Calculation: One score is 20. Two score is 40. Three score and 5 is 65.
1 answer:
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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 :)
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The length of the legs XY and YZ is equal to 39 units.
<h3>What is a triangle?</h3>A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°. An isosceles triangle has two sides out of three equal.
A.) The value of n can be found by equating XY and XZ together,
XY = XZ
9n + 12 = 15n - 6
12 + 6 = 15n - 9n
18 = 6n
n = 3
Hence, the value of n is 3.
The length of different legs of the triangle is,
B.) XY = 9n + 12 = 9(3) + 12 = 27 + 12 = 39
C.) YZ = 15n - 6 = 15(3) - 6 = 45 - 6 = 39
Hence, the length of the legs XY and YZ is equal to 39 units.
Learn more about Triangle:
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Answer:
5.5 days (nearest tenth)
Step-by-step explanation:
<u>Given formula:</u>
= initial mass (at time t=0)
- N = mass (at time t)
- k = a positive constant
- t = time (in days)
Given values:
- k = 0.125
Half-life: The <u>time</u> required for a quantity to reduce to <u>half of its initial value</u>.
To find the time it takes (in days) for the substance to reduce to half of its initial value, substitute the given values into the formula and set N to half of the initial mass, then solve for t:
Therefore, the substance's half-life is 5.5 days (nearest tenth).
Learn more about solving exponential equations here:
