Optimization. A rectangle is to have an area of 32 square cms. Find its dimensions so that
the distance from one corner to the mid point of a non-adjacent edge is a
minimum ...?

Answers

Answer 1
Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions here.

xy = 32 makes y = 32/x z² = (32/x)² + (x/2)²

Isolate z
z = 32/x + x/2 

Find dz/dx

fr(z) = (x² - 64)/ (2x²)

Set z' = 0, algebraically solving for x having
x +- 18

Since you cannot have a dimension of -8, the only answer for x is 8.

Go back to the original area equation; 32 = xy and plug in x making
32 = 8y
y = 4
Answer 2

To optimize the dimensions of a rectangle with an area of 32 square cm such that the distance from one corner to the midpoint of a non-adjacent edge is minimized, one must use the Pythagorean theorem and calculus. The minimum distance occurs when the rectangle is a square with sides measuring 4√2 cm.

Assume the rectangle's dimensions are length L and width W, with the given area 32 cm2 such that LW = 32. To minimize the distance (D) from one corner to the midpoint of the non-adjacent edge, we can use the Pythagorean theorem, given by D = √(L2 + (W/2)²).

Since the area is fixed, W can be expressed as 32/L, and we can write D as a function of L. After substituting 32/L for W and differentiating with respect to L, we can find the minimum by setting the derivative equal to zero and solving for L.

The minimum distance is achieved when the rectangle is a square, with length and width both equal to √32, which simplifies to 4√2 cm, which is approximately 5.66 cm for both dimensions.


Related Questions

A dvd costs $20 the sales tax is 6.5% how much sales tax do you have to pay

Answers

6.5% of 20....turn percent to decimal..." of " means multiply
0.065(20) = 1.30...so the sales tax is $ 1.30

Are 8:5 and 4:19 equivalent

Answers

no they aren't but 8:38 and 4:19 are

What is the gcf for 36, 54 and 135?

Answers

factor
36=2*2*3*3
54=2*3*3*3
135=3*3*3*5
gcf=3*3=9
The greatest common factor is 9.

math plzz I got turn it in Monday she just barely sent me it

Answers

A, B, A, A, E
Remember, the hypotenuse is the side opposite the right angle of the triangle.

the smaller of two containers has a capacity of 150 gallons. When it is 4/5 full, its contents are emptied into a larger container, filling exactly 2/3 of it. What is the capacity, in gallons, of the larger container?

Answers


x= capacity, in gallons, of the larger container.
We can suggest this equation:

(4/5)150+(2/3)x=x
120+2x/3=x
360+2x=3x
3x-2x=360
x=360

Answer: the capacity, of the larger container is 360 gallons.
Answer: the ca

show that if k is a positive constant, then the area between the x-axis and one arch of the curve y=sin kx is 2/k

Answers

sin(kx)=0=>x=0,π,...
∫0πsin(kx)dx=−1/kcos(kx)|π0=−1/k(cos(kπ)−cos(k∗0))
if k is odd then,=−1/k(−1−1)=−1/k(−2)=2/k
if k is even then,=−1/k(1−1)=0

K-X=V-W solve for the letter x

Answers

-X = (V - W) - K

Mul -1 X = -(V-W) + K

X = -V + W + K
Final answer:

To solve for 'x' in the equation 'K - X = V - W', we rearrange the equation to isolate 'x', resulting in 'X = K - V + W'.

Explanation:

To solve the equation for the letter x, you need to isolate x on one side of the equation. It's a simple process of rearranging the equation.

Here we start with the original equation:

K - X = V - W

First, to separate your desired variable, or in this case 'x', we add 'X' to both sides to cancel 'X' from the left hand side:

K = X + V - W

Finally, to isolate 'x', we just need to subtract 'V' and add 'W' to both sides

X = K - V + W

So, the solution to the equation when solved for the letter 'x' is X = K - V + W.

