Find the value of x. Assume that lines which appear to be tangent to the circle are tangent.

Suppose a rectangular pasture is to be constructed using 1 2 linear mile of fencing. The pasture will have one divider parallel

timama [110]

Answer:

$\displaystyle A=\frac{1}{192}$

Step-by-step explanation:

<u>Maximization With Derivatives</u>

Given a function of one variable A(x), we can find the maximum or minimum value of A by using the derivatives criterion. If A'(x)=0, then A has a probable maximum or minimum value.

We need to find a function for the area of the pasture. Let's assume the dimensions of the pasture are x and y, and one divider goes parallel to the sides named y, and two dividers go parallel to x.

The two divisions parallel to x have lengths y, thus the fencing will take 4x. The three dividers parallel to y have lengths x, thus the fencing will take 3y.

The amount of fence needed to enclose the external and the internal divisions is

$P=4x+3y$

We know the total fencing is 1/2 miles long, thus

$\displaystyle 4x+3y=\frac{1}{2}$

Solving for x

$\displaystyle x=\frac{\frac{1}{2}-3y}{4}$

The total area of the pasture is

$A=x.y$

Substituting x

$\displaystyle A=\frac{\frac{1}{2}-3y}{4}.y$

$\displaystyle A=\frac{\frac{1}{2}y-3y^2}{4}$

Differentiating with respect to y

$\displaystyle A'=\frac{\frac{1}{2}-6y}{4}$

Equate to 0

$\displaystyle \frac{\frac{1}{2}-6y}{4}=0$

Solving for y

$\displaystyle y=\frac{1}{12}$

And also

$\displaystyle x=\frac{\frac{1}{2}-3\cdot \frac{1}{12}}{4}=\frac{1}{16}$

Compute the second derivative

$\displaystyle A''=-\frac{3}{2}.$

Since it's always negative, the point is a maximum

Thus, the maximum area is

$\displaystyle A=\frac{1}{12}\cdot \frac{1}{16}=\frac{1}{192}$

6 0

3 years ago

Which functions domain consists of all real numbers except -2?

Eddi Din [679]

Answer:

option (a) f(x)= 1/x+2

Step-by-step explanation:

(a) f(x) = 1/ x+2

To find the restriction for domain , we set the denominator =0 and solve for x

x+2 =0, so x=-2

When x=-2 then denominator becomes 0 that is undefined.

So, domain is all real numbers except -2

(b) f(x)= 2x

In this function, there is no denominator or square root or log function

so there is no restriction for x, hence domain is all real numbers

(c) f(x) = 2x-2

In this function, there is no denominator or square root or log function

so there is no restriction for x, hence domain is all real numbers

f(x) = 1/ sqrt(x+2)

if we have square root in the denominator then we set the denominator >0 and solve for x. because square root of negative values are undefined

x+2>0, x>-2

Hence domain is all real numbers that are greater than -2

8 0

3 years ago

What are the zero(s) of the function f(x)=<img src="https://tex.z-dn.net/?f=%5Cfrac%7B4x%5E%7B2%7D-36x%20%7D%7Bx-9%7D" id="TexFo

Contact [7]

Answer:

D

Step-by-step explanation:

The function will be zero when the numerator is equal to 0. So, set the numerator equal to 0 and solve:

$0 = 4 {x}^{2} - 36x$

I will use the quadratic formula:

$\frac{ 36 + \sqrt{ {36}^{2} - 4(4)(0)} }{2(4)} \\ \frac{ 36 + 36}{8} = 9$

Therefore, x = 9 is a 0. Let's check with subtracted root now:

$\frac{ 36 - \sqrt{ {36}^{2} - 4(4)(0)} }{2(4)} \\ \frac{ 36 - 36}{8} = 0$

It appears 0 is also a root.

Therefore, the answer is D.

7 0

3 years ago

Help... with number 15 plz

statuscvo [17]

Answer:

P

Step-by-step explanation:

p is the ans

5 0

2 years ago

If a ray bisects an angle, each newly formed angle measures 90 degrees.

prohojiy [21]

Answer:

A) Sometimes

A ) Sometimes is the correct answer because b) always and c) never is not possible

it cannot be always measured 90 degrees

3 0

3 years ago

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