All categories

3 years ago

Calculate the second moment of area of a 4-in-diameter shaft about the x-x and yy axes, as shown.

1 answer:

6 0

Second moment of area about an axis along any diameter in the plane of the cross section (i.e. x-x, y-y) is each equal to (1/4)pi r^4.
The second moment of area about the zz-axis (along the axis of the cylinder) is the sum of the two, namely (1/2)pi r^4.

The derivation is by integration of the following:
int int y^2 dA
over the area of the cross section, and can be found in any book on mechanics of materials.

You might be interested in

What is 50x50x50x50? I really need help.

tensa zangetsu [6.8K]

Answer:

6,250,000

50x50x50x50 is 6,250,000

4 0

3 years ago

You plan on financing a new road bike for $2,500. The bike shop offers a 13.5% APR for a 24 month loan. Use this information, an

Mila [183]

This question can be approached using the present value of annuity formula. The present value of annuity is given by $PV=P\left( \frac{1-\left(1+ \frac{r}{t} \right)^{-nt}}{ \frac{r}{t} } \right)$ , where: PV is the present value/amount of the loan, P is the periodic (monthly in this case) payment, r is the APR, t is the number of payments in one year and n is the number of years.

Given that the financing is for a new road bike of $2,500 and that the bike shop offers a 13.5% APR for a 24 month loan.

Thus, PV = $2,500; r = 13.5% = 0.135; t = 12 payments (since payment is made monthly); n = 2 years (i.e. 24 months)

Thus,

 $2500=P\left( \frac{1-\left(1+ \frac{0.135}{12} \right)^{-2\times12}}{ \frac{0.135}{12} } \right) \\ \\ =P\left( \frac{1-\left(1+ 0.01125 \right)^{-24}}{ 0.01125 } \right)=P\left( \frac{1-\left(1.01125 \right)^{-24}}{ 0.01125 } \right) \\ \\ =P\left( \frac{1-0.764531}{ 0.01125 } \right)=P\left( \frac{0.235469}{ 0.01125 } \right)=20.9306P \\ \\ \Rightarrow P= \frac{2500}{20.9306} =119.44$

Therefore, his monthly payment is $119.44

6 0

3 years ago

Explain why the prices were the same in 13 and 14

kifflom [539]

Answer:

Step-by-step explanation:

8 0

3 years ago

44/12 in simplest form

NeTakaya

The fraction 44/12 is equivalent1 to 3 2/3.
This fraction is a IMPROPER FRACTION once the absolute value of the top number or numerator (44) is greater than the absolute value of the bottom number or denomintor (12). So, the equivalent fraction is a MIXED NUMBER which is made up of a whole number (3) and proper fraction (2/3).
The fraction 44/12 is equal to 44÷12 and can also be expressed in decimal form as 3.666667.

5 0

3 years ago

Read 2 more answers

A recent survey by the New Statesman on British social attitudes asked respondents if they believe that inequality is too large.

Reika [66]

Answer:

(a) The probability that in a a sample of six British citizens two believe inequality is too large is 0.0375.

(b) The probability that in a a sample of six British citizens at least two believe inequality is too large is 0.9944.

Step-by-step explanation:

The random variable X can be defined as the number of British citizens who believe that inequality is too large.

The proportion of respondents who believe that inequality is too large is, p = 0.74.

Thus, the random variable X follows a Binomial distribution with parameters n and p = 0.74.

The probability mass function of X is:

$P(X=x)={n\choose x}\ 0.74^{x}(1-0.74)^{n-x};\ x=0,1,2,3...n$

(a)

Compute the probability that in a a sample of six British citizens two believe inequality is too large as follows:

$P(X=2)={6\choose 2}\ 0.74^{2}(1-0.74)^{6-2}\\=15\times 0.5476\times 0.00456976\\=0.03753600864\\\approx 0.0375$

Thus, the probability that in a a sample of six British citizens two believe inequality is too large is 0.0375.

(b)

Compute the probability that in a a sample of six British citizens at least two believe inequality is too large as follows:

P (X ≥ 2) = 1 - P (X < 2)

= 1 - P (X = 0) - P (X = 1)

$=1-[{6\choose 0}\ 0.74^{0}(1-0.74)^{6-0}]-[{6\choose 1}\ 0.74^{1}(1-0.74)^{6-1}]\\\\=1-[1\times 1\times 0.000308915776]-[6\times 0.74\times 0.0011881376]\\\\=1-0.00031-0.0053\\\\=0.99439\\\\\approx 0.9944$

Thus, the probability that in a a sample of six British citizens at least two believe inequality is too large is 0.9944.

(c)

Compute the probability that in a a sample of four British citizens none believe inequality is too large as follows:

$P(X=0)={4\choose 0}\ 0.74^{0}(1-0.74)^{4-0}\\=1\times 1\times 0.00456976\\=0.00456976\\\approx 0.0046$

Thus, the probability that in a a sample of four British citizens none believe inequality is too large is 0.0046.

8 0

3 years ago