Learn more about Solving for a variable here:

https://brainly.com/question/35263223

#SPJ2

what is the answer to this : (3m 3 - y)(3m 3 - y)

Answers

Good evening Shalanda

(3m³ - y)(3m³ -y)
We need to simplify this
Distribute
(3m³)(3m³)+(3m³)(-y)+(-y)(3m³)+(-y)(-y)
= 9m^6 - 3m³y - 3m³y +y²
= 9m^6 -6m³y +y²

I hope that's help !

On April 11, 2012, two earthquakes were measured off the northwest coast of Sumatra. The first had a magnitude of 8.6. The second had a magnitude of 8.2. By what approximate factor was the intensity of the first earthquake greater than the intensity of the second earthquake?

0.40
1.02
1.05
2.51

Answers

Answer:

Option D. 2.51 is correct.

Step-by-step explanation:

Magnitude of first earthquake = 8.6

Let intensity of first earthquake be x

[tex]Magnitude = \log(\frac{x}{S}),\text{ where S is seismographic factor}\\\\\implies 8.6=\log(\frac{x}{S}).......(1)[/tex]

Magnitude of second earthquake = 8.2

Let intensity of second earthquake be y

[tex]Magnitude = \log(\frac{y}{S}),\text{ where S is seismographic factor}\\\\\implies 8.2=\log(\frac{y}{S}).......(2)[/tex]

Now, to find the factor by which intensity of first earthquake is greater than intensity of second : we divide equation (1) by equation (2)

[tex]\implies\log(\frac{x}{y})=8.6 - 8.2\\\\\implies \log(\frac{x}{y})=0.4\\\\\implies\frac{x}{y}=10^{0.4}\\\\\implies\frac{x}{y}=2.51[/tex]

Hence the required factor is 2.51

Therefore, Option D. 2.51 is correct.

Answer:

2.51

Step-by-step explanation:

Which of the following are not congruence theorems for right triangles? Check all that apply.

A. LA
B. HL
C. AA
D. HA
E. HH
F. LL

Answers

HA means that the hypotenuse and the acute angle of two triangles are congruent. This does prove congruence. 
LL means if two legs of two triangles are congruent, the two hypotenuses are congruent. This is similar to SSS congruence which proves congruence. 
LA : Since we have two right triangles, three angles of the triangle and a side are congruent. By ASA, the right triangles are congruent. 

Answer:

E. HH, C. AA

Step-by-step explanation:

Got these from the quiz

Calculate the average rate of change for the function f(x) = −x4 + 4x3 − 2x2 + x + 1, from x = 0 to x = 1.

0

1

2

7

Answers

really
just calculate the slope
slope is (y2-y1)/(x2-x1)

for x=0, y=1
for x=1, y=3

slope=(y1-y1)/(x-x1)=(3-1)/(1-0)=2/1=2

answer is 2

Answer:

C) 2

Step-by-step explanation:

I took the quiz and got a 100%.

What is the value of ∑n=13(17n−15)?

Answers

the value of [tex]\( \sum_{n=1}^{13} (17n - 15) \)[/tex] is indeed 1352.

To find the value of [tex]\( \sum_{n=1}^{13} (17n - 15) \)[/tex], we need to compute the sum of the expression 17n - 15 for n ranging from 1 to 13.

Using the formula for the sum of an arithmetic series, we can express this sum as:

[tex]\[ \sum_{n=1}^{13} (17n - 15) = \sum_{n=1}^{13} 17n - \sum_{n=1}^{13} 15 \][/tex]

We know that the sum of the first \(n\) natural numbers can be expressed as [tex]\( \sum_{n=1}^{N} n = \frac{N(N+1)}{2} \).[/tex]

So, the sum of [tex]\(17n\) from \(n=1\) to \(n=13\)[/tex] is:

[tex]\[ \sum_{n=1}^{13} 17n = 17 \sum_{n=1}^{13} n = 17 \cdot \frac{13 \cdot (13 + 1)}{2} \][/tex]

[tex]\[ = 17 \cdot \frac{13 \cdot 14}{2} = 17 \cdot 91 = 1547 \][/tex]

And the sum of 15, 13 times (since there are 13 terms) is[tex]\(15 \cdot 13 = 195\).[/tex]

Now, we can find the value of the given expression:

[tex]\[ \sum_{n=1}^{13} (17n - 15) = 1547 - 195 = 1352 \][/tex]

So, the value of [tex]\( \sum_{n=1}^{13} (17n - 15) \)[/tex] is indeed 1352.

can -2/5 be simplified

Answers

No it can't because nothing will go into 2 or 5 at the same time...

make a conjecture about the next item in the sequence.


