Some airlines have restrictions on the size of items of luggage that passengers are allowed to take with them. suppose that one has a rule that the sum of the length, width and height of any piece of luggage must be less than or equal to 204204 cm. a passenger wants to take a box of the maximum allowable volume. if the length and width are to be equal, what should the dimensions of the box be?

Answers

Answer 1

Length, width, and height are all 68 cm. I am assuming that there's a formatting issue with this question and that the actual size limit is 204 cm. With that in mind, let's create a function giving the width of the box in terms of its height. So w = (204 - h)/2 Now let's create an expression giving the volume of the box in terms of height. v = lwh Since the width and length are the same, replace l with w v = wwh And now replace w with (102-h/2) v = (102-h/2)(102-h/2)h And expand the equation. v = (102-h/2)(102-h/2)h v = (10404 -51h - 51h + 0.25h^2)h v = (10404 -102h + 0.25h^2)h v = 10404h -102h^2 + 0.25h^3 Since we're looking for a maximum, that can only happen when the slope of the above equation is equal to 0. The first derivative will tell you the slope of the function at each point. So let's calculate the first derivative. For each term, multiply the coefficient by the exponent and then subtract 1 from the exponent. So: v = 10404h - 102h^2 + 0.25h^3 v = 10404h^1 - 102h^2 + 0.25h^3 v' = 1*10404h^(1-1) - 2*102h^(2-1) +3*0.25h^(3-1) v' = 10404h^0 - 204h^1 + 0.75h^2 v' = 10404 - 204h^1 + 0.75h^2 We now have a quadratic equation with A=0.75, B=-204, and C=10404. Use the quadratic formula to find the roots, which are 68 and 204. These 2 zeros represent a local minimum and a local maximum. The value 204 is obviously the local minimum since the box would have a width and length of 0 resulting in a volume of 0. So the height must be 68 which means the length and width are (204 - 68)/2 = 136/2 = 68. To prove that 68 is the optimal height, let's use a height of (68+e) and see what that does to the volume of the box. v = (102-h/2)(102-h/2)h v = (102-(68+e)/2)(102-(68+e)/2)(68+e) v = (102-(34+e/2))(102-(34+e/2))(68+e) v = (68-e/2)(68-e/2)(68+e) v = (4624 - 34e - 34 e + 0.25e^2)(68+e) v = (4624 - 68e + 0.25e^2)(68+e) v = 314432 - 4624e + 17e^2 + 4624e - 68e^2 + 0.25 e^3 v = 314432 - 51e^2 + 0.25e^3 Now look at the 2 terms that use e. The -51e^2 term will always be negative, but the +0.25e^3 term will be negative if e is negative and positive if e is positive. So a positive e value (e.g. Make the height larger) does have a possibility of increasing the volume if it can overcome the -51e^2 term. So let's make that equation 0 < -51e^2 + 0.25e^3 51e^2 < 0.25e^3 51 < 0.25e 204 < e So if we make the height 68 + 204 = 272, then we could have a box with a larger volume. But that's impossible since the largest measurement for any edge is 204 and that's assuming you're willing to set the length of the other 2 dimensions to 0.

Related Questions

Find the standard form of the equation of the parabola with a focus at (5, 0) and a directrix at x = -5.

Answers

let's notice, the focus is at (5,0) and the directrix at x = -5.

keep in mind that there's a distance "p" from the vertex to either of those fellows, therefore, if the focus is at 5,0 and the directrix x = -5, the vertex is half-way between them, check the picture below.

notice the distance "p" there, now, is a horizontal parabola, opening to the right, meaning the value for "p" is positive, or just 5, thus

[tex]\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} \boxed{(y-{{ k}})^2=4{{ p}}(x-{{ h}})} \\\\ (x-{{ h}})^2=4{{ p}}(y-{{ k}}) \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\ -------------------------------\\\\ \begin{cases} h=0\\ k=0\\ p=5 \end{cases}\implies (y-0)^2=4(5)(x-0)\implies y^2=20x \\\\\\ \cfrac{y^2}{20}=x\implies \cfrac{1}{20}y^2=x[/tex]

What is y-x=2x-2/3y in slope intercept form

Answers

y - x = 2x - 2/3y
y = 3x - 2/3y
1 2/3y = 3x
y = 1.8x

Which fraction is equivalent to -7/8 ?

