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

STOP RIGHT THERE. Please help me.

Answers

Answer:

the answer is B

Step-by-step explanation:

Well we can get rid of A and D because we're not adding money, we're subtracting (thats what a sale is)

So we're left with B and C.

To find what 17% of 3 is, we multiply 3 x 0.17, which totals to 0.51. It can't be C because you find 51% of 3 which is not what we're looking for, so it is B.

Is this a function? Explain with full sentence
[(2,3) (2,4) (2,5) (2,3)]

Answers

Answer:

no their is not supposed to be any repeating x's

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

What is the common factor of 26 and 38

Answers

Answer: The GCF is 2 and the LCF is 1

Step-by-step explanation:


Write 89 tenths in standard form *

Answers

89 tenths......................

Answer:

.89

Step-by-step explanation:

Standard for is just the number version. Word for is it spelled out, eighty-nine tenths.

Multiply. Express your answer in simplest form.

Answers

Answer:

Bet

Step-by-step explanation:

It’s a simple one to write. There are many trios of integers (x,y,z) that satisfy x²+y²=z². These are known as the Pythagorean Triples, like (3,4,5) and (5,12,13). Now, do any trios (x,y,z) satisfy x³+y³=z³? The answer is no, and that’s Fermat’s Last Theorem.

On the surface, it seems easy. Can you think of the integers for x, y, and z so that x³+y³+z³=8? Sure. One answer is x = 1, y = -1, and z = 2. But what about the integers for x, y, and z so that x³+y³+z³=42?

That turned out to be much harder—as in, no one was able to solve for those integers for 65 years until a supercomputer finally came up with the solution to 42. (For the record: x = -80538738812075974, y = 80435758145817515, and z = 12602123297335631. Obviously.)

In a certain town there were 403 robberies last year. This year the number of robberies has gone down 35%. How many robberies were there this year, to the nearest whole number?

Answers

Answer:

262

Step-by-step explanation:

From the Question, we know that:

In a certain town there were 403 robberies last year. This year the number of robberies has gone down 35%.

Step 1

Find the amount decreased

35% × 403

= 35/100 × 403

= 141.05

Step 2

The amount of robberies this year is:

= 403 - 141.05

= 261.95

Approximately to the nearest whole number = 262

Substitute x=5 into the expression 4x-8 and simplify

Answers

Answer:

4(5) - 8

20 - 8

= 12

If you have a 10% off coupon and you buy a 20$ shirt how much you pay with the coupon?

Answers

Answer:

18.00$

Step-by-step explanation:

Answer:

$18.00

Step-by-step explanation:

Thus, a product that normally costs $20 with a 10 percent discount will cost you $18.00, and you saved $2.00.  You can also calculate how much you save by simply moving the period in 10.00 percent two spaces to the left, and then multiply the result by $20 as follows: $20 x .10 = $2.00 savings.  Furthermore, you can get the final price by simply deducting .10 from 1 and multiplying it by $20 as follows: (1 - .10) x $20 = $18.00 final price.

find the slope thanks PLEASE ​

Answers

Answer:

37) -1/3

38) 8/5

39) 0

40) -2/3

Step-by-step explanation:

An art class is making a mural for their school which has a triangle drawn in the middle. The length of the bottom of the triangle is x . Another side is 12 more than times two the length of the bottom of the triangle. The last side is 7 more than the bottom of the triangle. Write and simplify an expression for the perimeter of the triangle.

Answers

Answer:

P = 4x + 19

Step-by-step explanation:

Given triangle with sides:

a = xb = 2x + 12c = x + 7

Perimeter is:

P = a + b + c ⇒P = x + 2x + 12 + x + 7 = 4x + 19 ⇒P = 4x + 19

If csctheta=11/4 & tan Thea< 0 Use the fundamental identities to evaluate cottheta.

Answers

Answer:

[tex]\cot{\theta} = -\frac{\sqrt{105}}{11}[/tex]

Step-by-step explanation:

Fundamental identities:

These following trigonometric identities are used to solve this question:

[tex]\sin^{2}{\theta}+\cos^{2}{\theta} = 1[/tex]

[tex]\csc{\theta} = \frac{1}{\sin{\theta}}[/tex]

[tex]\cot{\theta} = \frac{\cos{\theta}}{\sin{\theta}}[/tex]

With the cossecant, we can find the sine. So:

[tex]\csc{\theta} = \frac{1}{\sin{\theta}}[/tex]

[tex]\frac{11}{4} = \frac{1}{\sin{\theta}}[/tex]

[tex]11\sin{\theta} = 4[/tex]

[tex]\sin{\theta} = \frac{4}{11}[/tex]

With the sine, we find the cosine.

