Answer:
see explanation
Step-by-step explanation:
Given that M is directly proportional to r³ then the equation relating them is
M = kr³ ← k is the constant of proportion
To find k use the condition when r = 4, M = 160, thus
160 = k × 4³ = 64k ( divide both sides by 64 )
2.5 = k
M = 2.5r³ ← equation of variation
(a)
When r = 2, then
M = 2.5 × 2³ = 2.5 × 8 = 20
(b)
When M = 540, then
540 = 2.5r³ ( divide both sides by 2.5 )_
216 = r³ ( take the cube root of both sides )
r = ![\sqrt[3]{216}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B216%7D)
= 6
Lets go step by step and factor out each as we go
first lets factor out a 3 since 3 is common in 9 and 3
3(3ab^2 - abc)
now lets factor out a since its common in both
3a(3b^2 - bc)
now lets factor out a b since its common in both
3ab(b - c)
we can't factor anything else out so we are done.
The answer to the area of the triangle is 21 because the base is equal to 6 and the height is 7 so you multiply 6 times 7 then divided by 2 because a triangle is 1 half of a square
Answer:
and 
.
Step-by-step explanation:
Equation:
Solution:
Set factors equal to zero,that is:
Solving for equation 1:
Solving for equation 2:
Hence,the solutions to the quadratic equation in factored form is and .
Good luck on your assignment!
