The standard diameter of a golf ball is 42. 67 mm. A golf ball factory does quality control on the golf balls it manufactures. G
1 answer:
Discrepancy is the difference of a the value from the uniform distribution. The function for the given situation can be given as,
Hence the option 2 is the correct option.
Given information-
The standard diameter of the golf ball is 42.67 mm.
The discrepancy in the diameter is 0.004 mm.
<h3>What is discrepancy?</h3>Discrepancy is the difference of a the value from the uniform distribution.
Suppose the discrepancy is x mm.
If the discrepancy in diameter is more than 0. 004 mm, the production is stopped.
As the discrepancy of 0.004 mm or more is stopped the production, we have to subtract the diameter to the discrepancy .
Thus the function for the situation can be given as,
Rearrange for the x,
Thus the function for the given situation can be given as,
Hence the option 2 is the correct option.
Learn more about the discrepancy here;
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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 :)