Solve graphically this linear system of equations
1 answer:
Answer:
(3,-1)
Step-by-step explanation:
The given equations are :
x = 3 ..(1)
y+1 = 0 ....(2)
We need to solve the equations graphically. x = 3 means draw a line parallel to y axis.
For y+1=0
y = -1
Draw a line parallel to the negative x axis. The attached figure shows the graph for the given equations. The solution is (3,-1).
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Answer:
Step-by-step explanation:
We will prove by mathematical induction that, for every natural n,
We will prove our base case (when n=1) to be true:
Base case:
As stated in the qustion,
Inductive hypothesis:
Given a natural n,
Now, we will assume the inductive hypothesis and then use this assumption, involving n, to prove the statement for n + 1.
Inductive step:
Let´s analyze the problem with n+1 stones. In order to move the n+1 stones from A to C we have to:
- Move the first n stones from A to C (
moves).
- Move the biggest stone from A to B (1 move).
- Move the first n stones from C to A (
- Move the biggest stone from B to C (1 move).
- Move the first n stones from A to C (
Then,
.
Therefore, using the inductive hypothesis,
With this we have proved our statement to be true for n+1.
In conlusion, for every natural n,
Answer:
csc θ = /6
sec θ = /7
tan θ = 6/7
Step-by-step explanation:
The first thing to do will be to compute the length of the hypotenuse using the Pythagoras theorem;
6^2 +7^2 = hypotenuse^2
hypotenuse =
csc θ = 1/sinθ
sinθ = opposite side/hypotenuse
= 6/
csc θ = /6
sec θ = 1/cosθ
cosθ = adjacent side/hypotenuse
sec θ = hypotenuse/adjacent side
= /7
tan θ = Opposite side/adjacent side
= 6/7