Answer:
- MN = (21 -6√3)/37 ≈ 0.286694
- RK = (14√3 -12)/37 ≈ 0.331046
Step-by-step explanation:
In the attached figure, we have defined LM to be length x. Then the other lengths on side AC are ...
AM = LR = x/√3
RC = (2/√3)RK = (2/√3)(2/√3)x = 4/3x
Then the sum of lengths along AC is ...
AC = AM +ML +LR +RC
1 = x(1/√3 +1 +1/√3 +4/3) = x(7/3 +2/√3) = x(7√3 +6)/(3√3)
Then the value of x is ...
Answer:
≈ 15.73 in
Step-by-step explanation:
Since the volume of a cylinder is , we can set the equation,
= 1000
Since the radius of the circle is 4.5, we square it to get
= 1000
Dividing by 20.25 on both sides, we get
≈ 49.38
Dividing by 3.14 on both sides, we get
≈ 15.73 in
Answer:
22:8 and 11:4
Step-by-step explanation:
22/8 = 2.75
11/4 = 2.75
28/9 does not equal 2.75
The net for a triangular prism consists of
2 identical triangles, here all nets have sides 5,12, and 13.
3 rectangles, all with a common dimension: the height H=14 of the prism.
Each of the 3 rectangles should have dimensions
H=14 plus one of the following:
each of 5, 12, 13 corresponding to one side of the base (triangle).
So the dimensions of the rectangles are
5x14, 12x14, 13x14
And dimensions of the triangles are
5,12 and 13.
The total surface area is therefore
(5+12+13)*14 + 2*(5*12/2)
=420+60
=480.
There is only one net that satisfies this condition.