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1 year ago

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Find the volume of the cone. Round your answer to the nearest tenth. A cone is shown. Its height is 3 meters and the diameter of

the base is 6 meters. The volume of the cone is about a cubic meters.

1 answer:

Effectus [21]1 year ago

6 0

Answer:

The answer to this question should be 28.3

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Find the taylor series for f(x) centered at the given value of a. [assume that f has a power series expansion. do not show that

Bond [772]

Taylor series is $f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }$

To find the Taylor series for f(x) = ln(x) centering at 9, we need to observe the pattern for the first four derivatives of f(x). From there, we can create a general equation for f(n). Starting with f(x), we have

f(x) = ln(x)

$f^{1}(x)= \frac{1}{x} \\f^{2}(x)= -\frac{1}{x^{2} }\\f^{3}(x)= -\frac{2}{x^{3} }\\f^{4}(x)= \frac{-6}{x^{4} }$

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Since we need to have it centered at 9, we must take the value of f(9), and so on.

f(9) = ln(9)

$f^{1}(9)= \frac{1}{9} \\f^{2}(9)= -\frac{1}{9^{2} }\\f^{3}(x)= -\frac{1(2)}{9^{3} }\\f^{4}(x)= \frac{-1(2)(3)}{9^{4} }$

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Following the pattern, we can see that for $f^{n}(x)$ ,

$f^{n}(x)=(-1)^{n-1}\frac{1.2.3.4.5...........(n-1)}{9^{n} } \\f^{n}(x)=(-1)^{n-1}\frac{(n-1)!}{9^{n}}$

This applies for n ≥ 1, Expressing f(x) in summation, we have

$\sum_{n=0}^{\infinite} \frac{f^{n}(9) }{n!} (x-9)^{2}$

Combining ln2 with the rest of series, we have

$f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }$

Taylor series is $f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }$

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3 0

1 year ago

What is the probability that the system does not have a type 2defect?b.What is the probability that the system has both type 1 a

Lana71 [14]

Answer:

a. 0.93 b. 0.06 c. 0.05

Step-by-step explanation:

Probability is commonly known as the chance of success of a particular event. The probability of failure of the event can also be estimated.

(a) Probability of not having type 2 defect is: $P(A_{2}^{'})$ $= 1 - P(A_{2})$ = 1 - 0.07 = 0.93

(b) Probability of having type 1 and 2 defects is: $P(A_{1} n A_{2}) = P(A_{1}) + P(A_{2}) - P(A_{1}U A_{2}) = 0.12 + 0.07 - 0.13 = 0.06$

(c) probability pf having both type 1 and type 2 defects but not type 3 defect is:

$P(A_{1} + A_{2} + A^{'} _{3}) = P(A_{1} n A_{2}) - P(A_{1} n A_{2} n A_{3}) = 0.06 - 0.01 = 0.05$

3 0

2 years ago

What can graphs be used for?

enot [183]

Answer:

D. All of the above.

Step-by-step explanation: Please brainliest if correct!

7 0

2 years ago

Estimate the value of √70 to the nearest integer. Describe your process.

Anastaziya [24]

Answer:

$\large\boxed{\sqrt{70}\approx8}$

Step-by-step explanation:

$\text{We know:}\\\\\sqrt{a}=b\iff a^2=b,\ \text{for}\ a\geq0\ \wedge\ b\geq0\\\\5^2=25$

5 0

3 years ago

Given g(x) = -x – 4, find g(-5).

riadik2000 [5.3K]

The value of g(-5) from the given. function; g(x) = -x – 4 is; g(-5) = 1

<h3>Evaluation of functions</h3>

The given function is;

g(x) = -x – 4

Hence, the value of g(-5) can be obtained by substituting -5 for x in the function as follows;

g(-5) = -(-5) -4

g(-5) = 5 -4

g(-5) = 1.

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2 years ago

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