Express the edge length of a cube as a function of the cube's diagonal length d. Then express the surface area and volume of the cube as a function of the diagonal length.

a. A function for the edge length of a cube is L(d) = _________________
b. A function for the surface area of a cube is Ald) = _____________
c. A function for the volume of a cube is V(d) = ________________

Answers

Answer 1

Answer:

Step-by-step explanation:

If L is the length of a side, the longest diagonal in the cube is

d = √(L² + L² + L²) = √(3L²) = L√3

meaning

a) L(d) = d/√3 = ⅓d√3

b) A(d) = 6(L(d))² = 6(⅓d√3)² = 6(⅟₉d²(3)) = 2d²

c) V(d) = (L(d))³ = (⅓d√3)³ = ⅟₂₇d³3√3 = ⅟₉d³√3


Related Questions

Someone please help
Don’t understand the question

Answers

9514 1404 393

Answer:

  22. E

  23. C

Step-by-step explanation:

These questions are asking you to make use of a couple of trig identities for converting products to sums.

  sin(x)cos(y) = 1/2(sin(x+y) +sin(x -y))

  cos(x)cos(y) = 1/2(cos(x+y) +cos(x -y))

  sin(-x) = -sin(x)

  cos(-x) = cos(x)

__

22. sin(2β/3)cos(4β/3) = (1/2)(sin((2+4)β/3) +sin((2-4)β/3))

  = 1/2sin(2β) +1/2sin(-2β/3) = 1/2sin(2β) -1/2sin(2β/3)

__

23. cos(3θ)cos(5θ) = (1/2)(cos(3θ+5θ) +cos(3θ -5θ)) = 1/2cos(8θ)+1/2cos(2θ)

Grace buys notebooks at a price of four for $5 and sells them at a price of three for $6. How many notebooks must she sell in order to make a profit of $120

Answers

Answer:

125 I think

I'm a lil slow

Grace needs to sell 160 notebooks to make a profit of $120

What is an equation?

Two algebraic expressions having the same value and the symbol '=' in between are called as an equation.

Given:

Grace buys notebooks at a price of four for $5.

Unit cost price,

= $5 / 4

= $1.25

And sells them at a price of three for $6.

Unit cost price,

= 6/3

= $2.

Profit = sales - cost

So, the equation,

120 = 2x - 1.25x

0.75x = 120

x = 120/0.75

x = 160

Therefore, 160 notebooks need to sell to maker profit of $120.

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Find the distance between (2,0) and (8, -3)
The distance d between the points (Xy, Yı) and (x2, Y2) is
d = Vixz - x,)2 + (y2 - y)2.
O 789
15
13
O 3V5

Answers

Answer:

3√5

Step-by-step explanation:

What is the smallest power of 10 that would exceed 987,654,321,098,765,432?



Use the ^ symbol to represent an exponent.

For example, 52 would be written as 5^2.

Answers

Answer:

10¹⁸

Step-by-step explanation:

Ten to the power of x, has x many zeroes behind 1

The original numbers had 18 digits. So, 10¹⁸ is the smallest number that would exceed the original number

Suppose a certain manufacturer deposits $7,000 at the beginning of each 3 month period for 8 years in an account paying 8% interest compounded quarterly.

Required:
a. How much (in $) will be in the account at the end of the 6 year period?
b. What is the total amount (in $) of interest earned in this account?

Answers

9514 1404 393

Answer:

  a) $217,212.10 after 6 years

  b) $91,780.99 interest earned

Step-by-step explanation:

The future value of this "annuity due" can be found using the formula ...

  FV = P(1 +n/r)((1 +r/n)^(nt) -1)

where P is the periodic payment made n times per year and r is the annual interest rate.

a) After 6 years, the value of the account is ...

  FV = $7000(1 +4/0.08)((1 +0.08/4)^(4·6) -1) = $217,212.10 . . . . 6-yr balance

__

b) After 8 years, the value in the account is ...

  FV = $7000(51)(1.02^32 -1) = $315,780.99

The total of payments is $7000×32 = $224,000, so the interest earned is ...

  I = $315,780.99 -224,000 = $91,780.99 . . . interest earned

Please help quickly as possible thank you! ​

Answers

Multiply [tex]Q\cdot P[/tex], quantity and price,

[tex]1.2\cdot5.95=7.14[/tex].

Hope this helps :)

Answer:

$7.14

Step-by-step explanation:

Price of 1 pound cheese=$5.95

Price of 1.2 pounds cheese=$5.95 * 1.2

Price of 1.2 pounds cheese=$7.14

Note:if you need to ask any question please let me know.

4 over 9 divided by 12 over 27

Answers

Answer:

1

Step-by-step explanation:

4/9÷12/27

=4/9×27/12

=3/3

=1

Temperatures this cold are rare.
Another 8°F colder, and it will be
-40°F.

