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9514 1404 393
Answer:
x ≈ {-2.80176, -0.339837}
Step-by-step explanation:
Write in terms of sine and cosine:
sec(x) -5tan(x) -3cos(x) = 0 . . . . . . given, subtract 3cos(x)
1/cos(x) -5sin(x)/cos(x) -3cos(x) = 0
Multiply by cos(x). (Note, cos(x) ≠ 0.)
1 -5sin(x) -3cos(x)² = 0
Use the trig identity to write in terms of sin(x).
1 -5sin(x) -3(1 -sin²(x)) = 0
3sin(x)² -5sin(x) -2 = 0 . . . . . . . . quadratic in sin(x)
(sin(x) -2)(3sin(x) +1) = 0 . . . . . . factor the quadratic
Values of sin(x) that make this true are ...
sin(x) = 2 . . . . . true only for complex values of x
sin(x) = -1/3
Then the possible values of x are ...
x = arcsin(-1/3), -π -arcsin(-1/3)
x ≈ {-2.80176, -0.339837} . . . . . rounded to 6 sf
Answer:
Keiko got a better answer on the test on her second test, and you could compare these two ratios as they are written.
Step-by-step explanation:
First: Convert each of the scores into percentages:
How do you convert ratios to percentages? Well, first we have to convert the ratio to a decimal or a fraction. Let's convert it to a fraction. So, 19 out of 25 will become , and 17 out of 20 will become
. To convert a fraction to a percentage:
- Divide the numerator by the denominator:
19 ÷ 25 = 0.76 AND 17 ÷ 20 = 0.85
- Multiply your quotient by 100
0.76 x 100 = 76 AND 0.85 x 100 = 85
- Add the percent sign
76% AND 85%
Now the two quantities are easier to compare. We can obviously see that 85% is bigger [and better] than 76%. So, the ratio that equals 85% - 17 out of 20 - is a better grade.
The second question was: Can you compare these two ratios as they are written? Explain why or why not.
Yes, you can compare these two ratios, just find the [positive] difference between the amount that she scored and the total number of scores that could be gained.
25 - 19 = 6
20 - 17 = 3
Since the equation with 20 and 17 in it has a smaller difference, it is most likely to have a greater value [because that means that Keiko got more right and less wrong, which means a greater mark which is also a greater quantity].
Thanks,
Topic: Quantity Relationships, Quantity Conversions