A )8/-7
B) 7/-8
C) -7/-8
D) 8/7

Answers

i am almost positive that it is C -7/-8

20 POINTS AND BRAINLIEST FOR CORRECT ANSWER

The pitch of a roof is its slope. The roof of a home rises vertically a distance of 8 ft through a horizontal distance of 15 ft. Find the pitch of the roof.

Answers

since slope is rise/run so by the problem, it is 8/15=.533ft

The pitch of a roof of a home rises vertically a distance of 8 ft through a horizontal distance of 15 ft is 0.53.

What is Slope?

The slope of line is a measure of its steepness.

Given that;

Vertical distance (rise) = 8 feet

Horizontal distance (running) = 15 feet

Now, To find the pitch (slope) of the roof, we would use the following formula:

Slope is the ratio of the vertical distance measured to the horizontal distance measured.

Hence, The pitch (slope) of a roof is given by the formula;

Pitch = V / R

Where:

V is the rising vertical distance of an object.

H is horizontal distance an object runs through.

Hence, Substituting the given parameters into the formula, we have;

Pitch = 8/15

= 0.53

Thus, Pitch (slope) = 0.53

So, The pitch of a roof of a home rises vertically a distance of 8 ft through a horizontal distance of 15 ft is 0.53.

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you borrow $200 from a friend to help pay for the new laptop computer. You pay your friend $12 per week. Write and solve an inequality to find when you will owe tour friend less than $60.

Answers

Final answer:

You will owe your friend less than $60 if you pay them $12 per week for more than 11.67 weeks, which means you'll need to make payments for at least 12 full weeks.

Explanation:

To solve the problem of when you will owe your friend less than $60, we need to set up and solve an inequality.

The amount owed after any number of weeks can be represented by the initial debt of $200 minus the total amount paid off, which is $12 times the number of weeks.

If we let x represent the number of weeks, the inequality we need to solve is 200 - 12x < 60.

To solve this inequality, we subtract 200 from both sides, getting -12x < -140.

Then, we divide both sides by -12, remembering to reverse the inequality sign because we are dividing by a negative number, which gives us x > 11.67.

Since we can't pay off part of a week, we would need to pay your friend for at least 12 full weeks to owe less than $60.

Final answer:

To find when you will owe less than $60, set up the inequality 200 - 12w < 60. After simplifying, we see that it will take just over 11.67 weeks, so you will owe less than $60 after making payments for 12 weeks.

Explanation:

To solve the problem at hand, we need to create an inequality to represent the situation where you will owe less than $60 to your friend. Let's denote the amount owed each week with w and the total amount owed with A. You start with an initial debt of $200, and each week you pay off $12. The inequality we are trying to establish is when the total amount owed will be less than $60.

The inequality will be in the form of A - 12w < 60, where A is the initial amount of $200 and w represents the number of weeks. Plugging in $200 for A, we get 200 - 12w < 60.

To solve for w, we'll perform the following steps:

Subtract $200 from both sides to isolate the variable term: -12w < -140.

Since we are dividing by a negative number, remember to flip the inequality sign: w > 140/12.

Simplify the fraction to get the minimum number of weeks: w > 11.67.

You will owe your friend less than $60 after roughly 12 weeks since fractions of a week don't apply in the context of a weekly payment schedule.

Use your properties of addition to find 37 + 58 mentally show your steps and identify the properties that you used

Answers

I would use my normal property... no calculator (optional) and i would show my work...
37+58=95 or..........
you can do......

