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:
<h3>B. It has infinite solutions</h3>
Step-by-step explanation:
Given the system of equations:
2t + w = 10 ..... 1
4t = 20 − 2w ... 2
From 1:
w = 10-2t ...3
Substitute 3 into 2 to have;
4t = 20 - 2(10-2t)
4t = 20-20+4t
4t = 4t
Let t = k
Substitute t = k into 1 and get w;
From 1: 2t + w = 10
2k + w =10
w = 10 - 2k
<em>k can take any integers. This shows that the solution to the equation is infinite</em>
<em></em>
Let us say that:
x = mass from Earl Grey Tea
y = mass from Orange Pekoe Tea
So that:
x + y = 600
and that:
6 x + 4 y = 4.5 * 600
6 (600 – y) + 4 y = 2700
3600 – 6y + 4y = 2700
-2y = -900
y = 450 pounds
x = 600 – 450 = 150 pounds
Answer:
<span> Earl Grey Tea = 150
pounds</span>
<span>Orange Pekoe Tea = 450 pounds</span>
Answer:
A and E
Step-by-step explanation:
substitute and odd number into every equation :)
Answer:
85 m
Step-by-step explanation:
5696/67=85