Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 529 square meters. Round each dimension to 4 decimal places

Answers

Answer 1

Answer:

[tex]x=23/\sqrt{6}[/tex],

[tex]y= \frac{23}{6\sqrt{6}}[/tex]

Step-by-step explanation:

From the question we are told that

Surface area is 529 square meters

Generally the dimensions of the cuboid

[tex]v=x^y[/tex]

[tex]D=4xy+2x^2 =529[/tex]

[tex]V=x^29(\frac{529-6x^2}{4x})[/tex]

[tex]V' =529-6x^2/4[/tex]

[tex]v'=0[/tex]

Therefore

[tex]529=6x^2[/tex]

[tex]x=\sqrt{\frac{529}{6} }[/tex]

[tex]x=23/\sqrt{6}[/tex]

Mathematically

[tex]v''=\frac{12x}{4}[/tex]

[tex]v''=-3\frac{23}{\sqrt{6} }<0[/tex]

[tex]y= \frac{529-2*(\frac{529}{6} }{4*\frac{23}{\sqrt{6} } }[/tex]

[tex]y= \frac{23}{6\sqrt{6}}[/tex]

Therefore

[tex]x=23/\sqrt{6}[/tex]

and

[tex]y= \frac{23}{6\sqrt{6}}[/tex]


Related Questions

write an expression that can be usedto find the nth termo of each sequence 9, 17, 25, 33

Answers

Answer:

The expression used to find the nth term of each sequence 9, 17, 25, 33 will be:

[tex]a_n=8n+1[/tex]

Step-by-step explanation:

Given the sequence

9, 17, 25, 33

a₁ = 9

Determining the common difference

d = 17-9 = 8

d = 25-17 = 8

d = 33-25 = 8

As the common difference between the adjacent terms is same and equal to

d = 8

Therefore, the given sequence is an Arithmetic sequence.

An arithmetic sequence has a constant difference 'd' and is defined by  

[tex]a_n=a_1+\left(n-1\right)d[/tex]

substituting a₁ = 9, d = 8 in the equation

[tex]\:a_n=9+8n-8[/tex]

[tex]a_n=8n+1[/tex]

Therefore, the expression used to find the nth term of each sequence 9, 17, 25, 33 will be:

[tex]a_n=8n+1[/tex]

I need help on this with solutions please

Answers

Answer:

See answers below:

1. AAS2. ASA3. SAS4. HL5. SSS6. ΔABC ≅ ΔDFE7. ΔTRS ≅ ΔTUV8. ΔTRS ≅ ΔSUT9. ΔCAB ≅ ΔFDE

Could you describe the expression 2(3+4) as a product of two factors?​

Answers

the answer will be 10 just multiply the numbers

Two submarines began dives in the same vertical position to meet at a designated point.

If one submarine was on a course approximated by the equation x + 4y = -14 and

the other was on a course approximated by the equation x + 3y = -8, at what location would they meet?

Answers

Answer:

(10, -6)

Step-by-step explanation:

The solution of the system of the equations given would be the location that they would both meet.

Let's solve:

x + 4y = -14 ----› Eqn. 1

x + 3y = -8 -----› Eqn. 2

Subtract Eqn. 2 from Eqn. 1

y = -6

Substitute y = -6 into Eqn. 1.

x + 4y = -14 ----› Eqn. 1

x + 4(-6) = -14

x - 24 = -14

x = -14 + 24 (addition property of equality)

x = 10.

The answer is: (10, -6)

Please help it’s so important

Answers

Given:

In [tex]\Delta ABC, \overline{CA}=\overline{CB}[/tex].

[tex]\overline{CD}[/tex] is an altitude drawn from C to [tex]\overline{AB}[/tex].

To prove:

[tex]\overline{CD}[/tex] bisects [tex]\overline{AB}[/tex].

Proof:

In [tex]\Delta ABC[/tex], [tex]\overline{CD}[/tex] is an altitude drawn from C to [tex]\overline{AB}[/tex].

It means, [tex]\Delta ACD\text{ and }\Delta BCD[/tex] are right angle triangles.

In [tex]\Delta ACD\text{ and }\Delta BCD[/tex],

Hypotenuse : [tex]\overline{CA}=\overline{CB}[/tex]       [Given]

Leg : [tex]\overline{CD}=\overline{CD}[/tex]       [Common]

If the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then by HL postulate both triangles are congruent.

[tex]\Delta ACD\cong \Delta BCD[/tex]        [HL postulate]

[tex]\overline{AD}\cong \overline{BD}[/tex]       [CPCTC]

[tex]\overline{AD}=\overline{BD}[/tex]

It means, point D is the midpoint of [tex]\overline{AB}[/tex].

So, [tex]\overline{CD}[/tex] bisects [tex]\overline{AB}[/tex].

Hence proved.

Answer questions 3,4, and 7.

Answers

3). They all equal eight. Set 2(x-6) and 3x-20 equal to each other, then solve.

You can apply this to the other problems as well, I hope this helps :)

Question
8 - (-7) =
Plz help me!!!

Answers

Answer:

8-(-7)=

8(7)=

8+7=15

Step-by-step explanation:

prove me wrong

Solve the following formula for the specified variable. B=1/4m(r+k) for r

Answers

Answer: r=4b/m-k

Step-by-step explanation: I think

The solution of the given formula B=1/4m(r + k) for r is r = 4(B/m) - k.

What is the equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

More than one variable may be present inside a linear equation. An equation is said to be linear if the maximum power of the variable is consistently unity.

Given the expression,

B=1/4m(r+k)

4B = m(r + k)

r + k = 4B/m

r = 4(B/m) - k

Hence "The solution of the given formula B=1/4m(r + k) for r is r = 4(B/m) - k".

For more about the equation,

brainly.com/question/10413253

#SPJ2

Simplify (65)2
O A. 670
O B. 67
C. 65
D. 63

Answers

130 If you multiply that’s what it would give you so I’m not sure what those answers are

find the measure of m

Answers

Answer:

m=42

Step-by-step explanation:

because all straight line equal 180, we can find angle C

180-98=82

now, all triangles add up to 180. If we add up all the values we can find x

82+6x+8+5x+2=180

92+11x=180

11x=88

x=8

Now, just plug the variable into the angle measure

5(8)+2

40+2

42

A chef is making pickles. he needs 15 gallons of vinegar. The store sells 2 gallons of vinegar for $3.00 and allows customers to buy any amount of vinegar. decide whether each of the following ratios correctly represents the price of vinegar.

a. 4 gallons to $3.00

b. 1 gallon to $1.50

c. 30 gallons to $45.00

d. $2.00 to 30 gallons

e. $1.00 to 2/3 gallon

Answers

a is incorrect

b is correct

c is correct

d is incorrect

e is incorrect

Answer:

its b

Step-by-step explanation:

can someone please help me.​

Answers

Answer:

Step-by-step explanation:

1. isosceles

2. right scalene

3. obtuse scalene

4. equilateral

5. right isosceles

6. acute scalene

7. equilateral

8. isosceles

Use the diagram to answer the question.

Answers

The answer to your question is D.

What is equivalent to 5(x + 12)

A x +12
B 2x - 60
C 5x + 60
D 2x - 60

Answers

Answer:

[tex]\boxed{\boxed{\pink{\sf Option \ C \ is \ correct .}}}[/tex]

Step-by-step explanation:

Given to us is , 5 ( x + 12 ) and we need to find which is its equivalent in the given options .

So,

[tex]\bf = 5 ( x + 12 ) \\\\=\bf 5x + 5\times 12 \\\\=\boxed{\red{\bf 5x + 60 }}[/tex]

Hence option C is correct.

A local pizza shop has a membership program for frequent buyers. The membership
costs $15 per month and members get a discounted price of $2 per slice of pizza.
Mayerlin purchased a membership to this pizza shop. How much would Mayerlin
have to pay the pizza shop if she bought 11 slices of pizza this month? What would be
the monthly cost for x slices of pizza?

Answers

The answer to this problem might be 5 slices

Answer:

cost of slices=2x

cost=monthly fee+cost of slices

15x+2x

Step-by-step explanation:

All you need the photo

Answers

The average rate of change of h(t) = -16t ² + 40t + 4 between t = 0 and t = 2 is

(h (2) - h (0)) / (2 - 0) = ((-16×2² + 40×2 + 4) - (-16×0² + 40×0 + 4)) / 2

… = ((-64 + 80 + 4) - 4) / 2

… = 16 / 2

… = 8

h(t) is measured in feet, so the average rate of change is measured in feet per second, so it's 8 feet per second.

A jewelry box contains two gold hoop earrings and two silver hoop earrings. You randomly choose two earrings. What is the probability that both are silver hoop earrings? Write your answer as a fraction or percent rounded to the nearest tenth.

The probability that both are silver hoop earrings is:

Answers

Answer:

2 + 2 = 4 total earrings in the box.

If you put the earring back into the box before taking out the second, it would be 1/2 * 1/2 = 1/4, 25%.

Answer:

1/6 or 16.7%

Step-by-step explanation:

There are a total of 4 earrings in the box: 2 pairs of earrings + 2 pairs of earrings.