6,8,-32,-30,120


answer choices....... a.122 b.-480 c. -488 d. 116 ...?

Answers

a.122
Previous number + 2

The sequence alternates between adding 2 and multiplying by -4. Starting with 6, the sequence progresses by these operations to reach 120. Following this pattern, the next term after 120 is a) 122 by adding 2.

The student has asked to make a conjecture about the next item in the sequence 6, 8, -32, -30, 120. To determine the pattern, let's look at the differences between each pair of numbers.

From 6 to 8, we add 2.

From 8 to -32, we multiply 8 by -4.

From -32 to -30, we add 2.

From -30 to 120, we multiply -30 by -4.

It appears that the sequence alternates between adding 2 and multiplying by -4. Following this pattern, after 120 the next operation should be adding 2.

Therefore, the next number in the sequence would be 120 + 2 = 122. Hence, the answer is option a. 122.

What is 6 1/2 as a decimal?

Answers

the answer to that question is...6.5

A restaurant manager recorded the number of people in different age groups who attended her food festival. She then created the following histogram:

Histogram with title Food Festival Participants, horizontal axis labeled Age Group (year) with bins 0 to 19, 20 to 39, 40 to 59, and 60 to 79 and vertical axis labeled Number of People with values from 0 to 60 at intervals of 10. The first bin goes to 20, the second goes to 40, the third goes to 60, and the last goes to 50.

Which of the following statements best compares the height of the bars of the histogram?

There are twice as many participants in the 60–79 age group than in the 0–19 age group.
There are 3 times as many participants in the 40–59 age group than in the 0–19 age group.
There are more participants in the 40–59 age group than in the 0–19 and 60–79 groups combined.
There are more participants in the 60–79 age group than in the 0–19 and 20–39 groups combined.

Answers

Answer:

Option: B

There are three times as many participants in the 40-59 age group than in the 0-19 age group.

Step-by-step explanation:

From the histogram we have following observations:

Number of people in the age group  0-19= 20

Number of people in the age group 20-39=40

Number of people in the age group 40-59=60

Number of people in the age group 60-79=50

Hence, from the data we could say that  there are three times as many participants in the 40-59 age group( which is 60) than in the 0-19 age group(which is 20).

Hence, option B is correct.


What are the x and y intercept of c = 0.75m + 2.25?

Answers

the y intercept is 2.25 and x intercept is -3
Yep because thank you I need help with this one too I'm surprise because there he same

What is the 8th term in the sequence?

Note: Use the explicit rule.

an=25−3n

Enter your answer in the box.
a8=

Answers

a8=25-3(8)
a8=25-24=1

On level ground, a 60-foot-tall vertical building casts a 10-foot shadow. at the same time, another vertical building casts a 25-foot shadow. how many feet tall is the second building?

Answers

150 ft. Hope this helps!
Final answer:

Using the concept of similar triangles, the height of the second building is calculated to be 150 feet, since its 25-foot shadow corresponds proportionally to the 60-foot building's 10-foot shadow.

Explanation:

To find the height of the second building given that a 60-foot-tall building casts a 10-foot shadow, and another building casts a 25-foot shadow, we can use the concept of similar triangles. The idea behind similar triangles is that corresponding sides of similar triangles are proportional. Therefore, if one building is 60 feet tall and casts a 10-foot shadow, the ratios of the height to shadow length will be the same for the second building.

To set up the proportion, we have:


 
 
 
 

We can write the proportion as:

h1/s1 = h2/s2

Substituting the known values into the proportion gives us:

60/10 = x/25

Now we solve for x:

x = (60/10) * 25

x = 6 * 25

x = 150

Therefore, the height of the second building is 150 feet.

Find the discriminant of the following equation.

4x2 + 12x + 9 = 0

Answers

for
ax^2+bx+c=0
discriminatn is b^2-4ac

a=4
b=12
c=9
discriinat is
12^2-4(4)(9)=
144-144
0

the discrminat is 0

What is the expression in simplest radical form?

√384

Answers

√384 = √2x2x2x2x2x2x3x2
          = 8√6

Hope this helps!

if x=t^2-1 and y=t^4-2t^3, then when t=1 what's d^2y/dx^2? if x=t^2-1 and y=t^4-2t^3, then when t=1 what's d^2y/dx^2?

Answers

The solution to the problem is as follows:

d^2y/dx^2    = d/dt(dy/dx) * dt/dx

                      = d/dt (2t^2 - 3t) * dt/dx

                      = ( 4t-3) * 1 / 2t = (4t-3)/2t

when t = 1 d^2y/dx^2 = 1/2


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

Final answer:

To find d^2y/dx^2 when t = 1, we need to first express y in terms of x. Then, differentiate y with respect to x to find dy/dx. Finally, differentiate dy/dx to find d^2y/dx^2 and substitute t = 1.

Explanation:

Given the equations x = t^2 - 1 and y = t^4 - 2t^3, we can find d^2y/dx^2 when t = 1.

First, we need to express y in terms of x. From the equation x = t^2 - 1, we can solve for t as t = sqrt(x + 1). Substituting this into the equation y = t^4 - 2t^3, we get y = (sqrt(x + 1))^4 - 2(sqrt(x + 1))^3.

Next, we need to find the first derivative of y with respect to x: dy/dx. Then, we can find the second derivative d^2y/dx^2 by differentiating dy/dx. Finally, substitute t = 1 into d^2y/dx^2 to find the value.

Factor the expression.

9x^2 + 48x + 64

Answers

(3x+8)(3x+8) is the answer :))

Shape 1 and shape 2 are plotted on a coordinate plane. Which rigid transformation can you perform on shape 2 to show that shape 2 is congruent to shape 1?

a 45° rotation clockwise about the origin

a translation 6 units to the left and 8 units up

a reflection across the x-axis

a translation 3 units to the left and 6 units up

Answers

According to given information, a translation 6 units to the left and 8 units up for shape 2 would show that it is congruent to shape 1.

So, option B is your answer.

Hope this helps!

Two translation rigid transformations are required to transform shape 1 to shape 2

The rigid transformation that can be performed on shape 2 to show that shape 2 is congruent to shape 1 is the option

A transformation of 6 units to the left and 8

Reasons:

The coordinates of the three points on shape 1 are; (2, 12), (4, 14), (6, 14)

The coordinates of the three points shape 2 are; (8, 4), (10, 6), (12, 6)

The difference in the coordinates are;

Difference in x-coordinate are;

Point 1 = 8 - 2 = 6

Point 2 = 10 - 6 = 6

Point 3 = 12 - 6 = 6

Therefore;

To get the x-value of shape 1 from the shape 2, the transform that is to be performed on shape 2 is a transformation of -6 units or 6 units left

Difference in y-coordinate are;

Point 1 = 4 - 12 = -8

Point 2 = 6 - 14 = -8

Point 3 = 6 - 14 = -8

Therefore;

To get the y-value of shape 1 from the shape 2, the transform that is to be performed on shape 2 is a transformation of 8 units or 8 units up

The composite transformation is therefore;

A transformation of 6 units to the left and 8 units up

Learn more here:

https://brainly.com/question/17957030

find g'(4) given that f(4)=3 and f'(4) = -5. g(x) = f(x)/x

Answers

the answer is
g' (x) = [f(x)/x ]' = f'(x)  x - f(x)  / x2
 
g' (4) = [f(4)/4]' = f'(4)  4 - f(4)  / 4² = -5x4) +5 /16= -15/16
 so  g' (4) = -15/16

A parabola has the equation –5x^2 + 30x – y – 34 = 0. Which equation is that of the parabola in vertex form? ...?