1
37
+
58
___
9 5

Plot the line for the equation on the graph.

y−4=−14(x−5)

Answers

Answer: I just did the test and the correct answer was (9,3) 9 on the x axis and 3 on the y and (4,9) 4 on the x axis and 9 on the y

Step-by-step explanation:

Part A: Solve –vp + 40 < 95 for v. Show your work. (4 points) Part B: Solve 8w – 3r = 45 for r. Show your work. (6 points)

Answers

Answer:

A)[tex]v>-\frac{55}{p}[/tex]

B)[tex]r=\frac{8}{3}w-15[/tex]

Step-by-step explanation:

The inequality is

–vp + 40 < 95

Subtract 40 to both sides

–vp < 95 - 40

-vp< 55

Now, divide both sides by -p. Whenever, we divide by a negative number inequality sign changes

[tex]v>\frac{55}{-p}\\\\

The given equation is

[tex]8w-3r=45[/tex]

Subtract 8w to both sides

[tex]-3r=45-8w[/tex]

Divide both sides by -3

[tex]r=-15+\frac{8w}{3}\\\\r=\frac{8}{3}w-15[/tex]

Answer:

Step-by-step explanation:

Part A:

The inequality is–vp + 40 < 95.

Work:

We subtract 40 to both sides = –vp < 55. Now, we divide both sides by -p. = v > 55/-p

Part B: Inequality is 8w − 3r = 45.

Work:

We Subtract 8w to both sides = 3r = 45 - 8w. Now, we divide both sides by -3 = r = -15 + 8w and then r = 8/3w - 15.

The difference of two numbers is 16 and the sum of their squares is 130. What are the numbers.

Answers

x - y = 16
x^2 + x^2 = 130

----------------
x^2 - y^2 = 256
+(x^2 + y^2 = 130)
2x^2 = 386
x^2 = 193
x = 13.892 (3DP)
----
x - y = 16
13.892 - y = 16
-y = 2.108
y = -2.108
The numbers are: 13.892 and -2.108

The following section is a statement from the rental agreement Tim signed when he rented his car this past weekend. "Upon checkout, the fuel level of the vehicle will be determined by turning the vehicle on and visually inspecting the fuel gauge. The approximate fuel level will be recorded on the Check-Out sheet and verified with initials by the vehicle Renter. One copy of the Check-Out sheet will be given to the customer. Another copy will be kept with the on-site records of the vehicle. "The rented vehicle must be returned with a minimum fuel level the same as that indicated on the Check-Out sheet. A vehicle returned with a fuel level less than the approximate level indicated on the Check-Out sheet will be completely refueled with on-site pumps. The price of the fuel used to refuel the vehicle will be added to the Renter's total charge at a cost of $4.50 per gallon plus a $5.00 refueling charge." Tim is running extremely late and has just 5 minutes to return his rental car to the agency. The fuel tank in the car is half empty. It was full when he picked it up. (The car has a 12-gallon fuel tank.) He doesn't think he can get gas and get to the agency to return the car in time. Returning the car a day late will result in an extra daily rental charge of $32.00 and refueling the car on his own will cost $2.59 per gallon at the local gas station. Which of the following statements is true?
a. It would be cheaper to refuel the car and return it a day late.
b. It would be cheaper to return the car on time and pay the refueling costs.
c. It would cost about the same to return the car on time without gas or one day late with gas.
d. Tim is not responsible for refueling the car when he returns it.

Answers

It is cheaper for Tim to return the car on time and pay the refueling costs. If the gas tank on the car is half empty and the rental agency charges $4.50 per gallon the costs to refill for him would be. $27.00 plus the $5.00 refueling fee. This would equal $32.00. If Tim returns the car late, he faces a $32.00 charge including the cost to refuel the car on his own. The cost of returning the car a day late is not the same costs as returning the car on time. Choice b is the better option and the best choice.

