Please i need help!

Dafna11 [192]

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument.

7 0

3 years ago

The cells of a bacteria doubles in every 15 minutes. A scientist begins with a single cell. How many cells will be there after (

Anastaziya [24]

Step-by-step explanation:

Given that:-

1 cell = 15 minutes

So, we can concert 15 minutes to hours.

So,

60 minutes = 1 hour

1 minute = 1/60

15 minutes =

$\frac{15}{60} = 0.25 \: hrs$

Okay, now we will apply first for 0.4 hours.

$0.25 \: hrs= 1 \: cell$

$1 \: hr = \frac{1}{0.25}$

$0.4 \: hrs = \frac{0.4}{0.25}$

$= 1.6 \: cells$

$= 16 \times {10}^{ - 1} \: cells$

Now, second one:-

$10 \: hrs = \frac{10}{0.25}$

$= 40 \: cells$

$= 0.4 \times {10}^{2} \: cells$

Hope it helps :D

6 0

3 years ago

Differentiate with respect to X <br><img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B%20%5Cfrac%7Bcos2x%7D%7B1%20%2Bsin2x%20%7D%20

Mice21 [21]

Power and chain rule (where the power rule kicks in because $\sqrt x=x^{1/2}$ ):

$\left(\sqrt{\dfrac{\cos(2x)}{1+\sin(2x)}}\right)'=\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'$

Simplify the leading term as

$\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}$

Quotient rule:

$\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'=\dfrac{(1+\sin(2x))(\cos(2x))'-\cos(2x)(1+\sin(2x))'}{(1+\sin(2x))^2}$

Chain rule:

$(\cos(2x))'=-\sin(2x)(2x)'=-2\sin(2x)$

$(1+\sin(2x))'=\cos(2x)(2x)'=2\cos(2x)$

Put everything together and simplify:

$\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{(1+\sin(2x))(-2\sin(2x))-\cos(2x)(2\cos(2x))}{(1+\sin(2x))^2}$

$=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2\sin^2(2x)-2\cos^2(2x)}{(1+\sin(2x))^2}$

$=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2}{(1+\sin(2x))^2}$

$=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac{\sin(2x)+1}{(1+\sin(2x))^2}$

$=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac1{1+\sin(2x)}$

$=-\dfrac1{\sqrt{\cos(2x)}}\dfrac1{\sqrt{1+\sin(2x)}}$

$=\boxed{-\dfrac1{\sqrt{\cos(2x)(1+\sin(2x))}}}$

5 0

3 years ago

Fill in the blank. increasing the side length of a cube by a factor of 3 increases the volume by a factor of ___________.

german

We have that
scale factor=3

we know that
[volume new cube]=[scale factor]³*[volume original cube]
[volume new cube]=[3]³*[volume original cube]-----> 27*[volume original cube]

the answer is
<span>the volume increases by a factor of 27</span>

6 0

3 years ago

you are taking a trip at the same time as another family. your family traveled 1.900 miles in 2 days, their family traveled 2.70

snow_tiger [21]

Answer:

your family

Step-by-step explanation:

1,900/2 = 950

2,700/3 = 900

your family travels 950 miles every day whereas their family travels 900 miles every day :)

6 0

2 years ago