1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
otez555 [7]
2 years ago
5

Given the speeds of each runner below, determine who runs the fastest.

Mathematics
1 answer:
Bingel [31]2 years ago
4 0

Answer:

Step-by-step explanation:

jake runs the fastest

You might be interested in
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 ln(x) (a) Find the interval on which f is incre
Ainat [17]

Answer: (a) Interval where f is increasing: (0.78,+∞);

Interval where f is decreasing: (0,0.78);

(b) Local minimum: (0.78, - 0.09)

(c) Inflection point: (0.56,-0.06)

Interval concave up: (0.56,+∞)

Interval concave down: (0,0.56)

Step-by-step explanation:

(a) To determine the interval where function f is increasing or decreasing, first derive the function:

f'(x) = \frac{d}{dx}[x^{4}ln(x)]

Using the product rule of derivative, which is: [u(x).v(x)]' = u'(x)v(x) + u(x).v'(x),

you have:

f'(x) = 4x^{3}ln(x) + x_{4}.\frac{1}{x}

f'(x) = 4x^{3}ln(x) + x^{3}

f'(x) = x^{3}[4ln(x) + 1]

Now, find the critical points: f'(x) = 0

x^{3}[4ln(x) + 1] = 0

x^{3} = 0

x = 0

and

4ln(x) + 1 = 0

ln(x) = \frac{-1}{4}

x = e^{\frac{-1}{4} }

x = 0.78

To determine the interval where f(x) is positive (increasing) or negative (decreasing), evaluate the function at each interval:

interval                 x-value                      f'(x)                       result

0<x<0.78                 0.5                 f'(0.5) = -0.22            decreasing

x>0.78                       1                         f'(1) = 1                  increasing

With the table, it can be concluded that in the interval (0,0.78) the function is decreasing while in the interval (0.78, +∞), f is increasing.

Note: As it is a natural logarithm function, there are no negative x-values.

(b) A extremum point (maximum or minimum) is found where f is defined and f' changes signs. In this case:

  • Between 0 and 0.78, the function decreases and at point and it is defined at point 0.78;
  • After 0.78, it increase (has a change of sign) and f is also defined;

Then, x=0.78 is a point of minimum and its y-value is:

f(x) = x^{4}ln(x)

f(0.78) = 0.78^{4}ln(0.78)

f(0.78) = - 0.092

The point of <u>minimum</u> is (0.78, - 0.092)

(c) To determine the inflection point (IP), calculate the second derivative of the function and solve for x:

f"(x) = \frac{d^{2}}{dx^{2}} [x^{3}[4ln(x) + 1]]

f"(x) = 3x^{2}[4ln(x) + 1] + 4x^{2}

f"(x) = x^{2}[12ln(x) + 7]

x^{2}[12ln(x) + 7] = 0

x^{2} = 0\\x = 0

and

12ln(x) + 7 = 0\\ln(x) = \frac{-7}{12} \\x = e^{\frac{-7}{12} }\\x = 0.56

Substituing x in the function:

f(x) = x^{4}ln(x)

f(0.56) = 0.56^{4} ln(0.56)

f(0.56) = - 0.06

The <u>inflection point</u> will be: (0.56, - 0.06)

In a function, the concave is down when f"(x) < 0 and up when f"(x) > 0, adn knowing that the critical points for that derivative are 0 and 0.56:

f"(x) =  x^{2}[12ln(x) + 7]

f"(0.1) = 0.1^{2}[12ln(0.1)+7]

f"(0.1) = - 0.21, i.e. <u>Concave</u> is <u>DOWN.</u>

f"(0.7) = 0.7^{2}[12ln(0.7)+7]

f"(0.7) = + 1.33, i.e. <u>Concave</u> is <u>UP.</u>

4 0
3 years ago
Right triangle FGH has midsegments of 15,36, and 39 centimeters given that area of a triangle is represented by the formula A=1/
Schach [20]

Answer:

Step-by-step explanation:

according to the midsegment theorem, a midsegment of a triangle is parallel to a side of a triangle and its length is 1/2 length of the side.

1/2FG= 15, SO FG=30,

1/2 GH=36 SO GH=72

AREA = 1/2(72*30)=1080 CM^2

3 0
3 years ago
Read 2 more answers
Evaluate 8-2.<br>A. -16<br>B. -64<br>C. -1/64<br>D. 1/64<br> ​
makvit [3.9K]

I'm assuming you meant to write 8^(-2) or 8^{-2} where the -2 is the exponent over the 8.

If my assumption is correct, then we use the rule a^{-b} = \frac{1}{a^b}

So,

a^{-b} = \frac{1}{a^b}\\\\8^{-2} = \frac{1}{8^2}\\\\8^{-2} = \frac{1}{64}

<h3>Answer: Choice D.  1/64</h3>
8 0
2 years ago
In which of the following intervals does the trigonometric inequality csc(x)&gt; -sec(x) always hold true?
Kaylis [27]
Answer:a is the answer
3 0
3 years ago
A number increased by 6 and the result divided by 3 is 21. what is the number?​
kogti [31]

Answer:

Step-by-step explanation:

let the number be x

(x+6)/3   =21

x+6=21*3

x+6=63

x=57

7 0
2 years ago
Read 2 more answers
Other questions:
  • 5/6 of 12 pls help this is hard
    5·2 answers
  • If 95mg is 50% is the sodium content, what is 100%
    7·2 answers
  • What are two zed numbers that have a sum of 3
    8·1 answer
  • What is the greatest common factor of 150, 275 and 420
    9·1 answer
  • Help see the pictures.
    11·1 answer
  • Carmen has 432 points, and Karissa has 563. how many points does carmen need so that she has more points than Karissa?
    7·2 answers
  • Find the common ratio of the geometric sequence 11, -55, 275,...
    10·2 answers
  • Tony sells sporting goods. He makes a 10% commission on every dollar of sales that he makes. One month Tony got a commission che
    6·2 answers
  • I gotta answer this but I don’t want to be wrong
    10·2 answers
  • Please help this is a unit test &lt;3
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!