Item 19 You pay $40 each month for satellite TV, plus $3.50 for every movie you purchase. Write and solve an equation to find the number of movies purchased during a month with a total bill of $57.50.

Answers

Let x be the number of movies purchased. If each movie you purchase costs $3.50 dollars, this means that the total cost of x movies in one month is $3.50x
In addition, you have to pay $40 for satellite TV. We can now find an equation to find the total cost per month:
40 + 3.50x

Now, by hypothesis, you paid $57.50 during a month as a total bill.
Which means that 40 + 3.50x = 57.50
We need to find the number of movies purchased during that month, or, in mathematical words, we need to solve for x.

40 + 3.50x = 57.50

First, let's put the variables apart and the numbers apart by subtraction 40 from each side, so we get:
40 - 40 + 3.50x = 57.50 - 40
3.50x = 17.50

Now divide both sides by 3.50
(3.50x)/(3.50) = 17.50 / 3.50
x = 5

So, during that month, you purchased 5 movies.

Hope this helps! :)

What is the value of x? 3x-3

Answers

i think its written 3x-3=0?
if it is then, you move the -3 over the equals
now 3x=3
then x=3/3 which is 1

The value of x in the given figure is 19.

What are Vertical angles?

Vertical angles are the angles formed when two lines intersect each other. The opposite angles formed by these lines are called vertically opposite angles.

Given that, a figure, we need to find the value of x,

Here, angles, 3x-3 and [6(x-10)] are vertical angles,

We know that,

Vertical angles are equal in measures,

Therefore,

3x-3 = [6(x-10)]

3x-3 = 6x-60

3x = 57

x = 19

Hence, the value of x is 19.

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The complete question is attached

What two consecutive odd integers have a sum of 48?

Answers

>>>>>>>23 & 25<<<<<<<

A packaging plant uses a machine that can bottle 30 fluid ounces of shampoo in 12 seconds. How many fluid ounces of shampoo can be bottled per second?
A) 2/5 fluid ounces
B) 19 fluid ounces
C) 2 ½ fluid ounces
D) 360 fluid ounces

Answers

30 fluid ounces / 12 seconds = 2.5 fluid ounces per second

C) 2.5 fluid ounces. Because 2.5 x 12 = 30, and in 1 second it would be 2.5.

to make 12 muffins, Mr. J's recipe requires 3/4 of a cup of sugar. If Mr. J wants to make 96 muffins, how much sugar will he need?

Answers

6 cups of sugar

12 x8 = 96
__ __
¾ x8 = 6

Ayuda porfavor.
esto es operaciones con los numeros reales.
necesito la respuesta con procedimiento

Answers

When the surd is the same, you do not need to do anything with it.

10 1/2 - 5 2/3 pleaseee

Answers

10 1/2 - 5 2/3 =
21/2 - 17/3 =
63/6 - 34/6 =
29/6 or 4 5/6 <==

First you convert both of the fractions into improper fractions:
10 1/2 = 21/2
5 2/3 = 17/3

Then you times the fractions by the other fractions denominator:
(21*3)/(2*3)= 63/6
(17*2)/(3*2)=34/6

The you can take the numerators away from eachother and place them over the denominator:
(64-34)/6 = 29/6

Then you take out as many 6's as possible from the 29 and you have that number before the fraction and the remainder as the numerator:
4 5/6

Hope this helps! :)

( variable son both sides of an equation)
SHOW ALL WORK AND MAKE SURE IT MAKES SENSE
I WILL GIVE BRAINLIEST WITH BEST ANSWER THAT INCLUDES ALL OF THE ABOVE

Solve: 7b-20=3b+12

Answers

b=8 i hope this helps!!

Start by adding 20 to both sides to isolate '7b'. This gives you 7b = 3b + 32.

Next, Subtract 3b from both sides in order to make it so that the variable, which is 'b' in this case, is on one side of the equation.

