inverse of subtraction, so you get 5x = 50 as 6 cancels 6 out.

2. Divide 5 from both sides and get x = 10

7 0
2 years ago
Read 2 more answers
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