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Kay [80]
3 years ago
12

HOW DO I SOLVE THIS FAST I NEED TO KNOW ASAP

Mathematics
1 answer:
artcher [175]3 years ago
8 0

Answer:

Solve what? lol

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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
4. A triangle with base (2x+2) and height (x-2) is cut out of a rectangular sheet of paper that is (3x+4) by (2x+3) what is the
juin [17]
So what we do is
area that remains=total area-triangle area that was cut out


we need to find 2 things
total area
triangle area

total area=rectange=base times height
area=(3x+4) times (2x+3)
FOIL or distribute
6x^2+8x+9x+12=6x^2+17x+12

triangle area=1/2 times base times height
triangle area=1/2 times (2x+2) times (x-2)=
(x+2) times (x-2)=x^2+2x-2x-4=x^2-4


so
total area=6x^2+17x+12
triangle area=x^2-4

subtract
area that remains=total area-triangle area that was cut out
area that remains=6x^2+17x+12-(x^2-4)=
6x^2+17x+12-x^2+4=
6x^2-x^2+17x+12+4=
5x^2+17x+16


area that remains is 5x^2+17x+16

5 0
3 years ago
Find x and y of the triangles
Diano4ka-milaya [45]

Answer:

X = 100

Y= 140

Step-by-step explanation:

The angle of y is same with 140, x u just need to 180= 2(180-140)+x

4 0
3 years ago
Darin has a rectangular vegetable garden. It is 5 yards long and 8 feet wide.
Lelu [443]

Answer:

about 15.328 yrds

Step-by-step explanation:

two sides are 5 yrds, so 5+5= 10yrds. two sides are 8 ft, 8+8=16 ft. there are .3333 yrds in 1 foot so 16*.3333 = about 5.328yrds

10+5.328 = 15.328

7 0
2 years ago
PLZ HELP ILL MARK AS BRAINLIEST
Rainbow [258]

Answer:

1092 cm^2

Step-by-step explanation:

Formula = 2 * Height (Length + Width)

2 * 26 (15 + 6) = 1092

6 0
2 years ago
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