This gives you 4b = 32.

Now divide both sides by 4 to cancel out 4b (opposite of multiplication is division).

This brings you to the answer b = 8 (32 divided by 4 is 8).

Hope this helps.

How many squares are along the side of a chessboard?

Answers

8 squares per side if all sides 32 squares

NEED HELP ASAP 30 POINTS WILL BE GIVEN TO BRAINLIEST
The coordinates of the vertices of △GHJ are G(−1, 3), H(1, 2), and J(−3, −1)
Drag and drop the choices into each box to correctly complete the sentences

been trying to solve this but just don't get it I keep getting it wrong on my homework

Answers

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

[tex]G(-1,3)\ H(1,2)\ J(-3,-1)[/tex]

Step 1

Find the slope GH

[tex]G(-1,3)\ H(1,2)[/tex]

substitute in the formula

[tex]m=\frac{2-3}{1+1}[/tex]

[tex]m=\frac{-1}{2}[/tex]

[tex]mGH=-\frac{1}{2}[/tex]

Step 2

Find the slope HJ

[tex]H(1,2)\ J(-3,-1)[/tex]

substitute in the formula

[tex]m=\frac{-1-2}{-3-1}[/tex]

[tex]m=\frac{-3}{-4}[/tex]

[tex]mHJ=\frac{3}{4}[/tex]

Step 3

Find the slope JG

[tex]J(-3,-1)\ G(-1,3)[/tex]

substitute in the formula

[tex]m=\frac{3+1}{-1+3}[/tex]

[tex]m=\frac{4}{2}[/tex]

[tex]mJG=2[/tex]

Step 4

Verify if triangle GHJ is a right triangle

we know that

if two lines are perpendicular, then the product of their slopes is equal to minus one

[tex]m1*m2=-1[/tex]

compare slope GH with slope JG

we have

[tex]mGH=-\frac{1}{2}[/tex]

[tex]mJG=2[/tex]

[tex]-\frac{1}{2}*2=-1[/tex] -----> side GH and side JG are perpendicular

The triangle GHJ is a right triangle

The answer in the attached figure

Answer:

- 1/2, 3/4, 2, is, two of these slopes have a product of -1

Step-by-step explanation:

I have a Brainliest for math

Answers

The answer is D. 280.50
Hoped this helped
Feel free to ask anymore questions here at brainly.com

Just find ten percent of 3298.

3298 * .10 = 329.8

Hope this helps. (:

If −5e^x^2 y=x and y(−5)=0, find y′(−5) by implicit differentiation

Answers

Differentiate:
-5×2(xe^x^2)y-5e^x^2dy/dx=1
-5e^x^2(2xy+y´)=1
When x=-5, y=0:
-5e²⁵y´=1, so y´(-5)=-eˉ²⁵/5

What is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10?

Answers

2x + 5y = 10
5y = -2x + 10
y = -2/5 x + 2
so slope = -2/5

passes through the point (5, −4)
y = mx + b
b = y - mx
b = -4 - (-2/5)(5)
b = -4 + 2
b = -2

equation
y = -2/5 x - 2

hope it helps

Answer:

y = -2/5 x - 2

Step-by-step explanation:

2x + 5y = 10

5y = -2x + 10

y = -2/5 x + 2

so slope = -2/5

passes through the point (5, −4)

y = mx + b

b = y - mx

b = -4 - (-2/5)(5)

b = -4 + 2

b = -2

equation

y = -2/5 x - 2

Drinks at the fair cost 2.50$ use an equation to represent the relationship between the numbers of drinks bought ad the cost define your variable and make a table to help write the equation

Answers

C=5/2*d where c-cost. d-drink

Answer:

[tex]C=2.5d[/tex]

Step-by-step explanation:

Your variable is always the number of drinks that you are going to drink, and the independent clause is the cost of the drink, which is $2.5.

