The answer to your math question is x=5
Answer:
262.12mph and 419kph
Step-by-step explanation:
Given: It takes 4 hours and 15 minutes to fly from Orlando, Florida, to Boston, Massachusetts. The distance between the two cities is 1114 miles
To Find: the average speend of the plane in miles per hour, If every mile is approximately 1.6 kilometers, the speed of the airplane in kilometers per hour
Solution:
Distance between Orlando,Florida and Boston, Massachusetts

Time taken to cover the distance
and 
We know that,




It is given that,

therefore,

Speed Of plane in Kilometers per hours 

Speed of in miles per hour is
and Speed in kilometer per hour 
The diffusion time of the red blood cell to take oxygen through the membrane is 25uS.
The small capillaries in the lungs are in close contact and it takes a red blood cell 0.5 seconds to squeeze through the capillary.
The diffusion time for the oxygen across the 1 um thick membrane separating the air is given by,
t = x²/2D
Where,
t is the diffusion time,
x is the thickness of the membrane,
D is the diffusion coefficient.
Putting values,
t = (1 x 10⁻⁹)²/2 x 2 x 10⁻¹¹
t = 10⁻⁷/4
t = 25 x 10⁻⁹ seconds.
t = 25 uS.
so, the diffusion time is 25uS.
To know more about Diffusion, visit,
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Answer:
![\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \frac{1}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B%5Csqrt%7Bcos%282x%29%7D%20-%20%5Csqrt%5B3%5D%7Bcos%283x%29%7D%7D%7Bsin%28x%5E2%29%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
General Formulas and Concepts:
<u>Calculus</u>
Limits
Limit Rule [Variable Direct Substitution]: 
L'Hopital's Rule
Differentiation
- Derivatives
- Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Chain Rule]: ![\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Step-by-step explanation:
We are given the limit:
![\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B%5Csqrt%7Bcos%282x%29%7D%20-%20%5Csqrt%5B3%5D%7Bcos%283x%29%7D%7D%7Bsin%28x%5E2%29%7D)
When we directly plug in <em>x</em> = 0, we see that we would have an indeterminate form:
![\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \frac{0}{0}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B%5Csqrt%7Bcos%282x%29%7D%20-%20%5Csqrt%5B3%5D%7Bcos%283x%29%7D%7D%7Bsin%28x%5E2%29%7D%20%3D%20%5Cfrac%7B0%7D%7B0%7D)
This tells us we need to use L'Hoptial's Rule. Let's differentiate the limit:
![\displaystyle \lim_{x \to 0} \frac{\sqrt{cos(2x)} - \sqrt[3]{cos(3x)}}{sin(x^2)} = \displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B%5Csqrt%7Bcos%282x%29%7D%20-%20%5Csqrt%5B3%5D%7Bcos%283x%29%7D%7D%7Bsin%28x%5E2%29%7D%20%3D%20%5Cdisplaystyle%20%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B%5Cfrac%7B-sin%282x%29%7D%7B%5Csqrt%7Bcos%282x%29%7D%7D%20%2B%20%5Cfrac%7Bsin%283x%29%7D%7B%5Bcos%283x%29%5D%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D%7D%7B2xcos%28x%5E2%29%7D)
Plugging in <em>x</em> = 0 again, we would get:
![\displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)} = \frac{0}{0}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B%5Cfrac%7B-sin%282x%29%7D%7B%5Csqrt%7Bcos%282x%29%7D%7D%20%2B%20%5Cfrac%7Bsin%283x%29%7D%7B%5Bcos%283x%29%5D%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D%7D%7B2xcos%28x%5E2%29%7D%20%3D%20%5Cfrac%7B0%7D%7B0%7D)
Since we reached another indeterminate form, let's apply L'Hoptial's Rule again:
![\displaystyle \lim_{x \to 0} \frac{\frac{-sin(2x)}{\sqrt{cos(2x)}} + \frac{sin(3x)}{[cos(3x)]^{\frac{2}{3}}}}{2xcos(x^2)} = \lim_{x \to 0} \frac{\frac{-[cos^2(2x) + 1]}{[cos(2x)]^{\frac{2}{3}}} + \frac{cos^2(3x) + 2}{[cos(3x)]^{\frac{5}{3}}}}{2cos(x^2) - 4x^2sin(x^2)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B%5Cfrac%7B-sin%282x%29%7D%7B%5Csqrt%7Bcos%282x%29%7D%7D%20%2B%20%5Cfrac%7Bsin%283x%29%7D%7B%5Bcos%283x%29%5D%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D%7D%7B2xcos%28x%5E2%29%7D%20%3D%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B%5Cfrac%7B-%5Bcos%5E2%282x%29%20%2B%201%5D%7D%7B%5Bcos%282x%29%5D%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D%20%2B%20%5Cfrac%7Bcos%5E2%283x%29%20%2B%202%7D%7B%5Bcos%283x%29%5D%5E%7B%5Cfrac%7B5%7D%7B3%7D%7D%7D%7D%7B2cos%28x%5E2%29%20-%204x%5E2sin%28x%5E2%29%7D)
Substitute in <em>x</em> = 0 once more:
![\displaystyle \lim_{x \to 0} \frac{\frac{-[cos^2(2x) + 1]}{[cos(2x)]^{\frac{2}{3}}} + \frac{cos^2(3x) + 2}{[cos(3x)]^{\frac{5}{3}}}}{2cos(x^2) - 4x^2sin(x^2)} = \frac{1}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B%5Cfrac%7B-%5Bcos%5E2%282x%29%20%2B%201%5D%7D%7B%5Bcos%282x%29%5D%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D%20%2B%20%5Cfrac%7Bcos%5E2%283x%29%20%2B%202%7D%7B%5Bcos%283x%29%5D%5E%7B%5Cfrac%7B5%7D%7B3%7D%7D%7D%7D%7B2cos%28x%5E2%29%20-%204x%5E2sin%28x%5E2%29%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D)
And we have our final answer.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits