Sienna has 80 yards of fencing to enclose a rectangular area. Find the dimensions that maximize the enclosed area. What is the m

aximum area?

Mathematics

1 answer:

Lubov Fominskaja [6]2 years ago

7 0

$2x+2y=80\ \ \ /:2\\\\2x:2+2y:2=80:2\\\\x+y=40\ \ \ /-x\\\\y=40-x\ \ \ (D_x:x\in(0;\ 40))$

$Area=xy\\\\substitute\ y=40-x\\\\Area=x(40-x)=-x^2+40\\(it's\ quadratic\ function\ where\ a=-1;b=40;c=0)\\\\vertex\ of\ parabola:p=\frac{-b}{2a}\to p=\frac{-40}{2\cdot(-1)}=\frac{-40}{-2}=20-it's\ max\\\\x=20\ then\ y=40-20=20\\\\Answer:dimensions\ of\ rectangular\ is\ 20\ yd\ \times\ 20\ yd,\\and\ area\ is\ 20^2=400\ yd^2.$

You might be interested in

A certain mixture of paint contains 5 parts white paint for every 4 parts blue paint. If a can of paint contains 75 ounces of wh

Len [333]

Answer:

60 ounces

Step-by-step explanation:

A certain mixture of paint contains 5 parts white paint for every 4 parts blue paint, that is, the white paint (w) to blue paint (b) ratio is 5:4. We can apply this ratio to different units such as ounces. This means that the mixture has 5 ounces of white paint to 4 ounces of blue paint. If a can of paint contains 75 ounces of white paint, the ounces of blue paint in the can are:

75 oz w × (4 oz b/5 oz w) = 60 oz b

3 0

3 years ago

Write a function that models 40mg of a substance that has a half life of 84 days

lubasha [3.4K]

Answer: The function is M(t) = 40mg*0.992^t

Step-by-step explanation:

Half life refers to the time that a given quantity to reduce to half its initial value.

This is usually a exponential decay, so we want a function of the form:

M(t) = A*r^(*t)

Were t is time, in this case, t is the number of days

A is the initial value

r is the rate of decrease, we will find that for exponential decays r must be a number between 0 and 1. If r is closer to 0, we will have a fast exponential decay, if r is closer to 1 we will have a slower exponential decay.

We have that the initial mass is 40mg, this is at t = 0.

M(0) = A*r^(0) = A = 40mg

So now we have the value of A.

Now, we know that in t = 84, the mass of the substance will be half its initial value, so it will be:

A/2 = 40mg/2 = 20mg

this means that:

M(84) = 40mg*r^(84) = 20mg

r^(84) = 20mg/40mg = 1/2

$r = \sqrt[84]{1/2}$ = 0.992