Answer:
The distance between points P(x
1
,y
1
,z
1
) and Q(x
2
,y
2
,z
2
) is given by
PQ=
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
+(z
2
−z
1
)
2
(i) Distance between points (2,3,5) and (4,3,1)
=
(4−2)
2
+(3−3)
2
+(1−5)
2
=
(2)
2
+(0)
2
+(−4)
2
=
4+16
=
20
= 2
5
(ii) Distance between points (−3,7,2) and (2,4,−1)
=
(2+3)
2
+(4−7)
2
+(−1−2)
2
=
(5)
2
+(−3)
2
+(−3)
2
=
25+9+9
=
43
(iii) Distance between points (−1,3,−4) and (1,−3,4)
=
(1+1)
2
+(−3−3)
2
+(4+4)
2
=
(2)
2
+(−6)
2
+(8)
2
=
4+36+64
=
104
=2
26
(iv) Distance between points (2,−1,3) and (−2,1,3)
=
(−2−2)
2
+(1+1)
2
+(3−3)
2
=
(−4)
2
+(2)
2
+(0)
2
=
16+4
=
20
= 2
5
Answer: 12, 12, and 23
Step-by-step explanation:
By definition, when three lengths form a triangle, the sum of two of them must be greater that the third lenght.
To find out which of the options given in the problem form a triangle, you must add the first two lenghts and verify that the sum is greater than the third lenght.
Keeping this on mind, when you verify the last option you have:
12+12=24
24>23
Therefore, the answer is the last option.
Answer:
d=10.0002
Step-by-step explanation:
Given That:
Height=h=28 inches
Volume=V=732.7 cubic inches
Required:
Diameter of the base of the cone=d=?
Solution:
the formula for the volume of a cone is
re-arranging the terms to get the radius (r)
putting values, we get
to find the diameter we know that diameter is double of the radius so
d=2r
d-2(2.0051)
d=10.0002
Answer:
11.7 hours
Step-by-step explanation:
According to data gathered between the years of 2015-2020 from full-time University Students at various Universities throughout the US, it was discovered that they spend roughly 11.7 hours completing these tasks (sleeping, grooming, eating/drinking, and traveling) per day. This applies strictly to full-time University Students that have the responsibilities associated with that life such as studying, attending class, group projects, etc. and does not include extra activities such as cooking.
