Find the slope of the graph

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gogolik [260]

Answer:

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Step-by-step explanation:

Please MARK AS BRAINLIEST

4 0

3 years ago

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

2 years ago

Find the midpoint and distance on a number line between 6, -15

SCORPION-xisa [38]

So it is distance from zero so 6+15=21

1 2 3 4 5 6 7 8 9 10 (11) 12 13 14 15 16 17 18 19 20 21
eliminate one from each side till you find the middle

7 0

3 years ago

Please help asap!!!!

Triss [41]

Answer: B

Step-by-step explanation: The answer would be B because you would add n the number and 6 then you would multiply it by 2

5 0

3 years ago

Will somebody please answer this question? I'm stuck and in a bit of a hurry. A surfboard shaper has to limit the cost of develo

ikadub [295]

Answer:

≥ 420 boards

Step-by-step explanation:

Write the required relation between cost per board and "x" (the number of boards that must be sold).

143 + 30240/x ≤ 215 . . . . . . . note that the first term is not 143x

Subtract 143

30240/x ≤ 72

Multiply by x/72. This is a positive number because x is a positive number.

30240/72 ≤ x

420 ≤ x

At least 420 surfboards must be sold to limit the final cost per board to $215.

8 0

3 years ago