Answer:
a) 
b) 
c) the points of the form (x, -x) for x≠0
Step-by-step explanation:
a)
If φ(x, y) = arctan (y/x), the vector field F = ∇φ would be
On one hand we have,
On the other hand,
So
b)
The domain of definition of F is
i.e., all the plane X-Y except the (0,0)
c)
Here we want to find all the points such that
where k is a real number other than 0.
But this means
So, all the points in the line y = -x except (0,0) are parallel to the vector field F, that is, the points (x, -x) with x≠ 0
Answer:
Marcy's math class starts at 9:35.
Step-by-step explanation:
11:55
-50 = 11:05 This gets rid of 50 minutes of math class.
11:05
-30 = 10:35 This gets rid of the 30 minutes of recess.
Now subtract one more hour to subtract the remainder of math class, and you get 9:35. Marcy's math class starts at 9:35.
Answer:
Angle(APR) = 43
x = 21.5
Step-by-step explanation:
The given angles are complementary :
So APR + RPW = 90
APR = 43
2x = 43
x = 21.5
Answer:
94 cm
Step-by-step explanation:
Set up and solve an equation of ratios:
wingspan length
60 meters 70.5 m
----------------- = ----------------
80 cm x
Cross multiplying:
(60 m)x = (70.5 m)(80 cm)
Solve for x by dividing both sides of this equation by 60 m:
x = (70.5 m)(80 cm) / (60 m) = 94 cm
The length of the model should be 94 cm.