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The moment of inertia for rotation about the z axis is  \(I & =\frac{a^2 M}{3}\).

A triangular prism of mass m, whose two ends are equilateral triangles.

Two ends are equal.

The xy plane with side 2a, is centered on the origin with its axis along the z axis.

Find the moment of inertia for rotation the z-axis.

It is divide into 4 triangles with side 'a' k one side is 3cm.

\($$\begin{aligned}& I_{\text {BiG }}=16 I_{\text {small }} . \\& I_{\text {BIG }}=4 I_{\text {small }}+P_{A T}\end{aligned}$$\)

It is fact that the big triangle is made up from four small triangles. connected with parallel axis theorem.

Now, we have to find the distance from the center of mas of small outer triangles to the origin. so, that it is PAT.

\($$\therefore z=2 \sqrt{x^2-\frac{a}{2} ^2}$$\)

\($$\begin{aligned}& =2 \sqrt{\left(\frac{a}{\sqrt{3}}\right)^2-\frac{a^2}{4}} \\& =2 \sqrt{\frac{a^2}{3}-\frac{a^2}{4}} \\I_{\text {Big }} & =\frac{\sqrt{3}}{3} a \cdot \\& \left.=4 I_{\text {small }}+3 m \frac{\sqrt{3}}{3} a\right)^2 \\I_{\text {Big }} & =4 I_{\text {small }}+\frac{3 m}{4} \frac{1}{3} a^2 \\& =\frac{a^2}{4}\end{aligned}$$\)

⇒ Now, by using the \($I_{\text {Big }}=I$\)

⇒\(I & =4\left(\frac{\sqrt{2}}{16}\right)+\frac{a^2 M}{4} \\\)

⇒\(4 I & =I+a^2 m\)

⇒\(4 I-I & =a^2 m \\\)

⇒\(3 I & =a^2 M . \\\)

⇒\(I \quad & =\frac{a^2 M}{3}\)

Therefore, the moment of inertia is \(I & =\frac{a^2 M}{3}\).

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Answer:

102 -52 =50 the age is 50 ufdhdgrthui

Let Rosemary's age = X

and Hannah's age = Y

According to question,

X + Y = 102           … (i)

X - Y = 52             … (ii)

Adding the equation (i) + (ii)

We get,

2X = 154

X = 77

now putting the value of X in Equation (ii)

We get,

77 - Y = 52

Y = 77-52

Y = 25

Hence, Rosemary's age =77 and Hannah's age = 25

Answer:

1/2=10

Step-by-step explanation:

it depends upon the area of the triwngle

If the length of the rectangle be (3x+2) units and width (4x+10)units then the area of the rectangle be \($x=-\frac{2}{3}, x=-\frac{5}{2}$$\).

The region enclosed by an object's shape is referred to as the area. The area of the shape is the area that the figure or any other two-dimensional geometric shape occupies in a plane.

A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.

Let the length of the rectangle be (3x + 2) units and width of the rectangle be (4x + 10)units.

Area of rectangle = length × breadth

= (3x +2) × (4x +10)

simplifying the above equation, we get

= (3x) × (4x +10) + 2(4x +10)

= 12x² + 30x +8x +20

12x² + 38x + 20 = 0

simplifying the above equation, we get

By using quadratic equation, then

\($x_{1,2}=\frac{-38 \pm \sqrt{38^2-4 \cdot 12 \cdot 20}}{2 \cdot 12}$$\)

simplifying the above equation, we get

\($$\begin{gathered}x_{1,2}=\frac{-38 \pm 22}{2 \cdot 12}\end{gathered}$$\)

Separate the solutions, we get

\($$\begin{aligned}& x_1=\frac{-38+22}{2 \cdot 12}, x_2=\frac{-38-22}{2 \cdot 12} \\& x=\frac{-38+22}{2 \cdot 12}:-\frac{2}{3} \\& x=\frac{-38-22}{2 \cdot 12}:-\frac{5}{2}\end{aligned}$$\)

The solutions to the quadratic equation are:

\($x=-\frac{2}{3}, x=-\frac{5}{2}$$\)

The complete question is:

Find the area of rectangle with length (3x+2) units and width (4x+10)units.

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The domain of the function, is : Domain → (- ∞ , + ∞) and the inverse of the function is y = 3 + √x.

Domain is the set of {x} - values for which a function {y - values} exists. It is one of the important parameter while defining the characteristics of a function.

