(3z-7)(z+2)The way that I arrived at that is to find two numbers that made (3*14)=42 by multiplying and 1 by subtraction. The outside product is 6 and the inside product is -7.
(3z + 5)(z -7)
let the width be z so length is (3z-10) Area=length x width Area=48 z(3z-10)=48 3z2-10z-48=0 3z2-18z+8z-48=0 3z(z-6)+8(z-6)=0 (3z+8)(z-6)=0 z= - (8/3) which is not possible since dimensions can not be negative So z=6 Width=6 length=3x6-10=8 Dimension= 6 ft x 8 ft
20y2 - 11yz - 3z2 = 20y2 + 4yz - 15yz - 3z2 = 4y(5y + z) - 3z(5y + z) = (4y - 3z)(5y + z)
3z2 + 45z + 42 = 3(z2 + 15z + 14) = 3(z + 1)(z + 14).
(3z-7)(z+2)The way that I arrived at that is to find two numbers that made (3*14)=42 by multiplying and 1 by subtraction. The outside product is 6 and the inside product is -7.
(3z + 5)(z -7)
The greatest common factor (GCF) refers to a factor that is COMMON to two or more numbers or expressions. You have only one expression in the question! The greatest factor of any number is itself.
let the width be z so length is (3z-10) Area=length x width Area=48 z(3z-10)=48 3z2-10z-48=0 3z2-18z+8z-48=0 3z(z-6)+8(z-6)=0 (3z+8)(z-6)=0 z= - (8/3) which is not possible since dimensions can not be negative So z=6 Width=6 length=3x6-10=8 Dimension= 6 ft x 8 ft
First off, this needs to be expressed in cylindrical coordinates, ρ, φ, and z, so as to not drive me crazy. By doing this, the magnitude of the resultant magnetic field from a magnetic material becomes φ independent and is expressed by: B = {μ0m/[4π(z2 + ρ2)3/2]}{√[1 + 3z2/(z2 + ρ2)]}, where μ0 is the permeability of free space and m is the dipole moment.