Answer:
10.7 years
Step-by-step explanation:
The decay equation can be written as ...
remaining = initial × (1/2)^(t/(half-life))
Filling in the given values, we can solve for t.
0.100 = 1.35 × (1/2)^(t/2.86)
0.100/1.35 = (1/2)^(t/2.86) divide by 1.35
Taking logs transforms this to a linear equation:
log(0.100/1.35) = (t/2.86)log(1/2)
Since log(a/b) = -log(b/a), we can multiply both sides by -1 and simplify the logs a bit.
log(1.35/.1) = t·(log(2)/2.86)
2.86·log(13.5)/log(2) = t ≈ 10.7 . . . . years
The decay time is about 10.7 years.
THE SOLUTIONS OF A SYSTEM OF EQUATIONS
A system of equations refers to a number of equations with an equal number of variables. We will only look at the case of two linear equations in two unknowns. The situation gets much more complex as the number of unknowns increases, and larger systems are commonly attacked with the aid of a computer.
A system of two linear equations in two unknowns might look like
This is the standard form for writing equations when they are part of a system of equations: the variables go in order on the left side and the constant term is on the right. The bracket on the left indicates that the two equations are intended to be solved simultaneously, but it is not always used.
<span>Let's do this step by step, we know that the guy steals $ 100
So it would be - $ 100 for the store.
The men buy $ 70 merchandise WITH THE MONEY THAT HE STOLE, but the money that he stole CAME BACK to the store
So up to this poin, : - $ 100 + $100 - $ 70 = - $ 70 for the store
After that , the store give $ 30 cash back,
So in the and : - $ 70 - $30 = - $ 100 lost for the store
</span>
Answer:
8
Step-by-step explanation:
if you have 6 pounds and you use 0.75 pounds per then you can make 6/0.75 dinners = 8
Answer:
<em>D. 5 for x less than or equal to 4, equals 2x for x between 4 and 6 including 6, and equals 4 for x greater than 6 Domain: All real number</em>s.
Step-by-step explanation:
Find the complete diagram attached
First we need to get the derivative of the functions
For the function f(x) = 5x - 6
Using the formula
If f(x) = axⁿ
f'(x) = naxⁿ⁻¹
For the function f(x) = 5x - 6
f'(x) = 1(5)x¹⁻¹
f'(x) = 5x⁰
f'(x) = 5
For the function f(x) =x²-2
f'(x) = 2x²⁻¹
f'(x) = 2x
For the function f(x) = 4x+10
f'(x) = 1(4)x¹⁻¹
f'(x) = 4x⁰
f'(x) = 4
Get the domain
The domain is the value of the input variable x for which the functions exists. For the functions given, the domain will be on all real numbers i.e the functions will exists for any value of x on the number line.
Hence Option D is correct
