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3 years ago

Need help please see attached

Mathematics

1 answer:

Dima020 [189]3 years ago

4 0

To find the unit price of the food, divide the price by the pounds.

For example to find the unit price for Grocery Mart-
$2.99 \div 2 =$
Repeat for the Scott Family and then compare for the lowest price- the best deal.

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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

Need help #1. The answer is shown, but I don’t know how to get to the answer. Please teach and show steps.

Rufina [12.5K]

Answer:

Step-by-step explanation:

We are given that x and y are functions of time t such that x and y is a constant. So, we can write the following equation:

$x(t)+y(t)=k,\text{ where $k$ is some constant}$

The rate of change of x and the rate of change of y with respect to time t is simply dx/dt and dy/dt, respectively. So, we will differentiate both sides with respect to t:

$\displaystyle \frac{d}{dt}\Big[x(t)+y(t)\Big]=\frac{d}{dt}[k]$

Remember that the derivative of a constant is always 0. Therefore:

$\displaystyle \frac{dx}{dt}+\frac{dy}{dt}=0$

And by subtracting dy/dt from both sides, we acquire:

$\displaystyle \frac{dx}{dt}=-\frac{dy}{dt}$

Hence, our answer is B.

3 0

2 years ago

Read 2 more answers

A department store buys 300 shirts for a total cost of 7,200 and sells them for $30 each. Find the percent markup.

worty [1.4K]

Step-by-step explanation:

7200 ÷ 300 = 24

30 - 24 = 6

6/24 × 100/1 = 25%

3 0

2 years ago

Read 2 more answers

Ron is 8 years old and 40 inches tall. If he grows at the same rate every year, how tall was he when he was 5 years old?

Vadim26 [7]

He would be 25 inches tall.

40 divided by 8 would equal 5 so at age 1, he was 5 inches tall. So 5 times 5 which is how old he was, would equal 25 inches.

5 0

2 years ago

Read 2 more answers

Five decimals between 0.42 and 0.44

Nata [24]

Answer: 0.421, 0.422, 0.423, 0.43, 0.434

Step-by-step explanation:

4 0

2 years ago