Drinks Cost

1 2.5

2 5

3 7.5

4 10

5 12.5

SO now you know that the cos of 3 drinks is 7.5 and that can be escalated to any number that you want just by puttin the number of drinks that are going to be bought and multiply it by the cost.

The diagram shows a trapezium ABCD in which BC parallel to AD

Answers

Answer:

if its the diagram i think then:

f = 6cm

g = 8cm

Step-by-step explanation:

square = 48cm²

triangle = 12cm²

24 / 4 = 6

AD = 6cm

BC = 6cm

CD = 48 / 6 = 8cm

CD = 8cm

f = 6cm

g = 8cm

In geometry, a quadrilateral with at least each pair of parallel sides is referred to as a trapezoid. Therefore, the length of BC is 6cm and the length of CD is 8cm.

What is trapezium?

In geometry, a quadrilateral with at least each pair of parallel sides is referred to as a trapezoid both Canadian and American English, and perhaps a trapezium in British as well as other forms of English. In Euclidean geometry, a trapezoid is a convex quadrilateral by definition.

The bases of a trapezoid are the parallel sides. If the remaining two sides are parallel, they are referred to as the legs; if not, the trapezoid is indeed a parallelogram, with 2 sets of bases. A trapezoid without equal-sized sides is called a scalene trapezoid.

area of square = 48cm²

area of triangle = 12cm²

24 / 4 = 6

AD = 6cm

BC = 6cm

CD = 48 / 6 = 8cm

CD = 8cm

f = 6cm

g = 8cm

Therefore, the length of BC is 6cm and the length of CD is 8cm.

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Your question is incomplete but most probably your full question was,

The diagram shows a trapezium ABCD in which BC parallel to AD. What is the length of BC and CD.

Find the next two terms in the sequence. 0, 1, 4, 9, ...

A. 13, 17

B. 13, 18

C. 16, 25

D 16, 23

Answers

0, 1, 4, 9, ...
+1, + 3, +5, +7, + 9, etc....

so
9 + 7 = 16
16 + 9 = 25

answer
C. 16, 25

Answer:

16, 25

Step-by-step explanation:

the next two terms in the sequence. 0, 1, 4, 9, ...

Lets find the difference between the two terms

1-0 = 1

4-1=3

9-4= 5

the terms are increasing by odd numbers

0, 1, 4, 9, ...

\/ \/ \/

+1 +3 +5

The next term will increase by +7

9+7= 16

Next term is 16

Next term will increase by 9

16 + 9 = 25

so , next two terms are 16 and 25

the equation y = 0.25x + 50 gives the cost y of renting a car if the car is driven x miles
According to the model, what is the best estimate of the cost for renting a car if you plan to drive 250 miles?
50$
62.50$
112.50$
300$

Answers

C. $112.50

y=0.25x+50

x = 250 miles

0.25*250=62.50

62.50+50= $112.50

at x=250miles
y=0.25(250)+50
y= 62.5+50
y= 112.5$

If angle m 9 =119,what is the sum of the measures of angle 11 and 16

Answers

m<9 = m<11 = m<16

so 119° * 2

238°

The measures of angles ∠11 and ∠16 are 119 and 119 respectively .

How to determine the values of the named angles

Using the parameters given for our Calculation;

∠9 = 119°

From the concept of corresponding angles ;

∠9 = ∠11 = 119° (corresponding angles are equal)

For ∠16 ;

∠11 and ∠16 are vertically opposite

Hence,

∠11 = ∠16 = 119° (vertically opposite angles are the same.)

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An airplane flies at a constant speed. It can travel a distance (
d. of 1,800 kilometer in 2 hours(t) Write an equation in the form is d=rt that represents the relationship between distance (
d. and time (t), where r is the constant of proportionality

Answers

I will be right back to help

Find the distance between the points (4, 2) and (-8, 7).

Answers

using distance formula, it is 13 units

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