The first five terms of the sequence are -8, -5/8, 0, 5/64 and 16/125
<h3>Recursive form of a sequence</h3>
Given the nth term of a sequence expressed as:
an= n^2-9/ n^3
Determine the first five terms
If n = 1
a1 = 1^2-9/ 1^3
a1 = -8/1
a1 = -8
If n = 2
a2 = 2^2-9/ 2^3
a2 = -5/8
If n = 3
a3= 3^2-9/ 1^3
a3 = 9-9/3^3
a3 = 0
If n = 4
a4 = 4^2-9/ 4^3
a4= 16-9/64
a4 = 5/64
If n = 5
a5 = 5^2-9/ 1^3
a5 = 25-9/5^3
a5 = 16/125
Hence the first five terms of the sequence are -8, -5/8, 0, 5/64 and 16/125
Learn more on recursive function here: brainly.com/question/489759
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To solve these type of problems you need to use the pythagoras theorem ⇨ Hypotenuse² = Base² + Altitude².
Here,
- Altitude = 1.6 cm.
- Base = 1.2 cm
- Hypotenuse = x
Now, let's solve for x.
Hypotenuse² = Base² + Altitude²
x² = (1.2)² + (1.6)²
x² = 1.44 + 2.56
x² = 4
x = √4
x = <em><u>2</u></em><em><u>.</u></em>
- So, the value of x is <em><u>2</u><u> </u><u>cm.</u></em>
<h3>
<u>NOTE</u><u> </u><u>:</u><u>-</u></h3>
- Pythagoras theorem can be used only in the cases of right-angled triangles. Here, it's given that the triangle is right angled so we can use this theorem.
- To solve the squares if decimals, take them as whole numbers & then just add the decimal points. For example, ⇨ for (1.2)², take it as 12² , then multiply 12 by 12, you'll get 144. Now, add the decimal place accordingly ⇨ 1.44 . So, (1.2)² = 1.44.
Answer:
The pink box
Step-by-step explanation:
Answer:
a) 74.0353 < u < 74.0367
b) 74.036 < u
Step-by-step explanation:
Given:
- Sample size n = 15
- Standard deviation s.d = 0.0001 in
- Sample mean x_bar = 74.036
Find:
A) Calculate the 99% two-sided confidence interval on the true mean piston diameter.
Solution:
- For 99% CI, We have a = 0.01 , and Z_a/2 = 2.58
------> (x_bar - Z_a/2*s.d / sqrt(n)) < u < (x_bar + Z_a/2*s.d / sqrt(n))
------> (74.036 - 2.58*0.0001 / sqrt(15)) < u < (74.036 + 2.58*0.0001 / sqrt(15))
------> 74.0353 < u < 74.0367
Find:
B) Calculate the 95% one-sided lower confidence interval on the true mean piston diameter.
Solution:
- For 95% lower CI, We have a = 0.05 , and Z_a = 1.645
------> (x_bar - Z_a/2*s.d / sqrt(n)) < u
------> (74.036 - 1.645*0.0001 / sqrt(15)) < u
------> 74.036 < u