Answers

The solution to your problem is as follows:

-5x^2 + 30x - y - 34 = 0
y = -5x^2 + 30x - 34
y = -5(x^2 - 6x) - 34
y = -5(x^2 - 6x + 9 - 9) - 34, by completing the square
y = -5(x^2 - 6x + 9) + 45 - 34
y = -5(x - 3)^2 + 11


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

b+c=10/a
solve for a ...?

Answers

Final answer:

To solve the equation b + c = 10/a for a, isolate a on one side of the equation by multiplying both sides by a, distribute a to both terms inside the parentheses, and then solve for a by dividing both sides by (b + c).

Explanation:

To solve the equation b + c = 10/a for a, we need to isolate a on one side of the equation. We can start by multiplying both sides of the equation by a to get rid of the denominator:

a(b + c) = 10

Next, we can distribute a to both terms inside the parentheses:

ab + ac = 10

Finally, we can solve for a by dividing both sides of the equation by (b + c):

a = 10 / (b + c)

You need to know the number of different arrangements possible for five distinct letters. You decide to use the permutations rule, but your friends tells you to use 5!. Who is correct? Explain.

Both methods are correct, since you are counting all possible arrangements of 5 items taken 5 at a time.

Your friend is correct because applying the permutations rule in this setting would be inappropriate.

Neither method is correct. The combinations rule should be applied in this setting.

Your method is correct because you are applying the permutations rule in the appropriate setting.

Answers

First option is correct

Both methods are correct, since you are counting all possible arrangements of 5 items taken 5 at a time.

Answer:

Option A

Step-by-step explanation:

Whenever we want to arrange a number of objects or letters or numbers n then we must check whether

i) repitition is allowed

If repitition is allowed then total number of ways = n!

ii) repitition not allowed.

In this case again we have to check whether order matters or not.

If order matters then no of ways nPn.  

Here n =5

We find that nPn = 5!

Thus both are correct.

Hence option A

car salesman sells cars with prices ranging from $5,000 to $45,000. The histogram shows the distribution of the numbers of cars he expects to sell over the next
10 years.
The salesman has observed that many students are looking for cars that cost less
than $5,000. If he decides to also deal in cars that cost less than $5,000 and projects selling 200 of them over the next 10 years, how will the distribution be affected?

The mean will shift to the right.

The mean and the median will be the same.

The median will shift to the right.

The mean will shift to the left.

I think it's B

Answers

Answer:

The mean will shift to the left.

Step-by-step explanation:

using the quadratic formula 3x2 – 13x + 4 = 0

Answers

the answer is x=10/13 see the picture for full solution
In this case, a=3, b= -13, and c=4. Use (-b + sqrt b^2 -4ac)/2a which will come out to 4. Then use (-b - sqrt b^2 -4ac)/2a which will come out to .33333.
So your two answers here are x=4 and x=0.3333  (:
Other Questions
49 % is what of 70 and why do you get the answer of my question. Why is it important to pick a narrator carefully when planning to write a narrative?A The narrator tells the story, but it is the reader who controls how events are imagined. B The narrator's point of view determines the sequence of events.C The narrator must know what all characters think at all times.D The narrative will change depending on the narrator's tone and point of view. Read this excerpt from Little Brother and answer the following questions in complete sentences using proper grammar and punctuation:Marcus manages to flag down a vehicle and they get more than they bargained forIt was a military-looking Jeep, like an armored Hummer, only it didn't have any military insignia on it. The car skidded to a stop just in front of me, and I jumped back and lost my balance and ended up on the road. I felt the doors open near me, and then saw a confusion of booted feet moving close by. I looked up and saw a bunch of military-looking guys in coveralls, holding big, bulky rifles and wearing hooded gas masks with tinted face-plates.I barely had time to register them before those rifles were pointed at me. I'd never looked down the barrel of a gun before, but everything you've heard about the experience is true. You freeze where you are, time stops, and your heart thunders in your ears. I opened my mouth, then shut it, then, very slowly, I held my hands up in front of me.The faceless, eyeless armed man above me kept his gun very level. I didn't even breathe. Van was screaming something and Jolu was shouting and I looked at them for a second and that was when someone put a coarse sack over my head and cinched it tight around my windpipe, so quick and so fiercely I barely had time to gasp before it was locked on me. I was pushed roughly but dispassionately onto my stomach and something went twice around my wrists and then tightened up as well, feeling like baling wire and biting cruelly. I cried out and my own voice was muffled by the hood. I was in total darkness now and I strained my ears to hear what was going on with my friends. I heard them shouting through the muffling canvas of the bag, and then I was being impersonally hauled to my feet by my wrists, my arms wrenched up behind my back, my shoulders screaming. I stumbled some, then a hand pushed my head down and I was inside the Hummer. More bodies were roughly shoved in beside me."Guys?" I shouted, and earned a hard thump on my head for my trouble. I heard Jolu respond, then felt the thump he was dealt, too. My head rang like a gong. "Hey," I said to the soldiers. "Hey, listen! We're just high school students. I wanted to flag you down because my friend was bleeding. Someone stabbed him." I had no idea how much of this was making it through the muffling bag. I kept talking. "Listenthis is some kind of misunderstanding. We've got to get my friend to a hospital"Someone went upside my head again. It felt like they used a baton or somethingit was harder than anyone had ever hit me in the head before. My eyes swam and watered and I literally couldn't breathe through the pain. A moment later, I caught my breath, but I didn't say anything. I'd learned my lesson.What conflict is Marcus facing? For the demand equation, express the total revenue R as a function of the price p per item. q = 5p + 500 R(p) = ? The earth is homogeneous substance. discuss Who was america's first female astronaut? Justin is considering two websites for downloading music.The costs are detailed here. Website 1: a yearly fee of $30 and $1.50 for each download Website 2: $2 for each download What is a system of equations to represent the costs for one year? Express your equations in the form of y=mx+b where x is the number of downloads for the year and y is the total cost for the year. Enter your equations in the boxes. Website 1: ____ Website 2: ____ Each decision maker wants to make a choice that ______ satisfaction Using the fafsa form, you can apply for? Create an interpretive question that can be answered by this excerpt from Little Brother: He slammed his hand down on the desk and then pointed his finger at me. "The *problem*, Mr. Yallow, is that you've been engaged in criminal conspiracy (a secret plan) to subvert (ruin, break) this school's security system, and you have supplied security countermeasures (ways around the system) to your fellow students. You know that we expelled Graciella Uriarte last week for using one of your devices." Uriarte had gotten a bad rap. She'd bought a radio-jammer from a head-shop near the 16th Street BART station and it had set off the countermeasures in the school hallway. Not my doing, but I felt for her. What component of medical record contains all records and documentation related to a request for a second opinion on a particular patients case Which of these sentences describes one of Ezra Pound's rules? There are 24 children in a class, 16 brown-haired and 8 black-haired. Two students are randomly selected for a stage performance. Find the probability of the following selection. P(2 black haired children) In order to file a claim to medicare, a physician's office submits a ___________ form. Which statement describes how the crusades affected the relationship between Christians of the east and west A eastern Christians feared that the Western Christians reclaim their holy land. B Western Christians feared that the pope would move theConstantinopleC The crusades restored peace between the two groups D. The crusades for the divided the two groups How many times does 50,000 go into 374,000,000,000? 1. My friends and I looked ""around"" for our sleds a. Preposition b. Adverb 2. Jamie had never been sledding ""before"". a. Preposition b. Adverb 3-5.Identify the preposition 3. The legendary Pony Express rode its way into American history. 4. The rider's trail began at St. Joseph, Missouri. 5. A weary rider would often reach California in 10 days. which equation when graph has x intercepts at (2,0) and (4,0) and a y-intercept of (0,-16)?A. F(x)= -(x-2)(x-4)B. F(x)= -(x+2)(x+4)C. F(x)=-2(x-2)(x-4)D. F(x)= -2(x+2)(x+4) In the phosphorus cycle, phosphorus can recycle through waste products, decomposition, and of terrestrial and aquatic ecosystems.food chainsthe atmosphereassimilation An 8-pound bag of tomatoes costs $5.60. At the same rate, what would be the cost of 11 pounds of tomatoes?A. $8.50B. $7.00C. $7.70D. $6.50 ...? Steam Workshop Downloader