Find four consecutive odd integers if the sun of the first and fourth is 3 less than 3 times the second

Mathematics

1 answer:

Ksju [112]3 years ago

7 0

Answer:

Step-by-step explanation:

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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

A ticket to a museum costs $8. A ticket to the dinosaur exhibit costs $5. The expression 8n+5n represents the cost in dollars fo

julia-pushkina [17]

The equation which represents the people that want to visit the museum and the exhibit is 8n+5n.
As you can see, the variable n is present in both terms 8n and 5n of the equation, so we can now factor the equation. You create parenthesis in which you put inside 8+5 and then you throw the variable n outside the parenthesis, and you get at last:
8n + 5n = (8+5)n

Hope this helps! :D

6 0

3 years ago

Read 2 more answers

Plzzzzz ill make u brainliest like frfr

Luden [163]

Answer:

3,520 yds in 2 hours

Step-by-step explanation:

5,280:1 ; 1 mile an hour is 5,280 feet in an hour

10,560:2 ; 2 miles in 2 hours is 5,280+5,280 (10,560) feet in 2 hours

3 ft = 1 yd ; every 3 feet is a yard, so divide 10,560 by 3

10,560/3 = 3520 yds ; Jorge can walk 3,520 yds in 2 hours

6 0

3 years ago

Select all of the solutions to the system graphed below.

ra1l [238]

0,-2

4,4

2,0

3,5

Step-by-step explanation:

that was my answer

3 0

3 years ago

Please answer this I really need help, Ariel spent a total of $3.42 buying dried apricots from the bulk bins, which were on sale

Kamila [148]

Answer:

1.2 lbs

Step-by-step explanation:

This problem is set up so that the total price is proportional to the price per pound, so to find the proportion you would divide the total cost by the cost per pound. 3.42/2.85 = 1.2, so the answer is 1.2 pounds.

5 0

3 years ago