Recall Euler's theorem: if , then
where is Euler's totient function.
We have - in fact, for any since and share no common divisors - as well as .
Now,
where the are positive integer coefficients from the binomial expansion. By Euler's theorem,
so that
Answer:
Step-by-step explanation:
Given the equation of motion;
S = ut + 1/2 at² where;
u is the initial velocity,
a is the acceleration, and;
t is the time.
We are to express a in terms of u, t and S
Making a the subject of the formula;
S = ut + 1/2 at²
S-ut = 1/2at²
2(S-ut) = at²
a = 2(S-ut)/t²
Hence the acceleration a in terms of other variables is expressed as a = 2(S-ut)/t²
Answer:
Step-by-step explanation:
5 men do 1 unit of work in 1 hr. 1 man does 1/5 unit of work in 1 hr. 2 men do 2/5 units of work in 1 hr. Therefore 2 men will take 5/2 hours to dig 1 hole and take 5/4 hrs to dig half a hole.
Answer:
You will have to sell $7,667 worth of sales in a week in order for the straight commission offer to be at least as good
Step-by-step explanation:
Step 1: Get the total straight commission offer
We can express the straight total commission as follows;
A=R×T
where;
A=straight total commission
R=commission rate
T=total sales
In our case;
R=5%=5/100=0.05
T=t
replacing
A=0.05×t=0.05 t....equation 1
Step 2: Total amount of the second offer
We can express the total amount of the second offer as follows;
A=F+(R×T)
where;
A=amount of income the second company offers
F=fixed salary per week
R=commission rate
T=total sales
In our case;
F=$230 per week
R=2%=2/100=0.02
T=t
replacing;
A=230+(0.02×t)=0.02 t+230....equation 2
Step 3: Equate equation 1 and 2
0.05 t=0.02 t+230
(0.05 t-0.02 t)=230
0.03 t=230
t=230/0.03
t=7,666.67 rounded up=7,667
You will have to sell $7,667 worth of sales in a week in order for the straight commission offer to be at least as good
The measurement of D can be anyone one of these but where's the rest of the problem like a pic or the measurements of any other angles?