Step-by-step explanation:
x² + 7x − 8 = 0
(x + 8) (x − 1) = 0
x = -8 or 1
Answer:500
Step-by-step explanation:So first u mutiply by 100 then divide by 90
Answer:
The mass of 3.13*10²³ molecules of carbon dioxide is 22.88 g.
Step-by-step explanation:
Avogadro's Number or Avogadro's Constant is the number of particles that make up a substance (usually atoms or molecules) and that can be found in the amount of one mole of said substance. Its value is 6.023*10²³ particles per mole and it applies to any substance.
Then you can apply the following rule of three: if 6.023*10²³ molecules are present in 1 mole, 3.13*10²³ molecules are present in how many moles?
![moles=\frac{3.13*10^{23}molecules*1 mole }{6.023*10^{23}molecules}](https://tex.z-dn.net/?f=moles%3D%5Cfrac%7B3.13%2A10%5E%7B23%7Dmolecules%2A1%20mole%20%7D%7B6.023%2A10%5E%7B23%7Dmolecules%7D)
moles= 0.52
Since the molar mass of carbon dioxide is 44 g / mole, then the following rule of three can be applied: if there are 44 g in 1 mole, how much mass is there in 0.52 moles?
![mass=\frac{0.52 moles*44 g}{1 mole}](https://tex.z-dn.net/?f=mass%3D%5Cfrac%7B0.52%20moles%2A44%20g%7D%7B1%20mole%7D)
mass= 22.88 g
<u><em>The mass of 3.13*10²³ molecules of carbon dioxide is 22.88 g.</em></u>
Answer: x = pi/6 and x = pi/3.
Step-by-step explanation:
We have the function:
y = x + 2*cos(x)
It will have a horizontal tangent at the point where it's derivate is equal to zero.
Then first let's differentiate y.
y' = dy/dx = 1 - 2*sin(x).
Then we must find the value of x between 0 and 2*pi (or 0° and 360°)
y'(x) = 1 - 2*sin(x) = 0.
Let's solve that:
2*sin(x) = 1
sin(x) = 1/2.
We know that:
sin(30°) = 1/2.
and
Sin(120°) = 1/2
Then let's convert 30° into radians.
We know that:
pi = 180°.
Then:
pi/180° = 1.
30° = 30°*(pi/180°) = (30°/180°)*pi = (3/18)*pi = pi/6
120° = (120°/180°)*pi = (12/18)*pi = (1/3)*pi = pi/3.
Then the two values of x are: pi/6 and pi/3.