Answer:
Step-by-step explanation:
1) In this question we've been given "a", the leading coefficient. and two roots:
2) There's a theorem, called the Irrational Theorem Root that states:
If one root is in this form then its conjugate
. is also a root of this polynomial.
Therefore
3) So, applying this Theorem we can rewrite the equation, by factoring. Remembering that x is the root. Since the question wants it in this expanded form then:
Answer:
a. 8.75 M NaOH
b. 0.425 M CuCl₂ or 0.43 M CuCl₂
c. 0.067 M CaCO₃ or 0.07 M CaCO₃
Step-by-step explanation:
Molality is computed using the formula:
So first thing you need to do is determine how many moles of solute there are and divide it by the solution in liters.
Converting mass to moles, you need to get the mass of each solute per mole. You can use the periodic table to get the atomic mass (which is the grams per mole of each atom) of each of the elements involved. Then add them up and you will have how many grams per mole of each compound.
1. 35.0g of NaOH in 100ml H₂O
Element number of atoms atomic mass TOTAL
Na 1 x 22.99g/mol = 22.99g/mol
O 1 x 16.00g/mol = 16.00g/mol
H 1 x 1.01g/mol =<u> 1.01g/mol</u>
40.00g/mol
This means that the molecular mass of NaOH is 40.00 g/mol
Then we use this to convert 35.0g of NaOH to moles:
Now that you have the number of moles we divide it by the solution in liters. Before we can do that you have to conver 100ml to L.
Then we divide it:
2. 20.0g CuCl₂ in 350ml H₂O
Element number of atoms atomic mass TOTAL
Cu 1 x 63.55g/mol = 63.55g/mol
Cl 2 x 34.45g/mol = <u>70.90g/mol</u>
134.45g/mol
350ml = 0.350L
3. 3.35g CaCO₃ in 500ml
Element number of atoms atomic mass TOTAL
Ca 1 x 40.08g/mol = 40.08g/mol
C 1 x 12.01g/mol = 12.01g/mol
O 3 x 16.00g/mol =<u> 48.00g/mol</u>
100.09g/mol
500ml = 0.5L
Let value intially be = P
Then it is decreased by 20 %.
So 20% of P =
So after 1 year value is decreased by 0.2P
so value after 1 year will be = P - 0.2P (as its decreased so we will subtract 0.2P from original value P) = 0.8P-------------------------------------(1)
Similarly for 2nd year, this value 0.8P will again be decreased by 20 %
so 20% of 0.8P =
So after 2 years value is decreased by (0.2)(0.8P)
so value after 2 years will be = 0.8P - 0.2(0.8P)
taking 0.8P common out we get 0.8P(1-0.2)
= 0.8P(0.8)
-------------------------(2)
Similarly after 3 years, this value will again be decreased by 20 %
so 20% of
So after 3 years value is decreased by
so value after 3 years will be =
taking common out we get
-----------------------(3)
so from (1), (2), (3) we can see the following pattern
value after 1 year is P(0.8) or
value after 2 years is
value after 3 years is
so value after x years will be ( whatever is the year, that is raised to power on 0.8)
So function is best described by exponential model
where y is the value after x years
so thats the final answer