Answer:
Step-by-step explanation:
To find the HCF of 144 and 180
By using product of prime method
Firstly express 144 as a product of it prime and express 180 as a product of it prime
140=2×2×2×2×3×3
180=2×2×3×3×5
Common factor =2×2×3×3
36
in term of m
m=36
13m-3
To find m
Substitute for m when m=36
13(36)-3=
465
Answer:
The answer is yes
Step-by-step explanation:
2*2.5=5
4*2.5=10
Let point C be (x, 0), then
AC = sqrt((x - 0)^2 + (0 - 2)^2) = sqrt(x^2 + 4) and
BC = sqrt((x - 9)^2 + (0 - 4)^2) = sqrt(x^2 - 18x + 81 + 16) = sqrt(x^2 - 18x + 97)
AC + BC = sqrt(x^2 + 4) + sqrt(x^2 - 18x + 97)
For minimum AC + BC, d(AC + BC)/dx = 0
d(AC + BC)/dx = x/sqrt(x^2 + 4) + (2x - 18)/sqrt(x^2 - 18x + 97) = 0
x(x^2 - 18x + 97) = -(2x - 18)(x^2 + 4)
x^3 - 18x^2 + 97x = -(2x^3 + 8x - 18x^2 - 72) = -2x^3 + 18x^2 - 8x + 72
3x^3 - 36x^2 + 105x - 72 = 0
x^3 - 12x^2 + 35x - 24 = 0
x = 8, 3, 1
Therefore, point C = (8, 0) or (3, 0) or (1, 0)
Answer:
Step-by-step explanation: