Find an equation of the plane that passes through the point (-1,1/2,3) with normal vector [1,4,1]

x + 4y + z = 4

Step-by-step explanation:

The standard equation is of the form, Ax + By + Cz = 0

The equation of the plane that passes through the point(-1, 1/2, 3)  and is perpendicular to [1, 4, 1] is

A = 1, B = 4, C = 1

x = -1; y = 1/2; z = 3

A(x-(-1)) + B(y-1/2) + C(z-3) = 0

(x+1) + 4(y-1/2) + (z-3) = 0

(x+1) + (4y-2) + (z-3) = 0

x + 1 + 4y -2 + z -3 = 0

x + 4y + z - 4 = 0

x + 4y + z = 4

3x + 18 = 147°

step-by-step explanation:

3x + 18 = 147°, because the value of the central angle is equal to the value of the arc formed by it.

i hope i you.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.