The velocity function (in meters per second) is given for a particle moving along a line. v(t) = 3t − 8, 0 ≤ t ≤ 3(a) find the displacement.(b) find the distance traveled by the particle during the given time interval.

a) - 10.5 m

b) 10.83 m

Step-by-step explanation:

Given:

Velocity function , v(t) = 3t - 8,      0 ≤ t ≤ 3

a)

For displacement, integerating the function form time 0 to 3

thus,

=

or

Displacement  =

or

Displacement  =

= - 10.5 m

b) For total distance, let us first find the intervals where the velocity went from positive to negative

thus,

3t - 8 = 0

t =

the velocity changed it direction

thus,

we have the interval for speed as t ∈

therefore,

total distance =  [/tex]

=

=  

=

=

= 10.83 m

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;

steve should create a type of business report called a business plan. the correct option among the options that are already given in the question is the last or the fourth option. this business report created by steve will actually influence the investors about investing their money in steve's business. this business report will have all the details about the business, the amount of investment required and the amount of expected profit.