Answer:
d ≈ 5.66
Step-by-step explanation:
given that F varies inversely with d squared, then the equation connecting them is
F = ← k is the constant of variation
to find k use the condition when F = 8, d = 6
k = Fd² = 8 × 36 = 288, hence
F =
when F = 9, then
9 = ← multiply both sides by d²
9d² = 288 ( divide both sides by 9 )
d² = 32 ( take the square root of both sides )
d = ± , hence
d ≈ 5.66 ← positive value only
Assuming that C is the hypotenuse...
The formula you want to use is:
a^2 + b^2 = c^2
We start by squaring 10, which is 100. 5^2 is 25. Now that we have the values, we can do the equation.
100+25=c^2 100+25=
Now, square root
C= 11.180
*I am assuming that the hexagons in all questions are regular and the triangle in (24) is equilateral*
(21)
Area of a Regular Hexagon: square units
(22)
Similar to (21)
Area = square units
(23)
For this case, we will have to consider the relation between the side and inradius of the hexagon. Since, a hexagon is basically a combination of six equilateral triangles, the inradius of the hexagon is basically the altitude of one of the six equilateral triangles. The relation between altitude of an equilateral triangle and its side is given by:
Hence, area of the hexagon will be: square units
(24)
Given is the inradius of an equilateral triangle.
Substituting the value of inradius and calculating the length of the side of the equilateral triangle:
Side = 16 units
Area of equilateral triangle = square units