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A rectangular block of aluminum30 mm×60 mm×90 mm is placed in apressurechamber and subjected to a pressure of 100 MPa. If the modulus of elasticity is 75GPa andPoisson's ratio is 0.35, what will be the decrease in the longest side of the block, assuming thatthe material remains within the linear elastic region? What will be the decrease in the volume oftheblock? g

Answers

Answer 1

Answer:

Answer:

$\Delta V = - 216.415 mm^3$

Step-by-step explanation:

we know that change is length is calculated by following strain relation

$\Delta L = L * \epsilon_x$

where strain is given as

$\epsilon_x = (\sigma_x - \nu(\sigma_y + \sigma_z))/(E)$

$\epsilon_x = (-10^8 - 0.35 ( -10^8 -10^8 (N/m^2)))/(7.5 * 10^10)$

$\epsilon_x = -4.453 * 10^(-4)$

plugging strain value in change in length formula

$\Delta L = 90 * -4.453 * 10^(-4) = - 0.04008 mm$

calculate the length on the longer side

$L_(long) = L = \delta L$

= 90 - 0.04008 = 89.95 mm

intial volume $= 90*60*30 = 1.62 * 10^5 mm^3$

change in volume

$\Delta V =V ( \epsilon_x +\epsilon_y + \epsilon_z )$

$\Delta V = 1.62 * 10^5 (-4.453 - 4.453 - 4.453) * 10^(-4)$

$\Delta V = - 216.415 mm^3$

Answer 2

Answer:

Final answer:

Calculations involve determining strain from given pressure and Modulus of Elasticity and then determining the decrease in length of the longest side and total volume of the aluminum block when subjected to pressure.

Explanation:

The question is about applying principles of material science under conditions of pressure. The decrease in length and volume of a rectangular block of aluminum when subjected to pressure can be calculated by using the concepts of Modulus of Elasticity and Poisson's Ratio.

First, the strain experienced can be calculated using the formula:

Strain = Pressure / Modulus of Elasticity

Substituting the given values, the strain is found. The change in the longest side (90mm) is calculated by multiplying the original length by the strain. The volume change is calculated using the formula:

Change in volume = Original volume * (-3) * strain

Where original volume is = 30mm * 60mm * 90mm. Here the negative indicates a decrease. This will provide the decrease in the longest side and the total volume of the block when subjected to the given pressure.

Learn more about Material Deformation under Pressure here:

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A recipe requires 3/4 cups of sugar for every 14 cookies how many cups of sugar will be needed to bake 168 cookies

Answers

Answer:

9 cups

Step-by-step explanation:

3/4 cups of sugar for 14 cookies

There are 168÷14 = 12 set of 14 cookies in 168

So we need 12 times 3/4 sugar

12 × 3/4 = 9 cups of sugar needed

Answer:

Step-by-step explanation:

ratio problem

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According to a recent survey of households, the poll found that 41 % of the adults watching a special event on TV enjoyed the commercials more than the event itself. Consider a random sample of nine adults who watched the special event. Complete parts a through d below.a. For this experiment, define the event that represents a "success".
i. A success is an adult who did not enjoy the commercials more than the event on TV itself.
ii. A success is an adult who enjoyed the commercials more than the event on TV itself.

b. What is the probability that less than four people enjoyed the commercials more than the event?
c. What is the probability that exactly six or seven people enjoyed the commercials more than the event?
d. What is the mean for this binomial distribution?

Answers

Answer:

a) ii. A success is an adult who enjoyed the commercials more than the event on TV itself.

b) P(X < 4) = 0.4576

c) P(X=6) + P(X=7) = 0.1064

d) Mean = 3.69

Step-by-step explanation:

a) The population parameter stated in the survey is the event that represents a success. Hence, A success is an adult who enjoyed the commercials more than the event on TV itself.

b) The probability that less than four people enjoyed the commercials more than the event

This is a binomial distribution problem

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = number of adults sampled = 9

x = Number of successes required = number of people that enjoyed the commercial more than the event on TV = less than 4

p = probability of success = probability of enjoying the commercial more than the event = 0.41

q = probability of failure = probability of NOT enjoying the commercial more than the event = 1 - 0.41 = 0.59

P(X < 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) = 0.00866299582 + 0.05418043148 + 0.15060323326 + 0.24419846296

P(X < 4) = 0.45764512351 = 0.4576

c) The probability that exactly six or seven people enjoyed the commercials more than the event = P(X=6) + P(X=7)

Using the Binomial distribution formula

P(X=6) + P(X=7) = 0.08194801935 + 0.02440582659 = 0.106353846 = 0.1064

d) Mean = expected value of people that would enjoy the commercial more than the main event = np = 9×0.41 = 3.69

Hope this Helps!!!

Answer:

a) ii. A success is an adult who enjoyed the commercials more than the event on TV itself.

b) $P(X=0)=(9C0)(0.41)^0 (1-0.41)^(9-0)=0.0087$

$P(X=1)=(9C1)(0.41)^1 (1-0.41)^(9-1)=0.0.54$

$P(X=2)=(9C2)(0.41)^2 (1-0.41)^(9-2)=0.151$

$P(X=3)=(9C3)(0.41)^3 (1-0.41)^(9-3)=0.244$

And adding we got:

$P(X<4) = P(X\leq 3) = P(X=0)+P(X=1) +P(X=2)+P(X=3)=0.0087+0.054+0.151+0.244=0.458$

c) $P(6 \leq X \leq 7)$

$P(X=6)=(9C6)(0.41)^6 (1-0.41)^(9-6)=0.082$

$P(X=7)=(9C7)(0.41)^7 (1-0.41)^(9-7)=0.0244$

And adding we got:

$P(6 \leq X \leq 7)=0.082+0.0244=0.106$

d) $\mu = np =9*0.41=3.69$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=9, p=0.41)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^(n-x)$

Where (nCx) means combinatory and it's given by this formula:

$nCx=(n!)/((n-x)! x!)$

Part a

The success on this case is:

ii. A success is an adult who enjoyed the commercials more than the event on TV itself.

Part b

For this case we want this probability:

$P(X<4) = P(X\leq 3) = P(X=0)+P(X=1) +P(X=2)+P(X=3)$

And we can find the individual probabilities and we got:

$P(X=0)=(9C0)(0.41)^0 (1-0.41)^(9-0)=0.0087$

$P(X=1)=(9C1)(0.41)^1 (1-0.41)^(9-1)=0.0.54$

$P(X=2)=(9C2)(0.41)^2 (1-0.41)^(9-2)=0.151$

$P(X=3)=(9C3)(0.41)^3 (1-0.41)^(9-3)=0.244$

And adding we got:

$P(X<4) = P(X\leq 3) = P(X=0)+P(X=1) +P(X=2)+P(X=3)=0.0087+0.054+0.151+0.244=0.458$

Part c

For this case we want this probability:

$P(6 \leq X \leq 7)$

$P(X=6)=(9C6)(0.41)^6 (1-0.41)^(9-6)=0.082$

$P(X=7)=(9C7)(0.41)^7 (1-0.41)^(9-7)=0.0244$

And adding we got:

$P(6 \leq X \leq 7)=0.082+0.0244=0.106$

Part d

For this case the mean is given by:

$\mu = np =9*0.41=3.69$

-8x-x=x-4x plz do it step by step ans show me

Answers

Answer: 3x - x = 0

Step-by-step explanation:

1.Simplify -8x - x to -9x.

2. Simplify x - 4x to -3x.

3. Divide both sides by -3.

4. Subtract x from both sides.

5. Simplify 3x - x to 2 x.

6. Divide both sides by 2.

The answer is 3x-x=0

Q #...10 somebody help me

Answers

The slope of a line can be found, given two points, as follows:

$P_(1)(-5.5,6.1) \n \n P_(2)(-2.5,3.1) \n \n m=(y_(2)-y_(1))/(x_(2)-x_(1)) \n \n m=(3.1-6.1)/(-2.5-(-5.5))=-1$

So this slope tells us the direction of a line and represents the vertical change divided by the horizontal change.

It is -1, at least thats what i got i hope this helped

Which equation represents the polar form of x2 + (y + 4)2 = 16?

Answers

The polar form of equation is r = -8sinθ.

What is polar form of complex number?

The combination of the complex number's modulus r and argument is how complex numbers are shown in polar form z = r cosθ + i r sinθ = r (cosθ + i sinθ), is the polar form of a complex number with coordinates (x, y). In the coordinate system, polar coordinates of real and imaginary numbers are used to represent the polar form.

Given x² + (y + 4)² = 16

here The following is the relationship between (r, θ) and (x, y) if they are in Cartesian form:

x = rcosθ, y = rsinθ and r² = x² + y² ad tanθ = y/x

x² + (y + 4)² = 16

x² + y² + 16 + 8y = 16

x² + y² + 8y = 0

r² + 8rsinθ = 0

r(r + 8sinθ) = 0

r =0 and r = -8sinθ

Hence the polar form of equation is r = -8sinθ.

Learn more about polar form of complex number;

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