Find the derivative of f(x) = 4 divided by x at x = 2.

Answers

Answer 1

Answer:

Hello!

The answer is:

$f'(2)=-1$

Why?

To solve this problem, first we need to derivate the given function, and then, evaluate the derivated function with x equal to 2.

The given function is:

$f(x)=(4)/(x)$

It's a quotient, so, we need to use the following formula to derivate it:

$f'(x)=(d)/(dx)((u)/(v)) =(v*u'-u*v')/(v^(2) )$

Then, of the given function we have that:

$u=4\nv=x$

So, derivating we have:

$f'(x)=(d)/(dx)((4)/(x)) =(x*(4)'-4*(x)')/(x^(2) )$

$f'(x)=(d)/(dx)((4)/(x)) =(x*0-4*1)/(x^(2) )$

$f'(x)=(d)/(dx)((4)/(x)) =(0-4)/(x^(2) )$

$f'(x)=(d)/(dx)((4)/(x)) =(-4)/(x^(2) )$

Hence,

$f'(x)=(d)/(dx)((4)/(x)) =(-4)/(x^(2) )$

Now, evaluating with x equal to 2, we have:

$f'(2)=(-4)/((2)^(2) )$

$f'(2)=(-4)/(4)$

$f'(2)=-1$

Therefore, the answer is:

$f'(2)=-1$

Have a nice day!

Answer 2

Answer:

ANSWER

$f'(2) = -1$

EXPLANATION

The given function is

$f(x) = (4)/(x)$

Recall that:

$\frac{c}{ {a}^( m) } = c {a}^( - m)$

We rewrite the given function using this rule to obtain,

$f(x) = 4 {x}^( - 1)$

Recall again that,

$f(x)= a {x}^(n)$

then

$f'(x)=n a {x}^(n - 1)$

We differentiate using the power rule to obtain,

$f'(x) = - 1 * 4 {x}^( - 1 - 1)$

$f'(x) = - 4 {x}^( - 2)$

We rewrite as positive index to obtain,

$f'(x) = - \frac{4}{ {x}^(2) }$

We plug in x=2 to obtain,

$f'(2) = - \frac{4}{ { (2)}^(2) } = - (4)/(4) = - 1$

Given that

At a local hospital, 35 babies were born.

There are 23 were boys.

We have to determine

What percentage of the newborns were boys?

According to the question

At a local hospital, 35 babies were born.

There are 23 were boys.

Then,

The percentage of the newborns were boys is determined by,

$\rm Percentage \ of \ new \ born \ boys = (Total \ number\ of \ boys * 100)/(Total \ number \ of \ babies)$

Substitute all the values in the formula.

$\rm Percentage \ of \ new \ born \ boys = (Total \ number\ of \ boys * 100)/(Total \ number \ of \ babies)\n\n\rm Percentage \ of \ new \ born \ boys = (23 * 100)/(35)\n\n\rm Percentage \ of \ new \ born \ boys = (2300)/(35)\n\n\rm Percentage \ of \ new \ born \ boys = 65.71 \ percent$

Hence, the percentage of newborns who were boys is 65.71%.

To know more about Percentages click the link given below.

brainly.com/question/8009466

so the fraction would be 23/35 are boys. If you do the division (23 ÷ 35) the answer is around 0.657.

That converted into a percentage (×100) is 65.7%

Can someone help me and explain the equation

Answers

Answer:

Jason would have to work 60 hours.

Step-by-step explanation:

The equation you would use would be 450 + 12.50t = 1200.

1200 is the money needed, 450 is a constant factor, but the 12.50 changes depending on how many hours Jason works.

You will have to use inverse operations so you would go 450 + 12.50t - 450 = 1200 - 450. That equals 12.50t = 750. Then you divide 12.50 by 750 because 12.50t is multiplying. 750 ÷ 12.5 = 60. So Jason has to work 60 hours!

If this helped I would appreciate it if you marked me Brainliest. thank you and have a nice day!

Four children have small toys. The first child has 1/10 of the toys, the second child has 12 more toys than the first, the third child has one more toy of what the first child has and the fourth child has double the third child. How many toys are there?

Answers

Call x the amount of toys the first child has.We write the equation x+(x+12)+(x+1)+2(x+1)=10x.This is equal to 5x+15=10x. Subtracting 5x, we see that 5x=15, so x=3. There are 10x toys, so we have 3*10=30 total toys.

Daisy works at an ice-cream parlor. She is paid $10 per hour for the first 8 hours she works in a day. For every extra hour she works, she is paid 1.5 times her hourly wage. If Daisy works for x hours in a day, and x is greater than 8, the expression giving her net earnings for the day is (blank).If Daisy works 13 hours, she will be paid (blank).

Answers

Answer:

Total net earnings = 80+15(x-8)

If Daisy works 13 hours, she will be paid $155.

Step-by-step explanation:

Let Daisy works for x hours a day

She is paid $10 per hour for the first 8 hours she works in a day.

So, pay for the first 8 hours =10\times8=80 dollars

For every extra hour she works, she is paid 1.5 times her hourly wage.

The number of hours worked over 8 hours is given by = x-8

So, pay for the hours worked over 8 hours = 15(x-8) dollars

Total net earnings = 80+15(x-8)

And when x = 13

The pay is : 80+15(13-8)

= 80+15(5)

= 80+75 = 155 dollars

Answer:

1) y = 15(x-8) + 80

2) $155

Step-by-step explanation:

First blank:

use the linear expression form: y = mx + b

If Daisy is working more than 8 hours, (since the problem says x > 8), then she is getting $10 per hour guaranteed, which is $80 overall. So 80 will be our constant term, b

for every hour after 8, she is being paid 1.5 x 10, which is $15. This is our slope term, m.

So our expression is: y = 15(x-8) + 80

The reason we use x-8 instead of just x, is because x is the number of hours she works, but she will only be paid 15 bucks/hour when she works after 8 hours. So we need to subtract 8 from x to get the number of hours she works after the minimum 8.

Second Blank:

If Daisy works 13 hours, just replace x with 13 in our formula:

y = 15(x-8) + 80

y = 15(13-8) + 80

y = 15(5) + 80

y = 75 + 80

y = $155

If she works for 13 hours, she gets paid $85

Hare Krishna! :)

The doubling time of a city's population is 13 years. How long does it take for the population to quadruple.

Answers

Lets say the population is 10. It takes 13 years to double to 20. Once it is at 20, it takes another 13 years to double again and be at 40. It takes 26 years for a city's population to quadruple because it will double in 13 years, and then that population will double and take another 13 years.

Well quadruple is 4x so all you have to do is multiply 13 by two because that itself is just a double population increase, and that's 2x, so naturally we multiply that by 2 again to get 4x

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