The 3rd degree Taylor polynomial for cos(x) centered at a = π 2 is given by, cos(x) = − (x − π/2) + 1/6 (x − π/2)3 + R3(x). Using this, estimate cos(86°) correct to five decimal places.
Answers
Answer:
The cosine of 86º is approximately 0.06976.
Step-by-step explanation:
The third degree Taylor polynomial for the cosine function centered at is:
The value of 86º in radians is:
Then, the cosine of 86º is:
The cosine of 86º is approximately 0.06976.
Final answer:
We estimate the cosine of 86 degrees by first converting 86 degrees to radians (approximately 1.50098) and substituting this into the Taylor polynomial. The result is -0.08716
Explanation:
To calculate the cosine of 86 degrees using the Taylor polynomial, we first have to convert the degrees to radians, as the Taylor polynomial is based on the radian definition. The conversion yields approximately 1.50098 radians.
Then, we substitute this value into the Taylor polynomial. We ignore R3(x) as it represents the remainder and tends to zero as x approaches π/2. So, cos(86°) ≈ - (1.50098 - π/2) + 1/6 * (1.50098 - π/2)³. Computing this gives us an estimate of cos(86°) = -0.08716 to five decimal places.
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Related Questions
Which functions have a maximum value greater than the maximum of the function g(x) = –(x + 3)2 – 4? Check all that apply. f(x) = –(x + 1)2 – 2 f(x) = –|x + 4| – 5 f(x) = –|2x| + 3
-4 1/4 as a decimal number HELP!!!
Is this right? please correct me if I'm wrong.
14) Centroid R is found in TriangleABC below with BZ = 42, CA = 40 and RY = 16. Determine theperimeter of Triangle ARZ.
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4
B.
6
C.
12
D.
7
Answers
Answer:
the answer is C. 12
Step-by-step explanation:
Answers
Answer:
see below
Step-by-step explanation:
9 x 8 = (10 x 8) - ( blank x 8) =80 - blank = blank
We are replacing 9 with 10 minus something
9 = 10 -1
9 x 8 = (10 x 8) - ( 1 x 8)
80 - 8
72
Answers
The perimeter of the quadrilateral is 4z 16.
What is Perimeter?
To calculate the perimeter, or distance around the rectangle, sum all four side lengths. This may be done quickly by adding the length and breadth and then multiplying the total by two because each side length has two lengths. The perimeter formula is perimeter=(length+width)2.
The 4 sides of quadrilateral is z-4.
Now, the Perimeter of quadrilateral
= (z-4) + (z-4) + (z-4) + (z-4)
= 4 (z-4)
= 4z- 16
Thus, the perimeter is 4z- 16.
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Answer:
4z-16 units
Step-by-step explanation:
The perimeter of the rectangle is 4z-16 units.
THE TABLE CAN YOU USE TO HELP YOU FIND THE Y-INTERCEPT?
B) WHATS THE SLOPE OF THIS TABLE? USE THE SLOPE FORMULA.
C) WHAT IS THE EQUATION OF THIS TABLE? USE YOUR SLOPE (M) AND Y-INTERCEPT (B) TO WRITE THE EQUATION IN Y=MX+B FORM.
Answers
Answer:
WHERE IS THE TABLES HM???
B. 173.9 mg less than < mu μ less than <196.1 mg
C. 173.8 mg less than < mu μ less than <196.2 mg
D. 173.7 mg less than < mu μ less than <196.3 mg
Answers
Answer:
option (C) 173.8 mg less than < mu μ less than <196.2 mg
Step-by-step explanation:
Data provided ;
number of sample, n = 12
Mean = 185 milligram
standard deviation, s = 17.6 milligrams
confidence level = 95%
α = 0.05 [for 95% confidence level]
df = n - 1 = 12 - 1 = 11
Now,
Confidence interval = Mean ± E
here,
E is the margin of error =
also,
=
= 2.201 [ from standard t value table]
Thus,
E =
or
E = 11.182 milligrams ≈ 11.2 milligrams
Therefore,
Confidence interval:
Mean - E < μ < Mean + E
or
185 - 11.2 < μ < 185 + 11.2
or
173.8 < μ < 196.2
Hence,
the correct answer is option (C) 173.8 mg less than < mu μ less than <196.2 mg
Final answer:
To construct a confidenceinterval for the population mean cholesterol content of all chicken eggs with a 95% confidence level, we use the sample mean, standard deviation, and sample size to calculate the margin of error. The confidence interval is then constructed by subtracting the margin of error from the sample mean and adding it to the sample mean.
Explanation:
To construct a confidenceinterval for the population mean cholesterol content of all chicken eggs, we first need to find the margin of error. The margin of error depends on the samplemean, standard deviation, sample size, and the desired level of confidence. In this case, we have a sample mean of 185 mg, a standard deviation of 17.6 mg, and a sample size of 12. Since we want a 95% confidence interval, we use a z-score of 1.96. The margin of error is then calculated as 1.96 * (17.6/sqrt(12)), which is approximately 9.61 mg. We can then construct the confidenceinterval by subtracting the margin of error from the sample mean and adding it to the sample mean. Therefore, the 95% confidence interval for the true mean cholesterol content of all such eggs is 175.9 mg to 194.1 mg.
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