Identify the holes, horizontal asymptotes, and virtual asymptotes

Ugo [173]

$ℎ = ± \sqrt{x} 10\\$

4 0

2 years ago

Consider the function below. f(x) = ln(x4 + 27) (a) Find the interval of increase. (Enter your answer using interval notation.)

andrezito [222]

Answer:

a) The function is constantly increasing and is never decreasing

b) There is no local maximum or local minimum.

Step-by-step explanation:

To find the intervals of increasing and decreasing, we can start by finding the answers to part b, which is to find the local maximums and minimums. We do this by taking the derivatives of the equation.

f(x) = ln(x^4 + 27)

f'(x) = 1/(x^2 + 27)

Now we take the derivative and solve for zero to find the local max and mins.

f'(x) = 1/(x^2 + 27)

0 = 1/(x^2 + 27)

Since this function can never be equal to one, we know that there are no local maximums or minimums. This also lets us know that this function will constantly be increasing.

6 0

3 years ago

Describe how the graph of y=x^2 can be transformed to the graph of the given equation y=x^2+13. A) shift the graph of y=x^2 righ

stiks02 [169]

Answer:

D

Step-by-step explanation:

when a number is added at the end it results in a vertical transformation

8 0

2 years ago

The distance from Gillette, New Jersey, to Irvington, New Jersey, is 1 mile more than four times the distance from Irvington to

vivado [14]

Answer:

distance from Irvington to Newark

.= 3 Miles

Step-by-step explanation:

distance from Irvington to Newark.= X

distance from Gillette, New Jersey, to Irvington, New Jersey,= y

Y= 1+4x

total distance from Gillette to Newark

= z

Z= 6x-2

But total distance = x+y

Total distance= x+1+4x

Total distance= 1+5x

1 +5x= 6x-2

1+2= 6x-5x

3= x

distance from Irvington to Newark.= X

distance from Irvington to Newark

.= 3 Miles

distance from Gillette, New Jersey, to Irvington, New Jersey,= 1+4x

distance from Gillette, New Jersey, to Irvington, New Jersey,= 1+4(3)

distance from Gillette, New Jersey, to Irvington, New Jersey,= 1+12

distance from Gillette, New Jersey, to Irvington, New Jersey,= 13 miles

Total distance= 1+5x

Total distance= 1+5(3)

Total distance= 16 miles

7 0

2 years ago

The anithistamine Benadryl is often prescribed for allergies. A typical dose for a 100-pound person is 25 mg every six hours. Fo

Firdavs [7]

Answer:

56 chewable tablets

280mL liquid Benadryl

Step-by-step explanation:

For the first part:

First we need to find out how many tablets of 12.5mg would we need per dose.

1 dose is 25 mg and the tablets are in 12.5 mg form.

$1 dose = \dfrac{25mg}{12.5mg} = 2$

That would mean you would need 2 tablets per dose.

Next you need to calculate how many times a day it needs to be taken. A day has 24 hours and it needs to be taken every 6 hours. Just divide 24 hours by 6 hours. So that would mean that it needs to be taken 4 times a day.

Next we need to see how many times a week it should be taken and you can get that by multiplying the number of times a day by the number of days a week.

4 x 7 = 28 times

Lastly, you multiply the number of times a week by the number of tablets per dose.

28 times a week x 2 tablets = 56 tablets.

For the second part:

12.5 mg/5mL

The needed dose is 25 mg so we need to find how many mL is needed for 25 mg. 12.5mg is only have of 25 mg we need to double it to attain the correct dosage.

$\dfrac{12.5mg}{5mL}$ x $\dfrac{2}{2}$ = $\dfrac{25mg}{10mL}$

This means that for every 25 mg, you will need to give 10mL.

Again we do the same procedure as the first to decide how much liquid Benadryl you need to give in a week. We know that based on the previous that we need to administer this 28 times a week, so just multiply the number of mL per dose by the number of times per week.

10mL x 28 = 280mL

4 0

3 years ago