Laws of Sines with find the angle. Find the measurement indicated. Round your answers to the nearest tenth. Part 3
2 answers:
Answer:
7. A ≈ 60.1°
8. B ≈ 34.0°
9. C ≈ 33.1°
Step-by-step explanation:
7.
The Law of Sines states that for a triangle with lengths a, b, and c and angles A, B, and C: .
Here, we can say that a = 7, b = 8, and B = 82, and we want to find A. Plug these values in:
Solve for A:
A ≈ 60.1°
8.
Again, use the Law of Sines as above:
Solve for B:
B ≈ 34.0°
9.
Use the Law of Sines as above:
Solve for C:
C ≈ 33.1°
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Answer:
There are significant differences among the mean tensile strengths for different temperatures.
Step-by-step explanation:
A one-way ANOVA is used to test whether there is significant difference between the means for more than two groups.
The hypothesis can be defined as follows:
<em>H₀</em>: There is no difference between the means, i.e. .
<em>Hₐ</em>: There is a significant difference between the means, i.e.at least one of the mean is different.
Use MS-Excel to perform the analysis of variance.
Go to Data → Data Analysis → Anova: Single Factor.
A dialog box will open.
Enter the data and enter Alpha as 0.05.
Press OK.
The output is attached below.
The F-value is, 8.40458.
The <em>p</em>-value of the test is, 0.00139.
Decision Rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected.
<em>p</em>-value = 0.00139 < <em>α</em> = 0.05
The null hypothesis will be rejected at 5% level of significance.
Concluding that there are differences among the mean tensile strengths for different temperatures.
You're missing symbols in both of your expressions, but considering the first limit has a value of 10, I suspect you meant to write
(which is true) but unfortunately I am nowhere near as confident about what the second one is supposed to say. So one proof will have to do, unless you come around to editing your question.
The claim,
is to say that, for any given <em>ε</em> > 0, we can find <em>δ</em> (a number that depends on <em>ε</em>) such that whenever |<em>x</em> - 2| < <em>δ</em>, this ensures that |(3<em>x</em> + 4) - 10| < <em>ε</em>.
Roughly speaking: if <em>x</em> is close enough to 2, this translates to <em>f(x)</em> = 3<em>x</em> + 4 being close enough to 10. It's our job to figure out how close <em>x</em> needs to be to 2 in order that <em>f(x)</em> is close enough to 10, where the closeness to 10 is some given threshold.
We want to arrive at the inequality,
|(3<em>x</em> + 4) - 10| < <em>ε</em>
so suppose we work backwards. With some simplification and rewriting, we have
|3<em>x</em> - 6| = |3 (<em>x</em> - 2)| = |3| |<em>x</em> - 2| = 3 |<em>x</em> - 2| < <em>ε</em>
and so
|<em>x</em> - 2| < <em>ε</em>/3
which suggests that we should pick <em>δ</em> = <em>ε</em>/3.
Now for the proof itself:
Let <em>ε</em> > 0 be given, and let <em>δ</em> = <em>ε</em>/3. Then
|<em>x</em> - 2| < <em>δ</em> = <em>ε</em>/3
3 |<em>x</em> - 2| < <em>ε</em>
|3<em>x</em> - 6| < <em>ε</em>
|(3<em>x</em> + 4) - 10| < <em>ε</em>
and this completes the proof of the limit. QED