Twenty-four 4-inch wide square posts are evenly spaced with 5 feet between adjacent posts to enclose a square field, as shown. W

If 30,000 cm2 of material is available to make a box with a square base and an open top, what is the largest possible volume (in

Inessa [12570]

Answer:

The highest achievable volume for the box is 2000000 cubic meters.

Step-by-step explanation:

Below is an outline of the volume ( $V$ ), measured in cubic centimeters, and surface area ( $A_{s}$ ), measured in square centimeters, for a box featuring a square base:

$A_{s} = l^{2}+h\cdot l$ (1)

$V = l^{2}\cdot h$ (2)

Where:

$l$ - The length of the base's side, in centimeters.

$h$ - The height of the box, in centimeters.

Using (2), we isolate $h$ in the formula:

$h = \frac{V}{l^{2}}$

Then, we substitute into (1) and simplify the outcome:

$A_{s} = l^{2}+ \frac{V}{l}$

$A_{s}\cdot l = l^{3}+V$

$V = A_{s}\cdot l -l^{3}$ (3)

Next, we calculate the first and second derivatives of this expression:

$V' = A_{s}-3\cdot l^{2}$ (4)

$V'' = -6\cdot l$ (5)

If $V' = 0$ and $A_{s} = 30000\,cm^{2}$ , then we find that the critical value for the base's side length is:

$30000-3\cdot l^{2} = 0$

$3\cdot l^{2} = 30000$

$l = 100\,cm$

Subsequently, we assess this outcome using the second derivative's expression:

$V'' = -600$

According to Second Derivative Test, this critical value signifies an absolute maximum. Consequently, the largest volume obtainable for the box is:

$V = 30000\cdot l - l^{3}$

$V = 2000000\,cm^{3}$

The highest achievable volume for the box is 2000000 cubic meters.

4 0

1 month ago

Which of the following functions is graphed below?

PIT_PIT [12445]

Answer:

D.

Step-by-step explanation:

This function is piece-wise, meaning you will have two equations along with distinct domains. The equation x squared plus 3 illustrates a parabolic curve, while x plus 4 is depicted as a linear function. There is a specific reason why the point on the parabola is open at x equals 4; this signifies that the value does not satisfy the equation. Therefore, x cannot equal 4 for the parabola, so its domain is x less than 4. The closed point on the linear function indicates that when x is 4, it is part of the solution for that equation and graph. Consequently, the domain for the linear function is x greater than or equal to 4. Hope this clarifies things!

8 0

3 months ago

In June 2012, Twitter was reporting 400 million tweets per day. Each tweet can consist of up to 140 characters (letter, numbers,

babunello [11817]

Each tweet could cost anywhere from 1 to 140 pennies, which can be expressed as an inequality [1 ≤ x ≤ 140]. Since it's impossible to tweet 0 characters or exceed 140. If required in pounds, simply divide by 100. A) 1 ≤ x ≤ 140 B) The cost per character is a penny, and tweeting fewer than 1 character or more than 140 is not permitted.

3 0

2 months ago

By law, all businesses outside the Parkville city limits must fence their lots. How many inches of fence will be needed to fence

AnnZ [12381]

There is no image below....

8 0

1 month ago

Jean lives about 10 miles from the college where she plans to attend a 10-week summer class. There are two main routes she can t

PIT_PIT [12445]

Answer:

We would recommend the Country Route as its travel time is consistently estimated between 15 and 18 minutes.

Step-by-step explanation:

Jean lives approximately 10 miles away from the college where she plans to attend a summer class lasting ten weeks. She has two primary routes available, one that traverses the city and another that goes through the countryside.

Jean has set up a randomized trial in which she flips a coin each day to determine her travel route, collecting data from five days for both.

Country Route - 17, 15, 17, 16, 18 (in minutes)

City Route - 18, 13, 20, 10, 16 (in minutes)

Next, we need to evaluate which route is superior for Jean.

The data indicates that the Country route has timing ranging from 15 to 18 minutes, suggesting she will typically arrive within this timeframe.

Conversely, the City route timings show significant variation with a minimum of 10 minutes and a maximum of 20 minutes, indicating uncertainty regarding her arrival time.

Hence, it is advisable for her to select the Country route.

7 0

1 month ago