In a certain region, the electric potential due to a charge distribution is given by the equation v(x, y,z) = 3x2y2 + yz3 - 2z3x, where x, y, and z are measured in meters and v is in volts. calculate the magnitude of the electric field vector at the position (x, y,z) = (1.0, 1.0, 1.0).

Magnitude = 11.05

Step-by-step explanation:

The electric potential due to a charge distribution is given by

(Equation 1)

V(x,y,z)=3x²y² + yz³ - 2z³x(1)

Differentiating the above equation 1 with respect to x,

(Equation 2)

Vx= 6xy² + 2z³

Differentiating the above equation 1 with respect to y,

(Equation 3)

Vy= 6x²y + z³

Differentiating the above equation 1 with respect to z,

(Equation 4)

Vz= 3yz² - 6z²x

Substituting the value of x,y and z in equations 2,3 and 4

Vx= 6+2=8

Vy=6+1=7

Vz=3-6= -3

Magnitude = √((Vx)²+(Vy)²+(Vz)²)

Magnitude = √(64)+(49)+(9)

Magnitude=√122

Magnitude = 11.05

the answer is the option b

the range is all real numbers

step-by-step explanation:

we know that

the absolute value parent function is equal to

see the attached figure to better understand the problem

so

a. it is v-shaped > is true

b. the range is all real numbers > is not true

because the range is the > [0,∞)

all real numbers greater than or equal to zero

c. it goes through the origin > is true

d. the domain is all real numbers > is true

step-by-step explanation:

42.4

step-by-step explanation:

convert to decimal