Since the tangent is negative, the cosine is negative. So

[tex]\sin^{2}{\theta}+\cos^{2}{\theta} = 1[/tex]

[tex](\frac{4}{11})^{2} + \cos^{2}{\theta} = 1[/tex]

[tex]\frac{16}{121} + \cos^{2}{\theta} = \frac{121}{121}[/tex]

[tex]\cos^{2}{\theta} = \frac{105}{121}[/tex]

[tex]\cos{\theta} = -\frac{\sqrt{105}}{11}[/tex]

Cotangent:

[tex]\cot{\theta} = \frac{\cos{\theta}}{\sin{\theta}}[/tex]

[tex]\cot{\theta} = \frac{-\frac{\sqrt{105}}{11}}{\frac{4}{11}}[/tex]

[tex]\cot{\theta} = -\frac{\sqrt{105}}{11}[/tex]

find the scalar product of two verton
Å - Git 3} and B-57-2} what is the
magnitude of vector product​

Answers

The obvious answer is c because c is to good

(Giving brainliest to correct answer)

Congruence

Answers

Answer:СССР в зеркале

Кто первый спустит курок

Убеждаешь - ложно заявляя свободу личности.

Бушующие войны и П-С-О,

Космос, О-С-В

Брежнев Рейган

Страх оружия С-Я-С

До взаимного уничтожения

Силой и мощью

Союза Советских Республик

Патриоты работают силой порядка

Светлое строят будущее

Наука, Творчество, Семья, Союз,

Образование, Коммуналка, Труд,

Дисциплина, Планировка, Доброта.

Родина – поём тебе,

В верности клянёмся,

Пролетарии всех стран Соединяйтесь

Серп и Молот!

Step-by-step explanation:

Which of the following expressions will help him determine the length of segment BE? BE = AD BE = CD BE equals CD times AD over AE BE equals CD times AB over AC

Answers

Answer:

BE equals CD times AB over AC

Step-by-step explanation:

took the test

Answer:

BE = CD times AB/AC

Step-by-step explanation:

I took the test. And also, we know that BE + CD. so, the only one that we can eliminate from that is BE =AD. That's about all the explanation I can give you, sorry, but that is the right answer.

Help me out hereeeeeeeeeeeeeee

Answers

Answer:

it is the first one because you times the 9 because it says twice and divide it by 3 because you donate to 3 parks

Step-by-step explanation:

PLEASE HELP zoom in to remove blur

Answers

Answer:

The answer is (x + 12) and (x - 12)

What the person above me said

For a submarine cable, the range of signalling is governed by the function


f(r) = r^2 ln⁡(1/r)

where 0
Find df/dr.

Answers

Answer:

 [tex]\frac{df}{dr} = (-r) + log(\frac{1}{r} )( 2 r)[/tex]

Step-by-step explanation:

Explanation

Given function f(r) = r² log r  ....(i)

Apply derivatives formula

              [tex]\frac{d}{dx} UV = U^{l} V + V^{l} U[/tex]

             [tex]\frac{d}{dx}x^{n} = nx^{n-1}[/tex]

            [tex]\frac{d}{dx}log x = \frac{1}{x}[/tex]

Differentiating equation (i) with respective to 'r' , we get

                [tex]\frac{df}{dr} = r^{2} (\frac{1}{\frac{1}{r} } )\frac{d}{dr} (\frac{1}{r } )+ log(\frac{1}{r} ) 2 r[/tex]

                [tex]\frac{df}{dr} = r^{2} (\frac{1}{\frac{1}{r} } )(\frac{-1}{r^{2} } )+ log(\frac{1}{r} ) 2 r[/tex]

Final answer:-                

               [tex]\frac{df}{dr} = (-r) + log(\frac{1}{r} )( 2 r)[/tex]

does anyone have a good website to solve for pythagorean theorem???

Answers

Answer:

you can't solve for the pythagorean theorem

Step-by-step explanation:

tyhe theorem is a theorem not a math problem

but you can just do sqrt(a^2+b^2) to get c

use desmo, wolfrm, gegebra, symblab, mahway etc

Make a 2/3 a fraction with a denominator of 36


Please show work

Answers

Answer:

24/36

Step-by-step explanation:

Do 36 divided by 3 which is 12 then multiply 12 by 2!

I hope this helps and have a great day! :)

Answer:

The correct answer is 24/36

Step-by-step explanation:

24/36 is correct because you divide 36 by the denominator of 3 to equal 12 so then multiply 12 by 2 to equal 24 so the correct answer is 24/36.

HAVE A GOOD DAY!

which function has a y-intercept of 3 ​

Answers

Answer:

2 and 3

1 also has a y-intercept of 3, but it is negative, so I don't know if that one will count

Step-by-step explanation:

Substitute X for 0 and solve from there.

3(0) - 2y = -6

0 - 2y = -6

y = 3

y - 3 = -2(0)

y - 3 = 0

y = 3

HELP with this problem please

Answers

Answer: 2

Step-by-step explanation:that is the one that is used the most?

2x - 2 = 3x - x - 2 solve for x

Answers

Answer:

i think x=0

Step-by-step explanation:

2x-2=2x-2

2x=2x

x=0

Answer:

NAN

Step-by-step explanation:

x + 2 = 3x - x^2 Simplifying x + 2 = 3x + -1x2 Reorder the terms: 2 + x = 3x + -1x2 Solving 2 + x = 3x + -1x2 Solving for variable 'x'. Combine like terms: x + -3x = -2x 2 + -2x + x2 = 3x + -1x2 + -3x + x2 Reorder the terms: 2 + -2x + x2 = 3x + -3x + -1x2 + x2 Combine like terms: 3x + -3x = 0 2 + -2x + x2 = 0 + -1x2 + x2 2 + -2x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 2 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -2x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -2x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2x + x2 = 0 + -2 -2x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2x + x2 = -2 The x term is -2x.  Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -2 + 1 Reorder the terms: 1 + -2x + x2 = -2 + 1 Combine like terms: -2 + 1 = -1 1 + -2x + x2 = -1 Factor a perfect square on the left side: (x + -1)(x + -1) = -1 Can't calculate square root of the right side. The solution to this equation could not be determined.

