Always foucus on the teacher ask help when needed
Answer:
a) (8,8,-6)
b) 4x+4y+3z = -3
Step-by-step explanation:
a)
The surface is given by the equation
f(x,y,z) = 0 where
The gradient of this function is the vector
If we evaluate it in the point P = (-2,2,1) we obtain the point
(8,8,-6)
b)
The vectors with their tails at P are of the form
(-2,2,1)-(x,y,z) = (-2-x, 2-y, 1-z)
as they must be orthogonal to the gradient, they must be orthogonal to the vector (8,8,6) so their inner product is 0
and the equation of the desired plane is
4x+4y+3z = -3
Answer:
D. The function f has 3 horizontal tangent lines
Step-by-step explanation:
Well whenever any function crosses the x-axis, it means that the y-value is equal to zero.
In this case when the derivative passes the x-axis it indicates the tangent line corresponding to that x-value has a slope of zero, which when plotted is a horizontal line.
This means that the graph f has 3 horizontal tangent lines.
She made 62 baskets by day 14. 4×13=52+10=62
Answer: the number of adult tickets sold is 400
the number of student tickets sold is 200
Step-by-step explanation:
Let x represent the number of adult tickets sold at the play.
Let y represent the number of student tickets sold at the play.
Adult tickets to a play cost $1.75 each and student tickets cost $1.25 each. If the income from the play was $1,700, it means that
1.75x + 1.25y = 1700 - - - - - - - - - -1
Suppose there are twice as many student tickets sold as adult tickets. This means that
y = 2x
Substituting y = 2x into equation 1, it becomes
1.75x + 1.25 × 2x = 1700= 1700
1.75y + 2.5y = 1700
4.25y = 1700
y = 1700/4.25 = 400
x = y/2 = 400/2 = 200