If you return the first earring to the box before removing the second, the answer is 1/2 * 1/2 = 1/4, or 25%.

If you remove the first earring from the package, the response is 1/2 * 1/3 = 1/6, or 16.7%.

What is the surface area?

Answers

Answer:

369 m²

Step-by-step explanation:

Area of Triangle (sides): 1/2bh

=1/2(bh)

=1/2 (9•16)

=1/2 (144)

=72

There are four sides of the prism:

72•4=288

Area of Square (base): l•w

=9•9

=81

Surface Area = 288+81=369 m²

Answer:

369 m²

Step-by-step explanation:

what is the slope of the line please help khan academy??

Answers

im not sure but i think it’s 3... tell me if it’s wrong

Answer:  The answer is -3

Step-by-step explanation:

The graph goes down 3 and over 1, since slope is written rise/run, it would be -3/1, which reduces to -3

L. Han ran 10 meters in 3 seconds, Priya ran 10 meters in 4 seconds, a. Who ran faster? Explain how you know,​

Answers

Answer:

L. Han

Step-by-step explanation:

L. Han only took 3 seconds and Priya took 4 seconds so L. Han won by one second.

Hope this helps!

Brainiest?

Can somebody help me with my math I’ll give u brainlest

Answers

Answer:

yess!!

Step-by-step explanation:

''-''

Answer:

where are questions

Step-by-step explanation:

is this table linear or exponential what us the slope and what is the equation ?​

Answers

Answer:

this table is exponential

Step-by-step explanation:

the way we can tell this is because we can find a common ratio of 4. we know this because linear tables have a common difference exponential tables have a common ratio. i found this answer by dividing 32,768 and 8,192

32,768/8,192 = 4

you can find a linear function by subtracting point 1 and point 2.

There are 5 times as many boys as girls in a school.
Together the school has 810 pupils.
How many boys are there?

Answers

There should be 675 boys
i think the answer is 675:)

There is 7/8 of the pretzel bag left. If one serving is 1/4 of the bag. How many servings are left? Use the model to answer the question.

Answers

Answer:

5/8

Step-by-step explanation:

andrea rents a bike for 8 hours and pays $42 for the rental tomorrow she wants the same bike but only needs it for 6 hours what equation can she use to figure out how much she will need to pay

Answers

Answer:

8x=42 where x is hourly cost

so x = 21/4

6*x = 63/2 $

Step-by-step explanation:

Rita earns 44dollars each week working part-time at a bookstore. She earns one additional dollar for each book that she sells.
Let A be the amount (in dollars) that Kala earns in a week if she sells B books.
Write an equation relating A to B. Then use this equation to find the amount of money Rita earns if she sells 35books.
Equation:
Amount Rita earns if she sells 35books: dollars

Answers

Answer 1: 44 + B = A
44 + (35) = A
Answer 2: 44 + 35 = $79

50 POINTS!!!43
what is 43 7/8% of $2.35?
Round your answer to the nearest cent

Answers

Answer:

$1.03

Step-by-step explanation:

7/8 = 0.875

then

43 7/8 = 43.875%

43.875/100 = 0.43875

2.35 * 0,43875 = 1.031

Round to the neares cent:

1.03

Step-by-step explanation:

[tex]43 \frac{7}{8} \% \: of \: 2.35 \\ \frac{351}{8} \% \: of \: 2.35 \\ \frac{351}{8 \times 100} \times 2.35 \\ \frac{824.85}{800} = \boxed{\$1.0310625}[/tex]

$ 1.0310625 is the right answer.

Ramona went out with her 3 sisters, they spent $58 plus
9% tax on their meal. They also left a 15% tip. If they divided
up the bill evenly, how much did each of them spend?

Answers

Problem:

Ramona went out with her 3 sisters, they spent $58 plus 9% tax on their meal. They also left 15% tip. If they divided up the bill evenly, how much did each of them spend?

Solution:

[tex] \frac{58 + 58(9\% + 15\%)}{3} [/tex]

[tex] = \frac{58 + 58(0.09 + 0.15)}{3} [/tex]

[tex] = \frac{58 + 58 \times 0.24}{3} [/tex]

[tex] = \frac{58 + 13.92}{3} [/tex]

[tex] = \frac{71.92}{3} [/tex]

[tex] = 23.97[/tex]

Answer:

Each of them did spend $23.97

#CarryOnLearning

#AnswerForTrees

#BrainlyBookSmart

what’s 2+2.
bet you don’t know.

Answers

Window come at me fam I’m smarter than you bruv

what is the slope of this line

Answers

Answer:

Step-by-step explanation: Do rise and run

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