Let x be the length and y be the width2x + 2y = 40x + y = 20change that into y = mx + b formy= 20 – x
Area =xy = x (20-x) = 20x - x^2Area=-x^2+20xcomplete the square:Area=-(x^2 – 20x + 100) +100=-(x - 10)^2 + 100This is an calculation of a parabola that opens downward with vertex at (10,100), which means maximum area of 100 happens when x, the length=10)Dimensions of the rectangle with maximum area? 10 yds. by 10 yds., a square.
Answer:
5/9
Step-by-step explanation:
(5/6)/1 1/2
5/9
Merry Christmas
Answer: the probability that a randomly selected tire will have a life of exactly 47,500 miles is 0.067
Step-by-step explanation:
Since the life expectancy of a particular brand of tire is normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = life expectancy of the brand of tire in miles.
µ = mean
σ = standard deviation
From the information given,
µ = 40000 miles
σ = 5000 miles
The probability that a randomly selected tire will have a life of exactly 47,500 miles
P(x = 47500)
For x = 47500,
z = (40000 - 47500)/5000 = - 1.5
Looking at the normal distribution table, the probability corresponding to the z score is 0.067
Answer: t-half = ln(2) / λ ≈ 0.693 / λExplanation:The question is incomplete, so I did some research and found the complete question in internet.
The complete question is:
Suppose a radioactive sample initially contains
N0unstable nuclei. These nuclei will decay into stable
nuclei, and as they do, the number of unstable nuclei that remain,
N(t), will decrease with time. Although there is
no way for us to predict exactly when any one nucleus will decay,
we can write down an expression for the total number of unstable
nuclei that remain after a time t:
N(t)=No e−λt,
where λ is known as the decay constant. Note
that at t=0, N(t)=No, the
original number of unstable nuclei. N(t)
decreases exponentially with time, and as t approaches
infinity, the number of unstable nuclei that remain approaches
zero.
Part (A) Since at t=0,
N(t)=No, and at t=∞,
N(t)=0, there must be some time between zero and
infinity at which exactly half of the original number of nuclei
remain. Find an expression for this time, t half.
Express your answer in terms of N0 and/or
λ.
Answer:
1) Equation given:
← I used α instead of λ just for editing facility..
Where No is the initial number of nuclei.
2) Half of the initial number of nuclei:
N (t-half) = No / 2So, replace in the given equation:
3) Solving for α (remember α is λ)
αt ≈ 0.693
⇒ t = ln (2) / α ≈ 0.693 / α ← final answer when you change α for λ