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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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Accountants at the Tucson​ firm, Larry​ Youdelman, CPAs, believed that several traveling executives were submitting unusually hi
77julia77 [94]

Answer:

a) Y= 90 +46.50(5) +0.35 (340) =441.50

b) The accountant should not question the voucher as the request is much higher than expected.

c) We can add the following variables

d) The percentage of variation in the trip cost that can be explained by the model​ = (0.64)^2 =0.4096 or 40.96%

A. Type of travel (air/car)

B. Gender of the executive (male/female)

The last option is not too important since we are analyzing the traveling executives not the type of business

Step-by-step explanation:

Part a

For this case we have the multiple regression model given by:

Y= 90 +46.50 x_1 +0.35 x_2

Where x_1 represent the number of days on the road and x_2 the distance traveled in miles.

And we want to find the expected amount from a 340​-mile trip that took her out of town for 5 ​days, so we just need to replace x1= 5 and x2=340 and we got:

Y= 90 +46.50(5) +0.35 (340) =441.50

Part b

The expected value taking in count that x1 = 5 and y = 340 is:

Y= 90 +46.50(55) +0.35 (340) =441.50

And the difference from the obtained value is : 685-441.50=243.5

So then the correct answer would be:

The accountant should not question the voucher as the request is much higher than expected.

Part c

We can add the following variables

A. Type of travel (air/car)

B. Gender of the executive (male/female)

The last option is not too important since we are analyzing the traveling executives not the type of business

Part d

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

The coefficient of determination "is a measure used in statistical analysis that assesses how well a model explains and predicts future outcomes. It is indicative of the level of explained variability in the data set".

The percentage of variation in the trip cost that can be explained by the model​ = (0.64)^2 =0.4096 or 40.96%

6 0
3 years ago
An ellipse has a center at the origin, a vertex along the major axis at (0, 17), and a focus at (0, −8). Which equation represen
Marianna [84]
We know that
<span>Since the focus and vertex are above and below each other, rather than side by side, I know that this ellipse must be taller than it is wide.
</span>Then 
a²<span> will go with the </span>y<span> part of the equation
</span>Also, since the focus is 8 <span>units below the center, then </span><span>c = 8
</span>since the vertex is 17<span> units above, then </span><span>a = 17
</span>The equation b²<span> = a</span>²<span> – c</span>²<span> gives me
</span>b²=17²-8²-----> b²=225
the equation is
y²/a²+x²/b²=1------> y²/289+x²/225=1

the answer is
y²/289+x²/225=1

see the attached figure

7 0
3 years ago
Read 2 more answers
Simplify completely quantity x squared minus 3 x minus 54 over quantity x squared minus 18 x plus 81 times quantity x squared pl
oee [108]
Your statemtent is incomplete.

I found the samestatment with the complete words: <span>Simplify completely quantity x squared minus 3 x minus 54 over quantity x squared minus 18 x plus 81 times quantity x squared plus 12 x plus </span>36 over x plus 6

Given that your goal is to learn an be able to solve any similar problem, I can teach you assuming that what I found is exactly what you need.

x^2 - 3x - 54            x^2 + 12x + 36
------------------    x   ---------------------
x^2 - 18x + 81              x + 6

factor x^2 - 3x - 54 => (x - 9)(x + 6)

factor x^2 - 18x + 81 => (x - 9)^2

factor x^2 + 12x + 36 = (x + 6)^2

Now replace the polynomials with the factors=>

(x - 9) (x + 6) (x + 6)^2        (x + 6)^2       x^2 + 12x + 36
------------------------------ =  --------------- = --------------------
    (x - 9)^2 (x + 6)                 (x - 9)               x - 9

4 0
3 years ago
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Ciao i am going into highschool next year and i was wondering does any one have tips
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Answer:

pay attention and do what your supposed to do and you'll be fine also dont pick the wrong group of friends.

Step-by-step explanation:

please mark brainliest... <3

5 0
3 years ago
When David was asked how old he was, he said " I'm three times younger than my dad, but twice as old as Rebecca. " Then little R
daser333 [38]

Using a system of equations, it is found that David is 12 years old.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The variables are given as follows:

  • Variable x: David's age.
  • Variable y: Dad's age.
  • Variable z: Rebecca's age.

David is three times younger than the dad and twice as old as Rebecca, then:

  • x = y/3 -> y = 3x.
  • x = 2z.

Rebecca is 30 years younger than the dad, hence:

z = y - 30.

Then, since x = 2z and z = y - 30 and y = 3x, we solve for x to find David's age.

x = 2(y - 30)

x = 2(3x - 30)

x = 6x - 60

5x = 60

x = 60/5

x = 12.

David is 12 years old.

More can be learned about a system of equations at brainly.com/question/24342899

#SPJ1

8 0
2 years ago
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