Check the picture below.
so then γ ≈ 180 - 69 - 43, γ ≈ 68.
A proportional relationship is shown in the table below: what is the slope and what numbers do i graph. ty besties
1 answer:
Answer:
The slope of the line is and the equation of the line is
.
Step-by-step explanation:
From table we understand that slope of the line is constant, that is, for each change of there is one and only change in
, fulfilling the main characteristic of a line and we can determine the slope for every point of the line by means of the following expression:
(1)
Where:
- Initial and final x-coordinates of the line.
- Initial and final y-coordinates of the line.
If we know that and
, then the slope of the line is:
From graph we conclude that x-intercept of the line is . Hence, the equation of the line is
and we proceed to plot the expression with the help of a graphing tool.
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Answer:
Step-by-step explanation:
We want to find the values between the interval (0, 2π) where the tangent line to the graph of y=sin(x)cos(x) is horizontal.
Since the tangent line is horizontal, this means that our derivative at those points are 0.
So, first, let's find the derivative of our function.
Take the derivative of both sides with respect to x:
We need to use the product rule:
So, differentiate:
Evaluate:
Simplify:
Since our tangent line is horizontal, the slope is 0. So, substitute 0 for y':
Now, let's solve for x. First, we can use the difference of two squares to obtain:
Zero Product Property:
Solve for each case.
Case 1:
Add sin(x) to both sides:
To solve this, we can use the unit circle.
Recall at what points cosine equals sine.
This only happens twice: at π/4 (45°) and at 5π/4 (225°).
At both of these points, both cosine and sine equals √2/2 and -√2/2.
And between the intervals 0 and 2π, these are the only two times that happens.
Case II:
We have:
Subtract sine from both sides:
Again, we can use the unit circle. Recall when cosine is the opposite of sine.
Like the previous one, this also happens at the 45°. However, this times, it happens at 3π/4 and 7π/4.
At 3π/4, cosine is -√2/2, and sine is √2/2. If we divide by a negative, we will see that cos(x)=-sin(x).
At 7π/4, cosine is √2/2, and sine is -√2/2, thus making our equation true.
Therefore, our solution set is:
And we're done!
Edit: Small Mistake :)