Given is the function as -

f(x) = (x - 3)²

{ 1 } -

The domain of the function f(x) = (x - 3)².

The function has no undefined points. So, we can write the domain as -

Domain → (- ∞ , + ∞)

{ 2 } -

The inverse of the function f(x) = (x - 3)².

We have -

f(x) = (x - 3)²

y = (x - 3)²

x = (y - 3)²

y - 3 = √x

y = 3 + √x

Therefore, the domain of the function, is : Domain → (- ∞ , + ∞) and the inverse of the function is y = 3 + √x.

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9514 1404 393

Answer:

  D. None

Step-by-step explanation:

If one of these is true for all values of k, we can see it for k=1.

 r = 1² +3·1 +9 = 13

This value is not even, not divisible by 3, and not the square of an integer.

None of the offered statements about r is true.

\(97.\)

Step-by-step explanation:

By using Pythagoras theorem

AC² = AB² + BC².

Let AB = 72 and BC = 65.

AC² = 72² + 65²

AC² = 5184 + 4225

AC² = 9409.

AC = √9409

AC = 97.

Answer:

148.5 ft²

Step-by-step explanation:

bottom area = (10(8.7)(0.5) = 43.5 ft²

side area = 3(10)(7)(0.5) = 105 ft²

43.5 + 105 = 148.5 ft²

The z score corresponding to the sample is -6.25

The formula for calculating the z-score is expressed as

z = x- μ/σ

Given the following parameters

x = 22 (sample size)

Mean  μ = 72

standard deviation σ = 8

Substitute

z = 22-72/8

z = -50/8

z = -6.25

Hence the z score corresponding to the sample is -6.25

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Answer: 39

Step-by-step explanation:

30-8=22

22/2=11

11+2=13

13 times 3 =39

Answer:

\(\large\boxed{\mathtt{9^{8}}}\)

Step-by-step explanation:

\(\textsf{For this problem, we are asked to simplify the given expression.}\)

\(\textsf{Let's begin by understand an important rule for problems like these.}\)

\(\mathtt{9^{3} \times 9^{5} = 9^{?}}\)

\(\large\underline{\textsf{We should remember that;}}\)

\(\textsf{When exponents multiply, they \underline{add}.}\)

\(\large\underline{\textsf{Why?}}\)

\(\textsf{If not, then the answer will be incorrect. Let's identify why in an example.}\)

\(\large\underline{\textsf{Bad Example:}}\)

\(\mathtt{2^{2} \times 2^{5} = 2^{2 \times 5 =10}}\)

\(\textsf{This means that;}\)

\(\mathtt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \neq 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2.}\)

\(\large\underline{\textsf{Good Example:}}\)

\(\mathtt{2^{2} \times 2^{5} = 2^{2+5=7}}\)

\(\textsf{This means that;}\)

\(\mathtt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2.}\)

\(\textsf{Let's follow the good example!}\)

\({\mathtt{9^{3} \times 9^{5} = 9^{3 + 5=8}}\)

\(\textsf{This means that;}\)

\(\mathtt{9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9 = 9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9 \times 9.}\)

\(\large\boxed{\mathtt{9^{8}}}\)

\(\huge\text{Hey there!}\)

\(\mathsf{9^3 \times 9^5}\\\mathsf{= 9\times 9 \times 9\ \boxed{\times}\ 9\times 9\times 9 \times 9 \times 9}\\\mathsf{= 81\times 9\ \boxed{\times}\ 81\times81\times9}\\\mathsf{= 729\ \boxed{\times}\ 6,561\times 9}\\\mathsf{= 729\ \boxed{\times}\ 59,049}\\\mathsf{= 43,046,721}\\\mathsf{= 9^3 \times 9^5 \rightarrow 9^{3 + 5}\rightarrow 9^8}\)

\(\huge\text{Therefore your answer should be:}\)

\(\huge\boxed{\mathsf{9^8}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Step-by-step explanation:

9,7,-1,-2..................

Answer:

9, 9, 9, 9, 7, 7, 7, 7, |-2|, |-2|, |-2|, |-2|, -1, -1, -1, -1

Step-by-step explanation:

any numbers inside |__| will equal positive, even if it's a negative number inside of it.

Answer:

Yes, there will be with a probability of 0.4096

Step-by-step explanation:

Given,

p = 0.2

1 - p = 0.8

Number of trials, n = 5

P(x = 1)

Using the binomial probability formula :

P(x =x) = nCx * p^x * (1 - p)^(n - x)

P(x = 1) = 5C1 * 0.2^1 * 0.8^4

P(x = 1) = 5 * 0.2^1 * 0.8^4

P(x = 1) = 0.4096

Yes, there will be with a probability of 0.4096

Answer:

No. If Aaron tunes into this station at 5 randomly selected times, there will not necessarily be exactly one time when a commercial is playing.

Step-by-step explanation:

trust

answer: A survey

explanation: The manager of the restaurant is conducting a survey to determine which sandwich is more preferred by customers. He is taking a random sample of customers that have tried both sandwiches and asking them which sandwich they like best. The survey method is a statistical way of collecting data and it is a non-experimental design, because the manager is not controlling the variables that may affect the outcome. The outcome of this survey is based on the customers' preference of the sandwiches, and it is a way to gather data on their opinion

The system of equation

y=8x and y=2x

To solve this using graphical method

The solution is the point of intersection of the two-lines

As shown from the graph above, the solution is (0,0)

Answer:

should be (5y-2)y = 72

Step-by-step explanation:

since the product of the two is 72, it's true that xy = 72. and it is also true that x is equal to five times y minus 2, so you can rewrite x as 5y-2. plug that in for x in the first equation, and you're set. hope this helps :)

From the given sequences following are the arithmetic sequences :

1. 3, 7, 11, 15, 19

5. 1, 1/2, 0, -1/2

7. 1, 0, -1, -2, -3

10. 9.5, 7.5, 5.5, 3.5, ...

As given in the question,

Arithmetic sequences are :-

1) yes, because the difference between the terms is same.

7 - 3 = 11-7 = 15 -11 = 4

5)yes, because the difference between the terms is same.

1/2 -1 = 0 -1/2 = -1/2 -0 = -1/2

7)yes, because the difference between the terms is same.

0 - 1 = -1 -0 = -2 -(-1) = -1

10)yes, because the difference between the terms is same.

7.5 - 9.5 = 5.5 - 7.5 = 3.5 -5.5 = -2

Difference between consecutive terms of these sequences are not equal . so these are not arithmetic sequences :-

2,3,4,6,8, 9

Arithmetic sequence

In an arithmetic sequence, the difference between consecutive terms is always the same. For example, the sequence 3, 5, 7, 9 .. is arithmetic because the difference between consecutive terms is always two.

Therefore, the arithmetic sequences are :

1. 3, 7, 11, 15, 19

5. 1, 1/2, 0, -1/2

7. 1, 0, -1, -2, -3

10. 9.5, 7.5, 5.5, 3.5, ...

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Step-by-step explanation:

The y-intercept of the function is: b=10

Step-by-step explanation:

Given the table

x                 y

1                 8

2                6

3                4

4                2

Taking any two points to find the slope

(1, 8)

(2, 6)

The slope between (1, 8) and (2, 6) is:

We know that the slope-intercept form of the line equation is

where m is the slope and b is the y-intercept.

Substituting m=-2 and any point i.e. (1, 8) in the slope-intercept form of the line equation to find the y-intercept (b).

8 = -2(1) + b

8 = -2 + b

b = 8+2

b = 10

Thus, the y-intercept of the function is: b=10

Answer:

Step-by-step explanation:

The sale price of the sofa is given as :

The dollar amount for the discount

The completion of the following table under different depreciation methods is as follows:

Method                           Year 1                     Year 2

Straight line                   $18,000                 $18,000

Units of production      $54,000                 $13,500

Declining balance        $37,600                $22,560

MACRS (5-year class)   $18,800                $30,080

Cost of machine = $94,000

Residual value = $4,000

Depreciable value = $90,000 ($94,000 - $4,000)

Estimated useful life = 5 years

Depreciation expense:

Straight-line method = $18,000 ($90,000/5)

Estimated units of produciton = 100,000

Unit depreciation rate = $0.90

Actual production   Depreciation

Year 1 = 60,000      $54,000 ($0.90 x 60,000)

Year 2 = 15,000      $13,500 ($0.90 x 15,000)

Declining Balance:

Year 1 = $37,600 ($94,000 x 40%)

Year 2 = $22,560 ($94,000 - $37,600) x 40%

MACRS:

Year 1 = $18,800 ($94,000 x 20%)

Year 2 = $30,080 ($94,000 x 32%)

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The thermometer reading would be 73.48°C.

