the number of moles in a liter is 0. 045 moles
<h3>What is mole?</h3>
Mole, in chemistry, is known as a standard scientific unit used for measuring large quantities or amounts of very small entities such as atoms, molecules, or other specified particles.
It is important to note that the number of units in a mole is also called its Avogadro’s number
The basis for the conversion of moles to liters is
1mol = 22.4Liter
Hence,
If 1 mol = 22. 4Liter
Then x mol = 1Liter
Cross multiply
x × 22. 4 = 1 × 1
22. 4x = 1
Divide through by 22.4
x = 1/ 22. 4
x = 0. 045 moles
Thus, the number of moles in a liter is 0. 045 moles
Learn more about moles here:
brainly.com/question/14464650
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By the product rule,
![\dfrac{dy}{dx} = \dfrac{x-1}{x+1} \dfrac{d(7x^7-x^2)}{dx} + \dfrac{7x^7-x^2}{x+1} \dfrac{d(x-1)}{x+1} + (7x^7-x^2)(x-1) \dfrac{d\left(\frac1{x+1}\right)}{dx}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cdfrac%7Bx-1%7D%7Bx%2B1%7D%20%5Cdfrac%7Bd%287x%5E7-x%5E2%29%7D%7Bdx%7D%20%2B%20%5Cdfrac%7B7x%5E7-x%5E2%7D%7Bx%2B1%7D%20%5Cdfrac%7Bd%28x-1%29%7D%7Bx%2B1%7D%20%2B%20%287x%5E7-x%5E2%29%28x-1%29%20%5Cdfrac%7Bd%5Cleft%28%5Cfrac1%7Bx%2B1%7D%5Cright%29%7D%7Bdx%7D)
By the power and chain rules,
![\dfrac{dy}{dx} = \dfrac{(x-1)(49x^6-2x)}{x+1} + \dfrac{7x^7-x^2}{x+1} - \dfrac{(7x^7-x^2)(x-1)}{(x+1)^2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%20%3D%20%5Cdfrac%7B%28x-1%29%2849x%5E6-2x%29%7D%7Bx%2B1%7D%20%2B%20%5Cdfrac%7B7x%5E7-x%5E2%7D%7Bx%2B1%7D%20-%20%5Cdfrac%7B%287x%5E7-x%5E2%29%28x-1%29%7D%7B%28x%2B1%29%5E2%7D)
When
, the first and last term vanish, and we're left with
![\dfrac{dy}{dx}\bigg|_{x=1} = \dfrac{7 - 1}{1 + 1} = \dfrac62 = \boxed{3}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%5Cbigg%7C_%7Bx%3D1%7D%20%3D%20%5Cdfrac%7B7%20-%201%7D%7B1%20%2B%201%7D%20%3D%20%5Cdfrac62%20%3D%20%5Cboxed%7B3%7D)
Answer:
m∠WXY + m∠YXZ = 180°
Replacing with the real values:
75° + m∠YXZ = 180°
m∠YXZ = 180° - 75°
<u>m∠YXZ = 105°</u>
Step-by-step explanation:
1. Let's review all the information provided to us to answer the question correctly:
∠WXY and ∠YXZ are supplementary angles
m∠WXY=75°
2. Prove : m∠YXZ=105°
Let's recall that supplementary angles are those angles whose sum is 180 degrees. Therefore,
m∠WXY + m∠YXZ = 180°
Replacing with the real values:
75° + m∠YXZ = 180°
m∠YXZ = 180° - 75°
<u>m∠YXZ = 105°</u>
Answer:
C B D E A
Im just gunna go ahead and send all the answers bro
For the Store with sales of 500 in first month just put (The sale for first month is $500.
The sale increases by $10 each month, as modelled by the equation: a_k=500+(k-1)10 = 131,400$)
The last one just copy and paste --> Distribute 2j to (j+3). Rewrite the summation as the sum of two individual summations. Evaluate each summation using properties or formulas from the lesson. The lower index is 1, so any properties can be used. The sum is 5,494,000.
Answer:
Water level in the reservoir is falling at the rate of 0.398 ft per minute.
Step-by-step explanation:
From the figure attached,
Water level in the reservoir has been given as 10 feet and radius of the reservoir is 4 feet.
Let the level of water in the reservoir after time t is h where radius of the water level becomes r.
ΔABE and ΔCDE are similar.
Therefore, their corresponding sides will be in the same ratio.
![\frac{r}{h}=\frac{4}{10}](https://tex.z-dn.net/?f=%5Cfrac%7Br%7D%7Bh%7D%3D%5Cfrac%7B4%7D%7B10%7D)
--------(1)
Now volume of the water V = ![\frac{1}{3}\pi r^{2}h](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E%7B2%7Dh)
From equation (1),
V = ![\frac{1}{3}\pi (\frac{2}{5}h)^{2} h](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%28%5Cfrac%7B2%7D%7B5%7Dh%29%5E%7B2%7D%20h)
V = ![\frac{4\pi h^{2}\times h}{75}](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Cpi%20h%5E%7B2%7D%5Ctimes%20h%7D%7B75%7D)
![\frac{dV}{dt}=\frac{4\pi }{75}\times \frac{d}{dt}(h^{3})](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B4%5Cpi%20%7D%7B75%7D%5Ctimes%20%5Cfrac%7Bd%7D%7Bdt%7D%28h%5E%7B3%7D%29)
![\frac{dV}{dt}=\frac{4\pi }{75}\times (3h^{2})\frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B4%5Cpi%20%7D%7B75%7D%5Ctimes%20%283h%5E%7B2%7D%29%5Cfrac%7Bdh%7D%7Bdt%7D)
![\frac{dV}{dt}=\frac{12\pi h^{2}}{75}\times \frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B12%5Cpi%20h%5E%7B2%7D%7D%7B75%7D%5Ctimes%20%5Cfrac%7Bdh%7D%7Bdt%7D)
Since
feet³ per minute and h = 5 feet
![5=\frac{12\pi (5)^{2}}{75}\times \frac{dh}{dt}](https://tex.z-dn.net/?f=5%3D%5Cfrac%7B12%5Cpi%20%285%29%5E%7B2%7D%7D%7B75%7D%5Ctimes%20%5Cfrac%7Bdh%7D%7Bdt%7D)
![5=4\pi \frac{dh}{dt}](https://tex.z-dn.net/?f=5%3D4%5Cpi%20%5Cfrac%7Bdh%7D%7Bdt%7D)
![\frac{dh}{dt}=\frac{5}{4\pi}](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%3D%5Cfrac%7B5%7D%7B4%5Cpi%7D)
feet per minute
Therefore, water level in the reservoir is falling at the rate of 0.398 feet per minute.