X=y x+2y =3 Solve using substitution
1 answer:
Answer:
Therefore the Final Solution is
x = 1 and y = 1
Step-by-step explanation:
Given:
...............Equation ( 1 )
................Equation ( 2 )
To Find:
x = ?
y = ?
Solution:
Equating Equation ( 1 ) in Equation ( 2 ) we get
Now Substituting y = 1 in Equation ( 1 ) we get
Therefore the Final Solution is
x = 1 and y = 1
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Answer:
The value of k = 4/3
Step-by-step explanation:
* Lets explain how to solve the problem
- An equilateral triangle ABC is inscribed in a circle N
- The area of the triangle is √3
- The shaded area is the difference between the area of the circle
and the area of the equilateral triangle ABC
- The shaded are = k π - √3
- We need to find the value of k
* <u><em>At first lets find the length of the side of the Δ ABC</em></u>
∵ Δ ABC is an equilateral triangle
∴ Its area = √3/4 s² , where s is the length of its sides
∵ The area of the triangle = √3
∴ √3/4 s² = √3
- divide both sides by √3
∴ 1/4 s² = 1
- Multiply both sides by 4
∴ s² = 4 ⇒ take √ for both sides
∴ s = 2
∴ The length of the side of the equilateral triangle is 2
* <u><em>Now lets find the radius of the circle</em></u>
- In the triangle whose vertices are A , B and N the center of the circle
∵ AN and BN are radii
∴ AN = BN = r , where r is the radius of the circle
∵ The sides of the equilateral angles divides the circle into 3 equal
arcs in measure where each arc has measure 360°/3 = 120°
∵ The measure of the central angle in a circle equal the measure
of the its subtended arc arc
∵ ∠ANB is an central angle subtended by arc AB
∵ The measure of arc AB is 120°
∴ m∠ANB = 120°
- By using the cosine rule in Δ ANB
∵ AB = 2 , AN = BN = r , m∠ANB = 120°
∴
∴
∴
∴
∴
- Divide both sides by 3
∴
- Take square root for both sides
∴ r = 2/√3
* <u><em>Lets find the value of k</em></u>
∵ Area circle = πr²
∵ r = 2/√3
∴ Area circle = π(2/√3)² = (4/3)π
∵ Area shaded = area circle - area triangle
∵ Area triangle = √3
∴ Area shaded = (4/3) π - √3
∵ Area of the shaded part is π k - √3
- Equate the two expressions
∴ π k - √3 = (4/3) π - √3
∴ k = 4/3
* The value of k = 4/3
Answer:
a and b are perpendicular to each other, as are b and d, b and g
Step-by-step explanation:
To check whether two vectors are perpendicular to each other, we need the angle between these vectors to be 90 degrees.
We can find the angle between to vectors a and b from the following relation:
The cosine of the angle between two vectors is equal to the dot product of this vectors divided by the product of vector magnitude.
So
cos(90) = 0, so when the dot product between vectors a and b is 0, it means that these vectors are perpendicular to each other.
Now, for your exercise, let's compute the dot product between these vectors.
-----------
a.b = (3,1,-1).(1,1,4) = 3+1-4 = 0
So a and b are perpendicular to each other.
------------
a.c = (3,1,-1).(1,3,1) = 3+3-1 = 5
a and c are not perpendicular to each other.
--------------
a.d = (3,1,-1).(-1,-3,1) = -3-3-1 = -7
So not perpendicular
---------------
a.g = (3,1,-1).(-3,-1,1) = -9-1-1 = -11
Not
-----------------
b.c = (1,1,4).(1,3,1) = 1+3+4 = 8
Not
------------------
b.d = (1,1,4).(-1,-3,1) = -1 -3 +4 = 0
b.d = 0, so b and d are perpendicular to each other
--------------------
b.g = (1,1,4).(-3,-1,1) = -3-1+4 = 0
b.g = 0, perpendicular
---------------------
c.d = (1,3,1).(-1,-3,1) = -1-9+1 = -9
No
-----------------------
c.g = (1,3,1).(-3,-1,1) = -3-3+1 = -5
No
------------------------
d.g = (-1,-3,1).(-3,-1,1) = 3+3+1 = 7
No