Find the geometric mean between each pair of numbers.
1 answer:
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From an absolute value inequality, we have that:
- The minimum diameter is 6.46 mm.
- The maximum diameter is 6.54 mm.
- The absolute value measures the <u>distance of a point or a function to the origin</u>.
- One example of inequality is:
Which has solution:
In this problem:
- Bolts with a diameter of 6.5 mm, with a tolerance of 0.04 mm, thus the <u>absolute value of the difference of the diameter D and 6.5 has to be of at most 0.04</u>, that is:
Applying the solution:
- The minimum diameter is 6.46 mm.
- The maximum diameter is 6.54 mm.
A similar problem is given at brainly.com/question/24835634
Answer: Sample size required is 35
Step-by-step explanation:
The attachment below shows the calculations.
Step-by-step explanation:
In this case we have:
Δx = 3/n
b − a = 3
a = 1
b = 4
So the integral is:
∫₁⁴ √x dx
To evaluate the integral, we write the radical as an exponent.
∫₁⁴ x^½ dx
= ⅔ x^³/₂ + C |₁⁴
= (⅔ 4^³/₂ + C) − (⅔ 1^³/₂ + C)
= ⅔ (8) + C − ⅔ − C
= 14/3
If ∫₁⁴ f(x) dx = e⁴ − e, then:
∫₁⁴ (2f(x) − 1) dx
= 2 ∫₁⁴ f(x) dx − ∫₁⁴ dx
= 2 (e⁴ − e) − (x + C) |₁⁴
= 2e⁴ − 2e − 3
∫ sec²(x/k) dx
k ∫ 1/k sec²(x/k) dx
k tan(x/k) + C
Evaluating between x=0 and x=π/2:
k tan(π/(2k)) + C − (k tan(0) + C)
k tan(π/(2k))
Setting this equal to k:
k tan(π/(2k)) = k
tan(π/(2k)) = 1
π/(2k) = π/4
1/(2k) = 1/4
2k = 4
k = 2
