Identify the absolute extrema of the function and the x-values where they occur. f(x)=6x+(24/x^sqr)+3, x>0

Answers

Answer 1

Answer: $f(x)=6x+(24)/(x^2)+3\nf'(x)=6-(48)/(x^3)\n6-(48)/(x^3)=0\n6x^3-48=0\n6x^3=48\nx^3=8\nx=2\n$

For $x<2 \wedge x\not=0$ the derivative is negative.
For $x>2$ the derivative is positive.
Therefore at $x=2$ there's a minimum.

$f_(min)=6\cdot2+(24)/(2^2)+3=12+6+3=21$

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Andrew has a cell phone plan that provides 300 free minutes each month for a flat rate of $19. For any minutes over 300, Andrew is charged $0.39 per minute. Which of the following piecewise functions represents charges based on Andrew's cell phone plan?

Answers

Answer:

$f(x)=\left\{\begin{array}{l}19,\ \ x\le 300\n \n19+0.39(x-300),\ \ x>300\end{array}\right.$

Step-by-step explanation:

Andrew has a cell phone plan that provides 300 free minutes each month for a flat rate of $19. For any minutes over 300, Andrew is charged $0.39 per minute.

Let x be the number of minutes Andrew uses per month and f(x) be the charges based on Andrew's cell phone plan.

If $x\le 300,$ then $f(x)=19.$

If $x>300,$ then first 300 minutes are free and each minute of next (x-300) minutes costs $0.39, therefore

$f(x)=19+0.39(x-300).$

Hence,

$f(x)=\left\{\begin{array}{l}19,\ \ x\le 300\n \n19+0.39(x-300),\ \ x>300\end{array}\right.$

Answer:

19, x≤ 300

19+.39(x-300), x>300

Step-by-step explanation:

I just did this quiz

Estimate to the nearest integer for 28 square root

Answers

Answer: Sqrt(28) = 5.29150262213

There were 42 runners to start a race. In the first half of the race, 1 over 3 of them dropped out. In the second half of the race, 4 over 7 of the remaining runners dropped out. How many runners finished the race?

Answers

42 runners total

$(1)/(3)$ of 42 (14) dropped out in first half.

42 - 14 = 28 remaining.

$(4)/(7)$ of 28 (16) dropped out in second half.

28 - 16 = 12 runners finished the race.

1/3 of 42 is 14 (42 divided by 3 is 14) so u subtract 14 from 42 which is 28. Then you would divide 28 by 7 which is 4 and then since the fraction is 4/7, u would multiply 4 and 4 to get 16. and finally subtract 28 and 16.

answer is 12 runners

The area of a right triangle is 270 m². The height of the right triangle is 15 m. What is the length of the hypotenuse of the right triangle?

Answers

The area of a triangle is calculated by the expression given as:

Area = bh/2

where b is the base and h is the height.

We calculate as follows:

270 = b (15) / 2
b = 36

hypotenuse = sqrt ( 15^2 + 36^2 ) = 39

Answer:

hypotenuse = 39m

Step-by-step explanation:

Area of a triangle= 1/2 * base * height

where base = ?

height = 15

Plugin values into the formula:

270 = 1/2 base (15)

base = 270 (2)

base = 36

hypotenuse = √(base² + height²)

= √( 36² + 15² )

= 39

A sprinter on the track team ran the 100 meter dash and redcorded the time for each race. The race times (in seconds) were:12.4 13.1 12.7 12.8 13.0 12.9 13.1 13.5

Answers

Answer:

What is the question please post the full question next time

PLEEESE HELLLLLLP If you have a test average of 92 and a standard deviation of 1.8, you generally do well on tests.t f

Answers

Yes, that's true PROVIDED your test scores are normally distributed.

If they are, then more than 99% of your test scores are within three
standard deviations of the mean.

You told us that 3-sigma = 5.4 . So less than one score out of every
hundred tests you take is lower than 86.6 or higher than 97.4 .

You are remarkably consistent, so I guess Jupiter must have been
in its ascendancy next door to the house of Andromeda about an
hour before you were born, or some such nonsense.

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