Pleaae show the work

Answers

Answer:

-32°F

Step-by-step explanation:

8°F - 40°F

=> 32°F

There are ten times as many silver cars than red cars. If there 88 silver and red cars altogether, find the number of cars of each colour

Answers

Answer:

80 silver, 8 red

Step-by-step explanation:

let x be the number of red cars then 10x is the number of silver cards , so

x + 10x = 88

11x = 88 ( divide both sides by 11 )

x = 8

10x = 10 × 8 = 80

There are 80 silver cars and 8 red cars

30=26-a/6
Solve for a

Answers

Answer:

the answer is 24

Step-by-step explanation:

30=26-a\6

collect like terms

30-26 =a\6

4=a\6

Cross multiply

a=4×6

a=24

The solution to the given equation is 24.

The given equation is 30 = 26-a/6.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Here, 30 = 26-a/6

Transpose 26 to the other side of the equation, we get

30-26 = -a/6

-4 = -a/6

4 =  a/6

Transpose 6 to the other side of the equation, we get

a = 4×6

a = 24

So, the solution is 24.

Therefore, the solution to the given equation is 24.

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Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.) {-4, 8/3, -16/9, 32/27, -64/81, . . . } an =

Answers

Step-by-step explanation:

a1 = -4 = -4/1, a2 = 8/3

r = a2/a1 = (8/3) / (-4/1) = -2/3

the formula :

an = a1. r^(n-1)

so,

an = (-4). (-2/3)^(n-1)

Step-by-step explanation:

[tex]-4, \dfrac{8}{3}, -\dfrac{16}{9}, \dfrac{32}{27}, -\dfrac{64}{81},..., (-1)^n\dfrac{2^{n + 1}}{3^{n - 1}}, ...[/tex]

chose all that apply

Answers

Answer:

Rational

Integer

Step-by-step explanation:

B AND C NOT SURE IF ITS CORRECT

PLS HELPP , i tried solving this and i wrote 56 but it was wrong so i don’t know anymore pls pls help

Answers

Answer:

y = 68

A = 44

Step-by-step explanation:

No matter what may be true, that doesn't look like an a to me.

x = y = 68                x and y are opposite equal sides and are therefore =.

68 + 68 + A = 180  all triangles are 180 degrees.

136 + A = 180          Subtract 136 from both sides

A = 180 - 136

A = 44

Express the formula V=l x w x h in terms of the width, w. Use your formula to find the width when the volume is 192, the length is 8, and the height is 4

Answers

Answer:

6

Step-by-step explanation:

192=8*4*w

make w subject to formula

w=192/32

w=6

The expression of width is w = V/(l*h) and the value of width is 6.

What is substitution of equation to find the expression of width ?

Given formula of volume is V = l * w * h .

Substituting width (w) from the above equation,

w = V/(l*h) .

Finding the value of width from the expression -

Given expression after substitution is w = V/(l*h) .

⇒ w = 192/(8 * 4)

∴  w = 6 .

Thus the value of width is 6.

Therefore, the expression of width is w = V/(l*h) and the value of width is 6.

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You and your family are planning a vacation of a lifetime around the world that will cost $25,000. You borrowed this amount from your bank with an annual interest rate of 10.5%. You decided to pay it back in 5 years. What is the interest that will accrue on this loan?

$3,125.00

$131,250

$13,125.00

$312.50

Answers

Answer:

$13,125

Step-by-step explanation:

The value of the interest that will accrue on this loan will be;

⇒ $13,125

What is Simple interest?

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

Given that;

You and your family are planning a vacation of a lifetime around the world that will cost $25,000.

And, You borrowed this amount from your bank with an annual interest rate of 10.5%.

Now,

Since, You borrowed this amount from your bank with an annual interest rate of 10.5%.

Hence, The total interest amount after five years is,

⇒ 5 × (10.5% of $25,000)

⇒ 5 × (10.5/100 × 25,000)

⇒ 5 × 2,625

⇒ $13,125

Thus, The total interest amount after five years = $13,125

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Need the answers in 1 minute ASAP

Answers

Answer:

d=f(c)=15-c/4

Step-by-step explanation:

The expression 1/x+y
is equal to which quantities?
(1/x) + y
1/x + y
1/(x + y)

Answers

The equivalent form of the given expression is 1 /(x + y)

The given expression:

[tex]\frac{1}{x+y}[/tex]

To find:

the equivalent form of the expression:

The equivalent form of the expression can be written as follows:

[tex]\frac{1}{x+y} = 1 /(x + y)[/tex]

For example, if x = 1 and y = 2, the inverse of the expression can be written as;

[tex]\frac{1}{x + y} = \frac{1}{(1 + 2)} = \frac{1}{3}[/tex]

Also, if x = 2 and y = 3, the inverse of the expression can be written as;

[tex]\frac{1}{x + y} = \frac{1}{(2 + 3)} = \frac{1}{5}[/tex]

Thus, the equivalent form of the given expression is 1 /(x + y)

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Evaluate piecewise functions
f (4) = ?