Write the slope intercept form of the equation of the line that passes through the points (6,1) and (12,2)

Answers

Answer:

y=1/6x

Step-by-step explanation:

If each of the following represents the slope of a line (or line segment), give the slope a line that is perpendicular to it. (a) 4 3 m (b) 3 7 m ( c )4 m (d) 1 3

Answers

Answer:

[tex]m_2 = -\frac{3}{4}[/tex] -- (a)

[tex]m_2 = -\frac{7}{3}[/tex] -- (b)

[tex]m_2 = -\frac{1}{4}[/tex] --- (c)

[tex]m_2 = -3[/tex] -- (d)

Step-by-step explanation:

Given

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

[tex]b.\ m = \frac{3}{7}[/tex]

[tex]c.\ m = 4[/tex]

[tex]d.\ m = \frac{1}{3}[/tex]

Required

Determine the slope of a perpendicular line

In geometry, the condition for perpendicularity is:

[tex]m_2 = -\frac{1}{m}[/tex]

This formula will be applied in solving these questions.

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

[tex]m_2 = -\frac{1}{m}[/tex]

Substitute 4/3 for m

[tex]m_2 = -\frac{1}{4/3}[/tex]

Express as a proper division

[tex]m_2 = -1/ \frac{4}{3}[/tex]

Convert to *

[tex]m_2 = -1* \frac{3}{4}[/tex]

[tex]m_2 = -\frac{3}{4}[/tex]

[tex]b.\ m = \frac{3}{7}[/tex]

[tex]m_2 = -\frac{1}{m}[/tex]

Substitute 3/7 for m

[tex]m_2 = -\frac{1}{3/7}[/tex]

Express as a proper division

[tex]m_2 = -1/ \frac{3}{7}[/tex]

Convert to *

[tex]m_2 = -1* \frac{7}{3}[/tex]

[tex]m_2 = -\frac{7}{3}[/tex]

[tex]c.\ m = 4[/tex]

[tex]m_2 = -\frac{1}{m}[/tex]

Substitute 4 for m

[tex]m_2 = -\frac{1}{4}[/tex]

[tex]d.\ m = \frac{1}{3}[/tex]

[tex]m_2 = -\frac{1}{m}[/tex]

Substitute 1/3 for m

[tex]m_2 = -\frac{1}{1/3}[/tex]

Express as a proper division

[tex]m_2 = -1/ \frac{1}{3}[/tex]

Convert to *

[tex]m_2 = -1* \frac{3}{1}[/tex]

[tex]m_2 = -\frac{3}{1}[/tex]

[tex]m_2 = -3[/tex]

THIS IS 90 POINTS:
what is 15m+35 graphed?

Answers

Well, you can’t add them because 15 has a m and 35 doesn’t have a variable sooo? What are the answer choices?

Answer:

Factor

5

out of

15

m

+

35

.

5

(

3

m

+

7

)

Step-by-step explanation:

Is the following table proportional or non-proportional?

Answers

Answer:

proportional

Step-by-step explanation:

y= -7x

PLEASE ANSWER!!!!!!!!!!!!!!!!!!!

Answers

Answer:

answer attached

Step-by-step explanation:

In how many ways can Anna arrange 2 math books, 3 physics books, and 5 chemistry books on her shelf if all books of the same subject must be adjacent? (The books are distinguishable.)

Answers

Answer:

8640 ways

Step-by-step explanation:

Arranging the books of each subject:

Math:

Combination of 2 books → 2! = 2

Physics:

Combination of 3 books → 3! = 6

Chemistry:

Combination of 5 books → 5! = 120

We also need to consider the subjects.

There are 3 subjects, kept separately, they will be arranged in 3! = 6 ways

So the total number of combinations is:

2*6*120*6 = 8640

Answer:

2 maths books can be arranged as (2!=2) ways 3 physics books can be arranged as (3!=6) ways5 chemistry books can be arranged as (5!=120) waysBooks can be arranged in suject-wise in (3!=6) ways

Hence, total ways are (2×6×120×6) ways =8640 ways.

8640 is the right answer.

hi, back at it agian. i dont think this would be to hard. delta math sucks... i need this asap! ·ω·

Answers

Answer:

I can't read the words the picture is to grainy

Answer:

10% would be 6

Step-by-step explanation:

First you want to find the 100 percent amount  to turn 40 into 100 you need to multiply it by 2.5 so you want to take 24 and multiply by 2.5 which equal 60 and 60 divided by 10  is 6

Geometry question plz help

Answers

Answer:

I think A

Step-by-step explanation:

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