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Montano1993 [528]
3 years ago
8

A farmer has 1,800 feet of fencing and wants to fence off a rectangular field that borders a straight river. he needs no fence a

long the river. write the function that will produce the largest area if x is the short side of the rectangle.
Mathematics
2 answers:
astra-53 [7]3 years ago
4 0
There are 2 short sides x and 1 long side y.

x+x+y=1,800
2x+y=1,800
y=1,800-2x

The area of the rectangle is A=x(1,800-x).


A is a function with variable x. Moreover it is a quadratic (second degree) function.

The graph of the function is a parabola which opens downwards, because the signs of the leading coefficients of the factors, multiply to minus:

(x)(-x)=-x^2.


This means that the highest point of the parabola, is its vertex V(h,k), so the function takes its largest value for x=h.


The roots of A=x(1,800-x) are x=0 and x=1,800, thus the x coordinate of the vertex, must be the midpoint of 0 and 1,800, that is 900.


Answer:

A=x(1,800-x)

largest area is when x=900

Bas_tet [7]3 years ago
3 0

Answer:

-2x^2 + 1800x

Step-by-step explanation:

2x + l = 1800

l = 1800 - 2x

l * x = area

x(1800 - 2x) = area

-2x^2 + 1800x

You might be interested in
If y varies inversely as x and y = 27 when x = 2, find x when y = 9. *
torisob [31]
Given that y varies inversely as x then:
y=k/x
where
k is the constant of proportionality given by:
k=yk
but
y=27 when x=2
thus
k=27×2=54
hence the function will be:
y=54x
The value of x when y is 9 will be:
9=54x
thus
x=9/54
x=1/6

4 0
3 years ago
A company is in the business of finding addresses of long-lost friends. The company claims to have a 70% success rate. Suppose t
Galina-37 [17]

Answer:

a) Figure attached

b) E(X) =\mu= np = 9*0.7=6.3

Sd(X) =\sigma= \sqrt{np(1-p)}= \sqrt{9*0.7*(1-0.7)}=1.375

c) For the case n= 6

P(X \leq 2) = 0.9891

For the case n= 5

P(X \leq 2) = 0.9692

So then we need at least  n=5 or n=6 to satisfy the condition required.

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

X \sim Binom(n=9, p=0.7)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

Part a

For this case we can use the following R code:

> x <- seq(0,9,by = 1)

> y <- dbinom(x,9,0.7)

> plot(x,y,main="Histogram",type = "h")

And we can see on the figure attached the solution.

We see that the higher probabilities are from 4 to 9

Part b

The expected value is given by:

E(X) =\mu= np = 9*0.7=6.3

The variance is given by:

Var (X) =\sigma^2= np(1-p) = 9*0.7*(1-0.7)= 1.89

And the standard deviation is:

Sd(X) =\sigma= \sqrt{np(1-p)}= \sqrt{9*0.7*(1-0.7)}=1.375

Part c

First we can find the probability that at least two addresses will be found in the list of 9 that we have like this:

P(X \geq 2)

We can use the complement rule and we have:

P(X \geq 2) = 1-P(X

We find the indicidual probabilities:

P(X=0)=(9C0)(0.7)^0 (1-0.7)^{9-0}=0.00001968

P(X=1)=(9C1)(0.7)^1 (1-0.7)^{9-1}=0.000413

P(X \geq 2) = 1-[0.00001968+0.000413]=0.9996

If we use the case of n=8 and we find P(X\leq 2), we got:

P(X \leq 2) = 0.9987

For the case n= 7

P(X \leq 2) = 0.9962

For the case n= 6

P(X \leq 2) = 0.9891

For the case n= 5

P(X \leq 2) = 0.9692

So then we need at least  n=5 or n=6 to satisfy the condition required.

5 0
3 years ago
Solve the following real-life problems.
Anika [276]

Answer:

a) The two numbers are x = 11 and y = 41

b) Leon gets $33, Kokyangwuti gets $16.5, Jill gets $38 and Isaac gets $6.5

c) Elizabet started with $106

Step-by-step explanation:

These problems can be solved by systems of equations

a)

I am going to say that the first number is x and the second number is y

The problem states that the sum of two numbers is 52. So x + y = 52.

The problem also states that one number is three less than quadruple the other number. So y = 4x - 3

We have the following system

1) x + y = 52

2) y = 4x - 3

Replacing 2) in 1)

x + 4x -3 = 52

5x = 55

x = 11

------

y = 4x - 3 = 4(11)-3 = 44-3 = 41

The two numbers are x = 11 and y = 41

b)

I am going to say that x is how much money Leon gets, y is how much Kokyangwuti, z is how much Jill gets and w is how much Isaac gets.

Martha divides $94 amongst her four friends. So x + y + z + w = 94

Leon gets twice as much money as Kokyangwuti. So x = 2y.

Jill gets five more dollars than Leon, so z = 5 + x

Isaac gets ten less dollars than Kokyangwuti, so w = y-10

We have the following system:

1) x + y + z + w = 94

2) x = 2y

3) z = 5 + x

4) w = y - 10

I am going to replace 2) in 3), so we have z = 5 + 2y

Now i am going to replace 2), 3) and 4) in 1), so:

2y + y + 5 + 2y + y - 10 = 94

6y -5 = 94

6y = 99

y = $16.5

From 2): x = 2y = 2*16.5 = $33

From 3) z = 5 + x = 5 + 33 = $38

From 4): w = y - 10 = $16.5-10 = $6.5

So, Leon gets $33, Kokyangwuti gets $16.5, Jill gets $38 and Isaac gets $6.5

c)

Elizabeth spent:

2 shirts for $22.99 each = $45.98

a drink for $2.02 = $2.02

2 books for $16 each = $32

In all, she spent 45.98 + 2.02 + 32 = $80

She has $26 left.

She started with $26 + $80 = $106.

4 0
3 years ago
What is the value of 9x÷y³?
scoundrel [369]
I think the answer is:
Y=0
8 0
3 years ago
Need math help please!!
s2008m [1.1K]
Just by looking at it, 2 seems to be the correct answer. I mean if you think about it, when the triangle is split in two smaller triangles, side LN is longer than LP so that means x needs to be a small number. I could either be 2 or 1. Well if you look at the big picture, side LM is longer than LN so it’s gonna need to be bigger. If you say x=1 then you are saying 2(1) +4 = 6 (therefore LM is 6) but if you say x=2 then you are saying 2(2) +4 = 8 which makes more sense


If x=2 then you can use the Pythagorean’s theorem

a2 + b2 = c2
4^2 + b^2 = 5^2
16 + b^2 = 25
25-16= 9
b^2= 9
b= 3


Now that we know what NP is we can do Pythagorean’s theorem to figure out what side LP is (we already know it but you can do it again to check lol)

So the answer is 2
5 0
3 years ago
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