What is the true solution to 2 l n e Superscript l n 5 x Baseline = 2 l n 15 x = 0 x = 3 x = 9 x = 15

Find the volume of a regular hexahedron if one of the diagonals of its faces is 8 root 2 inches.

Naily [24]

The answer is 114sqrt{6} in³

A regular hexahedron is actually a cube.

Diagonal of a cube D is a hypotenuse of a right triangle which other two legs are face diagonal (f) and length of a side (a):
D² = f² + a²

Face diagonal is a hypotenuse of a right triangle which sides are a and a:
f² = a² + a² =2a²

D² = f² + a²
f² = 2a²

D² = 2a² + a² = 3a²
D = √3a² = √3 * √a² = √3 * a = a√3

Volume of a cube with side a is: V = a³
D = a√3
⇒ a = D/√3

V = a³ = (D/√3)³

We have:
D = 8√2 in

$V= (\frac{D}{ \sqrt{3} } )^{3} =( \frac{8 \sqrt{2} }{ \sqrt{3} } )^{3}=( \frac{8 \sqrt{2} * \sqrt{3} }{ \sqrt{3}* \sqrt{3}} )^{3} =( \frac{8 \sqrt{2*3} }{ \sqrt{3*3}} )^{3} =( \frac{8 \sqrt{6} }{ \sqrt{3^{2} }} )^{3} =( \frac{8 \sqrt{6} }{ 3} )^{3} = \\ \\ = \frac{ 8^{3} *( \sqrt{6} )^{3}}{3^{3}} = \frac{512* \sqrt{6 ^{2} }* \sqrt{6} }{27} = \frac{512*6* \sqrt{6} }{27} = 114sqrt{6}$

8 0

3 years ago

the width of a rectangle is 8 feet and the diagnal length of the rectangle is 13 feet which measurement is closest to the length

____ [38]

Answer:

Well the whole answer is 10.246950 smth smth but I don’t have the multiple choices so your gonna have to round yourself

Step-by-step explanation:

Okay so you have a weigh of 8 and a diagonal of 13.

If you look, theres a triangle there. One side has 8 and the diagonal that was cut forms a 13. So we have a leg and a hypotnuse. To find the other leg (length) just follow the Pythagorean theroum and solve for b or a.

Pythagorean theroum: a^2+b^2=c^2

Now subsitute c for 13 since its the hypotnuse and a or b as 8 but only one.

In this case I’m substituting a for 8.

8^2+b^2=13^2

Solve the squares

64+b^2= 169

Isolate the b

b^2=105

Now square root 105

√105 will give the answer above on a normal calculator but if you have to round, I don’t know what place but you can round.

7 0

2 years ago

Please hurry!

KengaRu [80]

A) Because the 80 is by itself that would be the start up fee.

B) We are told x is the number of months. Since the X is being multiplied by 30, we know that would be the total monthly cost. This is being added to the 80, which does not have an exponent, so we know this is a single cost, which would be the start up fee.

C) Copying the same format as the given equation above, change the numbers:

f(x) = 20 + 35x

D) I used the same format as the first equation, which meant replacing the start up cost from the original one ( 80) with the start up of the new one (20). Then I changed the monthly cost from the original one (30) with the monthly cost of the new one (35).

E) Replace x in each equation with 8 and calculate the cost of each:

80 + 30(8) = 80 + 240 = $320

20 + 35(8) = 20 + 280 = $300

The second club (club B) is the cheaper option for her.

4 0

2 years ago

The school's production of Romeo and Juliet began at 7:45 P.M. The first act lasted 1 hour and 35 minutes. The act was followed

Anika [276]

It should be 9:30 P.M.

7:45+ 15= 8
1 hour 35 minutes - 15= 1 hour 20

8+ 1 hour 20 minutes= 9:20
9:20+ 10= 9:30 P.M.

3 0

3 years ago

Read 2 more answers

Hector earned $60 this week, which is 5 times the amount he earned last week. The model shows how much money he earned this week

Ede4ka [16]

It would be 5x?=60 because to find "?" you would need to divide 60 and 5. Since Hector earned 5 times what he did last week it would be modeled by 5 times "?"

6 0

3 years ago