24 feet
Set up a ratio of object height to shadow length.
So x/32=6/8
8(4)=32 so 6(4) would be 24.
Answer: The volume of the tetrahedron is 2 units.
Step-by-step explanation:
Let A = (1, 1, 1)
B = (1, 5, 5)
C = (2, 2, 1)
The volume of a tetrahedron is given as
V = (1/6)|AB, AC, AD|
Where |AB, AC, AD| is the determinant of the matrix of AB, AC, AD.
We need to determine AB, AC, and AD
Suppose A = (a1, a2, a3)
B = (b1, b2, b3)
C = ( c1, c2, c3)
AB = ( b1 - a1, b2 - a2, b3 - a3)
Similarly for AB, AC, BC, etc.
AB = (1 - 1, 5 - 1, 5 - 1)
= (0, 4, 4)
AC = (1, 0, 2)
AD = (1, 1, 0)
Volume =
(1/6) |0 4 4|
|1 0 2|
|1 1 0|
= (1/6)[0(0 - 2) - 4(0 - 2) + 4(1 - 0)
= (1/6)(0 + 8 - 4)
= (1/6)(12)
V = 12/6 = 2 units
Answer:
x=-9, y=5. (-9, 5).
Step-by-step explanation:
x-3y=-24
5x+8y=-5
--------------
x=-24+3y
5(-24+3y)+8y=-5
-120+15y+8y=-5
-120+23y=-5
23y=-5-(-120)
23y=-5+120
23y=115
y=115/23
y=5
x-3(5)=-24
x-15=-24
x=-24+15
x=-9
Answer:
wow that's one lucky worm
Step-by-step explanation:
<span>1) 3x + y = 23
6x + y = 44
Subtract 1st from 2nd,
3x = 21
x = 7
Then, y = 23 - 3(7) = 2
In short, Your Answer would be: (7, 2)
2) </span><span>4x - 3y = 21
2x + 3y = 33
Add the equations,
6x = 54
x = 9
Then, 2(9) + 3y = 33
3y = 33 - 18
y = 15/3
y = 5
In short, Your Answer would be: (9, 5)
3) </span><span>5x + 2y = 13
6y + 5x = 29
Subtract 1st from 2nd equation,
4y = 16
y = 4
Then, 5x = 13 - 2(4)
x = 5/5 = 1
In short, Your Answer would be: (1, 4)
4) </span><span>5x - 4y = 2
10x - 4y = 32
Subtract 1st from 2nd equation,
5x = 30
x = 6
Then, 5(6) - 2 = 4y
y = 28/4 = 7
In short, Your Answer would be: (6, 7)
5) </span><span>2x + 7y = 48
x + 3y = 21
Here, x = 21-3y
Substitute in in 1st equation,
2(21-3y) + 7y = 48
42 - 6y + 7y = 48
y = 6
Then, x = 21 - 3(6) = 3
In short, Your Answer would be: (3, 6)
6) </span><span>8x - 3y = 44
2y - 4x = -20
Multiply 2nd equation by 2
-8x + 4y = -40
Now, add it to 1st equation,
y = 4
Then, 2(4) - 4x = -20
4x = 8 + 20
x = 28/4 = 7
In short, Your Answer would be: (7, 4)
Hope this helps!</span>
