Find the volume of the tetrahedron with the given vertices. (2, 0, 0), (0, 4, 0), (0, 0, 4), (2, 4, 4)
Katarina [22]
Answer:
The volume of the tetrahedron is
Step-by-step explanation:
To find the volume of a tetrahedron with vertices (2, 0, 0), (0, 4, 0), (0, 0, 4), (2, 4, 4).
We know by definition that the volume of a tetrahedron with vertices 
is
From here we have:
Finding the determinant of that matrix we have:
=
Answer:
The triangle with side lengths 7 in, 11 in, 13 in will be an acute angled triangle.
Step-by-step explanation:
If we assume that the triangle with height 7 inches and base 11 inches of a right triangle then its hypotenuse will have the length of
inches.
But the third side of the triangle is given to be 13 inches which is less than 13.04 inches i.e. 13 < 13.04.
Therefore, the triangle with side lengths 7 in, 11 in, 13 in will be an acute-angled triangle. (Answer)
He spent $65 of his total $650 leaving him with $585.
650/10=65
650-65=585
or (650/10)-65=585
the / is the division symbol.
Answer:In this problem,
a
n
=x
a
1
=1
d=6−1=5
∴x=1+(n−1)×5
∴x−1=(n−1)×5
∴(n−1)=
5
x−1
∴n=
5
x−1
+1
∴n=
5
x−1+5
∴n=
5
x+4
Equation (1)
2) Sum of n terms of A.P. is
∑a
n
=
2
n
[2a+(n−1)d]
As given in problem, ∑a
n
=148
∴
2
n
[2a+(n−1)d]=148
∴
2
(
5
x+4
)
[(2×1)+(
5
x+4
−1)5]=148
∴
10
x+4
[2+(
5
x+4−5
)5]=148
∴
10
x+4
[2+x−1]=148
∴
10
x+4
[x+1]=148
∴(x+4)(x+1)=1480
∴x
2
+5x+4=1480
∴x
2
+5x−1476=0
∴x=
2×1
−5±
(5)
2
−4×1×(−1476)
∴x=
2
−5±
25+5904
∴x=
2
−5±
5929
∴x=
2
−5±77
neglecting negative root, we get,
x=
2
−5+77
∴x=
2
72
∴x=36
Step-by-step explanation: i hope it was helpfu;;
