Angle θ between two vectors is given by, 
; where 
; 
and 
.
Therefore,
Therefore,
What is the solution to the system of equation 5x-2y=21 3x+4=10
1 answer:
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We have the following equations:
So we are asked to write a system of equations or inequalities for each region and each point.
Part a)
Region Example A
Region B.
Let's take a point that is in this region, that is:
So let's find out the signs of each inequality by substituting this point in them:
So the inequalities are:
Region C.
A point in this region is:
So let's find out the signs of each inequality by substituting this point in them:
So the inequalities are:
Region D.
A point in this region is:
So let's find out the signs of each inequality by substituting this point in them:
So the inequalities are:
Point P:
This point is the intersection of the two lines. So let's solve the system of equations:
Accordingly, the point is:
Point q:
This point is the
of the line:
So let:
Then
Therefore, the point is:
Part b)
The coordinate of a point within a region must satisfy the corresponding system of inequalities. For each region we have taken a point to build up our inequalities. Now we will take other points and prove that these are the correct regions.
Region Example A
The origin is part of this region, therefore let's take the point:
Substituting in the inequalities:
It is true.
Region B.
Let's take a point that is in this region, that is:
Substituting in the inequalities:
It is true
Region C.
Let's take a point that is in this region, that is:
Substituting in the inequalities:
It is true
Region D.
Let's take a point that is in this region, that is:
Substituting in the inequalities:
It is true
So we are asked to write a system of equations or inequalities for each region and each point.
Part a)
Region Example A
Region B.
Let's take a point that is in this region, that is:
So let's find out the signs of each inequality by substituting this point in them:
So the inequalities are:
Region C.
A point in this region is:
So let's find out the signs of each inequality by substituting this point in them:
So the inequalities are:
Region D.
A point in this region is:
So let's find out the signs of each inequality by substituting this point in them:
So the inequalities are:
Point P:
This point is the intersection of the two lines. So let's solve the system of equations:
Accordingly, the point is:
Point q:
This point is the
So let:
Then
Therefore, the point is:
Part b)
The coordinate of a point within a region must satisfy the corresponding system of inequalities. For each region we have taken a point to build up our inequalities. Now we will take other points and prove that these are the correct regions.
Region Example A
The origin is part of this region, therefore let's take the point:
Substituting in the inequalities:
It is true.
Region B.
Let's take a point that is in this region, that is:
Substituting in the inequalities:
It is true
Region C.
Let's take a point that is in this region, that is:
Substituting in the inequalities:
It is true
Region D.
Let's take a point that is in this region, that is:
Substituting in the inequalities:
It is true
Answer:
Given that,
In right triangle ABC, C is the right angle.
sin A=0.4
To find cos B,
we get the triangle as,
we know that,
Hypotenuse of the triangle is AB
For the angle A, opposite side is CB
For the angle B, adjacent side is CB
From the definition of sine and cosine we get,
Also,
Comparing both we get,
It is given that sinA=0.4
Hence we get, cosB=0.4
Answer is: 0.4