The boiling point of water is generally considered to be 100°C. According to the given information, the temperature of the liquid in the thermometer is 26.52°C lower than the boiling point of water. Therefore, to find the thermometer reading, we subtract 26.52 from 100.

100 - 26.52 = 73.48

Hence, the thermometer reading would be 73.48°C.

In this scenario, we are assuming that the thermometer is calibrated to measure temperature in Celsius. The boiling point of water at standard atmospheric pressure is 100°C, and the given information states that the liquid in the thermometer is 26.52°C lower than the boiling point.

By subtracting 26.52 from 100, we obtain a reading of 73.48°C.

Thermometers work by utilizing the principle that certain substances, such as mercury or alcohol, expand or contract with changes in temperature. The expansion or contraction is measured using a scale, which is marked with various temperature values.

In this case, the thermometer is calibrated in Celsius, so we refer to the Celsius scale. By subtracting 26.52 from 100, we find the temperature at which the liquid in the thermometer is settled, which is 73.48°C.

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Answer:

−2.5<x<2.5

Step-by-step explanation:

Let's find the critical points of the inequality.

4x2−25=0

4x2−25+25=0+25(Add 25 to both sides)

4x2=25

4x24=25/4(Divide both sides by 4)

x2=25/4

x=±√254(Take square root)

x=2.5,−2.5

Check intervals in between critical points. (Test values in the intervals to see if they work.)

x<−2.5(Doesn't work in original inequality)

−2.5<x<2.5(Works in original inequality)

x>2.5(Doesn't work in original inequality)

Answer:

114.93?

Step-by-step explanation:

might be wrong but theres a website I forgot the name of it but you can find out the answers to stuff like that.

Answer:

4 1/3

Step-by-step explanation:

this is just a subtraction problem. What you know is that it snowed 5ft yesterday and 2/3ft today. So that means that the amount of more snow yesterday can be calculated with 5 - 2/3ft (this will show how much more snow there was yesterday). The result of this expression would be 4 1/3. Hope this helps!

9514 1404 393

Answer:

Step-by-step explanation:

Rewrite as a quadratic in sin(θ) and solve that in the usual way.

  3cos(2θ) +sin(θ) = 1

  3(1 -2sin²(θ)) +sin(θ) = 1 . . . . use an identity for cos(2θ)

  6sin²(θ) -sin(θ) -2 = 0 . . . . . rearrange to standard form

  (3sin(θ) -2)(2sin(θ) +1) = 0 . . . . factor

The values of sin(θ) that make this true are ...

  sin(θ) = 2/3, sin(θ) = -1/2

In the range 0 < θ < 180°, we're only interested in ...

  sin(θ) = 2/3

  θ = arcsin(2/3) or 180° -arcsin(2/3)

  θ ≈ {41.81°, 138.19°}

Answer:

Explanation:

Answer: the answer to question 6 is order least to greatest

Step-by-step explanation:

Answer:

238

Step-by-step explanation:

juans has 10 more than kevin's, so you just subtract 10 from 248, getting 238

The total distance of the obstacle course can be calculated by finding the distance between each pair of consecutive points and adding them up. The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2).

Using this formula, we can calculate the distances between each pair of consecutive points as follows:

Start to Tire Race: distance = sqrt((-40 - (-40))^2 + (-30 - (-10))^2) = 20 yards

Tire Race to Rope Climb: distance = sqrt((40 - (-40))^2 + (-30 - (-30))^2) = 80 yards

Rope Climb to Monkey Bars: distance = sqrt((40 - 40)^2 + (20 - (-30))^2) = 50 yards

Monkey Bars to Finish: distance = sqrt((10 - 40)^2 + (20 - 20)^2) = 30 yards

Adding up all these distances, we get a total distance of 20 + 80 + 50 + 30 = 180 yards for the obstacle course.

The figure which is most likely the next step in the given series is figure B.

Patterns are defined as the models where something is repeated in a definite order or we can predict the next outcome.

Here given a definite pattern.

We have to find the fourth step of the pattern.

In the first figure two line segments from the center are coincided.

In the second figure, one line is moved clockwise to 90 degrees.

In the next figure the line moves to another 90 degrees clockwise.

So in this pattern, in the forth figure, the line again will move another 90 degrees clockwise.

Hence the correct figure is B.

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