Answer:
1. 301.6
2. 576
3. 274.41
Step-by-step explanation:
We know that the diameter of one of the spheres must be 4 in, because the length of the box is 12 in and there are 3 spheres along each side, and . That means that the radius of a sphere is 2 in. Put 2 into the formula for the volume of a sphere, and then multiply your solution by 9, to get the total volume.
Then, you can find the volume of the box, because you know its dimentions are 12x12x4.
Subtract your answer for part 1 from your answer for part 2, and you have the solution to part 3. Hope this helps!! :-)
Step-by-step explanation:
OK so add the 66 and the square=90, so add 66 and 90 then subtract it from 180 and then you will get x
Answer:
Options C and D are the correct options.
Step-by-step explanation:
Option A
cos(H) = 0.3846
By applying cosine rule in ΔFGH,
cos(H) =
=
= 0.9231
False
Option B
cos(G) = 0.9231
By applying cosine rule in ΔFGH,
cos(G) =
=
= 0.3846
False
Option C
sinG = 0.9231
By applying sine rule in ΔFGH,
sin(G) =
=
= 0.9231
True
Option D
tanG = 2.4
By applying tangent rule in ΔFGH,
tanG =
=
= 2.4
True
Therefore, Options C and D are the correct options.
9514 1404 393
Answer:
B. 4
Step-by-step explanation:
There are a couple of ways you can look at this question.
<u>Triangle relationships</u>
The value of x must satisfy the requirements of the triangle inequality, and that the legs of the triangle are shorter than the hypotenuse.
(x -1) +(2x -4) > (x -1) +2 ⇒ x > 3 . . . . from UW +UV > VW
2x -4 < (x -1) +2 ⇒ x < 5 . . . . from UV < VW
The only integer strictly between 3 and 5 is ...
x = 4 . . . . . . . gives a 3-4-5 right triangle
__
<u>Pythagorean theorem</u>
The side lengths of this right triangle must satisfy the Pythagorean theorem:
UW² +UV² = VW²
(x -1)² +(2x -4)² = ((x -1) +2)²
x² -2x +1 +4x² -16x +16 = x² +2x +1
4x² -20x +16 = 0 . . . . . put in standard form
4(x -4)(x -1) = 0 . . . . . . .factor
Solutions are x = 4 and x = 1. Only the solution x = 4 is viable in this geometry.
x = 4