Find quotient (2x-3/x) / (7/x^2)

A rancher wishes to build a fence to enclose a 2250 square yard rectangular field. Along one side the fence is to be made of hea

Bess [88]

Answer:

The least cost of fencing for the rancher is $1200

Step-by-step explanation:

Let x be the width and y the length of the rectangular field.

Let C the total cost of the rectangular field.

The side made of heavy duty material of length of x costs 16 dollars a yard. The three sides not made of heavy duty material cost $4 per yard, their side lengths are x, y, y. Thus

$C=4x+4y+4y+16x\\C=20x+8y$

We know that the total area of rectangular field should be 2250 square yards,

$x\cdot y=2250$

We can say that $y=\frac{2250}{x}$

Substituting into the total cost of the rectangular field, we get

$C=20x+8(\frac{2250}{x})\\\\C=20x+\frac{18000}{x}$

We have to figure out where the function is increasing and decreasing. Differentiating,

$\frac{d}{dx}C=\frac{d}{dx}\left(20x+\frac{18000}{x}\right)\\\\C'=20-\frac{18000}{x^2}$

Next, we find the critical points of the derivative

$20-\frac{18000}{x^2}=0\\\\20x^2-\frac{18000}{x^2}x^2=0\cdot \:x^2\\\\20x^2-18000=0\\\\20x^2-18000+18000=0+18000\\\\20x^2=18000\\\\\frac{20x^2}{20}=\frac{18000}{20}\\\\x^2=900\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{900},\:x=-\sqrt{900}\\\\x=30,\:x=-30$

Because the length is always positive the only point we take is $x=30$ . We thus test the intervals $(0, 30)$ and $(30, \infty)$

$C'(20)=20-\frac{18000}{20^2} = -25 < 0\\\\C'(40)= 20-\frac{18000}{20^2} = 8.75 >0$

we see that total cost function is decreasing on $(0, 30)$ and increasing on $(30, \infty)$ . Therefore, the minimum is attained at $x=30$ , so the minimal cost is

$C(30)=20(30)+\frac{18000}{30}\\C(30)=1200$

The least cost of fencing for the rancher is $1200

Here’s the diagram:

3 0

3 years ago

Determine the slope of the line 5x − 3y − 12 = 0.

givi [52]

Answer:

slope of a line is given by -A/B

Here A=5 and B= -3

so , when we plug in the values: -(5/-3) = 5/3

five thirds lol.

6 0

3 years ago

True or false: for any 2 nonzero integers, the product and quotient have the same sign.

scoray [572]

Yes, it is true.
________________
For example,

take two integers 12 and 4

12 × 4 = 48 : product is positive

12 ÷ 4 = 3: quotient is positive
____________________

If you take -12 and 4

-12 × 4 = -48 : product is negative

-12 ÷ 4 = -3: quotient is negative

4 0

3 years ago

Jordy was living in a third story apartment in his complex. up there he was paying an annual renters insurance premium of $325.0

Margaret [11]

New annual renter's insurance premium = 325(1 + 0.18) = 325 x 1.18 = $383.50

6 0

3 years ago

Read 2 more answers

Please help don’t understand

pshichka [43]

Answer:You are going to put and X by the rhombus, the paralleogram, and the trapezoid. All of these shapes have 4 sides.

Step-by-step explanation:

3 0

3 years ago