Answers

F(4) = 4^2 - 7 = 16 - 7 = 9

Answer:

f(4) = 9

Step-by-step explanation:

x = 4 corresponds to the middle piece of the function, therefore:

f(4) = 4² - 7 = 16 - 7 = 9

16.
Select all transformations that carry rectangle
ABCD onto itself.

A. Rotate by 90 degrees clockwise using center P.
B. Rotate by 180 degrees clockwise using center P.
C. Reflect across line m.
D. Reflect across diagonal AC.
E. Translate by the directed line segment from A to B.

Answers

Answer:

I got B and C.

Step-by-step explanation:

When you rotate by 180° you turn it so that it is facing the other way (ie D is B, C is A, etc) since it's a rectangle, when you rotate by 180°, you still have the same rectangle with angles in the same corners. when you reflect across the midpoint, you are just flipping your rectangle over, and so would again have the same effect as turning it 180°.

4/8 divided by 4/6


thank you for your answer

Answers

3/4 exact form

Hope you get the right answer!

Answer:

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

Step-by-step explanation:

[tex] \frac{4}{8} \div \frac{4}{6} [/tex]

[tex] \frac{4}{8} \times \frac{6}{4} [/tex]

[tex] \frac{1}{4} \times 3[/tex]

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

Hi fellow Army^^

Maggies brother is 4 years younger than three times her age the sum of there ages is 28 how old is maggie

Answers

Answer:

24

Step-by-step explanation:


19. Solve 5x^2 - 6x + 1 = 0 using the quadratic formula.
Please give detailed steps!!

Answers

Answer:

x = -b ± √b²-4ac /2a

a = 5

b= -6

c= 1

x = -(-6) ± √(-6)² - 4(5)(1) /2(5)

x = 6 ± √36 - 20 / 10

x = 6 ± √16 /10

x = 6 ± 4/10

Breaking into respective signs

x = 6 + 4/10 or 6 - 4/10

x = 10/10 or 2/10

x = 1 or 1/5

x = 1 or 1/5.

Answer:

1/5 and 1

Brainliest, please!

Step-by-step explanation:

5x^2 - 6x + 1 = 0

a = 5, b = -6, c = 1

(-b +-sqrt(b^2 - 4ac))/2a

(-(-6) +-sqrt((-6)^2 - 4(5)(1))/2(5)

(6 +- sqrt(16)/10

(6 +- sqrt(16))/10

(6 +- 4)/10

2/10 and 10/10

1/5 and 1

2. Which type of variation is represented by the following equation?

Answers

indirect variation

Verification

[tex]\\ \rm\Rrightarrow s\propto \dfrac{1}{y}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{s_1}{t_2}=\dfrac{s_2}{t_1}[/tex]

[tex]\\ \rm\Rrightarrow s_1t_1=s_2t_2[/tex]

Evaluate 5x -3x when x=2

Answers

Answer:

4

Step-by-step explanation:

5*2-3*2=10-6=4

Write the scientific notation for 127.5. Please! And tell me how so I can learn too. ​

Answers

1.275 x 10 to the second power

In scientific notation, you move the decimal place until you have a number between 1 and 10. Then you add a power of ten that tells how many places you moved the decimal. In scientific notation, so 127.5 becomes 1.275 x 10 to the second power.

Source: https://www.infoplease.com/math-science/mathematics/numbers-formulas/scientific-notation

-4x+9y=9
x-3y=-6

solve. systems of equations

Answers

Answer:

-3x + 6y = 3

Step-by-step explanation:

-4x + x = -3x

9y - 3y = 6y

9 - 6 = 3

9514 1404 393

Answer:

  (x, y) = (9, 5)

Step-by-step explanation:

My preferred method is to solve a system using a graphing calculator. That result is attached.

__

Here, you can multiply the second equation by 4 and add the first equation.

  4(x -3y) +(-4x +9y) = 4(-6) +(9)

  -3y = -15 . . . . . . . . . . simplify

  y = 5 . . . . . . . . . . . . divide by -3

  x -3(5) = -6

  x = -6 +15 = 9

The solution is (x, y) = (9, 5).

I know the answer don’t know how though

Answers

Answer:

16384

Step-by-step explanation:

As,

[tex] {2}^{15} [/tex]

Meaning that 2 multiplied 15 times here,

Equals 32 768

Now,

[tex] {2}^{14} [/tex]

Meaning that 2 multiplied 15 times then divided by one time 2,

Equals 32 768 ÷ 2 = 16384 (Ans)

If y = -18 when x = 3, find x when y =30

Answers

Answer:

when x = 18. Putting x = 18 into the equation y = 6/x, we have y = 6/18. Simplifying the fraction gives us y = 1/3.

Step-by-step explanation:

if a metalic cylinder having volume 18cm3 is melted to form a hemisphere. find the radius of the hemisphere.​

Answers

Answer:

R = 2.05 cm

Step-by-step explanation:

Volume of a hemisphere

V = ½(4/3)πR³ = (2/3)πR³

18 = (2/3)πR³

R³ = 27/π

R = 2.04835218...

A school store buys pencils in bulk and sells them to students for a small profit. The school pays $2.00 for 100 pencils and sells them for 10 cents each. How many pencils would they have to sell to make a $100 profit?

Answers

Answer:

Step-by-step explanation:

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