Help pls I don't understand

The moment of inertia about the y-axis of the thin semicircular region of constant density is given below.

[tex]\rm I_y = \dfrac{1}{8} \times \pi r^4[/tex]

Any item that can be turned has rotational inertia as a quality. It's a scalar value that indicates how complex it is to adjust an object's rotational velocity around a certain axis.

Then the moment of inertia about the y-axis of the thin semicircular region of constant density will be

[tex]\rm I_x = \int y^2 dA\\\\I_y = \int x^2 dA[/tex]

x = r cos θ

y = r sin θ

dA = r dr dθ

Then the moment of inertia about the x-axis will be

[tex]\rm I_x = \int _0^r \int _0^{\pi} (r\sin \theta )^2 \ r \ dr \ d\theta\\\\\rm I_x = \int _0^r \int _0^{\pi} r^3 \sin ^2\theta \ dr \ d\theta[/tex]

On integration, we have

[tex]\rm I_x = \dfrac{1}{8} \times \pi r^4[/tex]

Then the moment of inertia about the y-axis will be

[tex]\rm I_y = \int _0^r \int _0^{\pi} (r\cos\theta )^2 \ r \ dr \ d\theta\\\\\rm I_y = \int _0^r \int _0^{\pi} r^3 \cos ^2\theta \ dr \ d\theta[/tex]

On integration, we have

[tex]\rm I_y = \dfrac{1}{8} \times \pi r^4[/tex]

Then the moment of inertia about O will be

[tex]\rm I_o = I_x + I_y\\\\I_o = \dfrac{1}{8} \times \pi r^4 + \dfrac{1}{8} \times \pi r^4\\\\I_o = \dfrac{1}{4} \times \pi r^4[/tex]

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Answer:

62.83

Step-by-step explanation:

Circumference=2 pi r

diameter=20

20*pi= about 62.83

so it sould be around 62.83

Answer:

Number 2 is the correct answer. The cube root of 27 is 3.

Step-by-step explanation:

[tex] {x}^{3} = 27[/tex]

[tex]x = \sqrt[3]{27} = 3[/tex]

Answer:

50

Step-by-step explanation:

I have none I got it wrong lol

Answer:

116.2

Step-by-step explanation:

The circumference formula is C= 2 (pi)r

Plugin our number

C=2(pi )18.5

Then mulitply and we get the product

116.24

round to the nearest tenth

116.24

The circumference of the circle to the nearest tenth is approximately 116.1 meters.

Circumference refers to the distance around the edge or boundary of a circular object or shape. It is the measurement of the total length of the circle.

The formula for the circumference of a circle is given by:

C = 2πr

where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14159.

Substituting the given value of the radius into the formula, we get:

C = 2π(18.5)

= 37π

≈ 116.1

Therefore, the circumference of the circle to the nearest tenth is approximately 116.1 meters.

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Answer:

Step-by-step explanation:

Answer:

BC = 18.385

Step-by-step explanation:

You can look at ABC as a right triangle and use the Pythagorean theorem to solve for BC. 26 squared is 676, 676 divided by 2 is 338, and finally the square root of 338 is 18.385. This is the length of BC and AB as well. Hope that helped

The minima of the quadratic function is at the vertex, it is at  (2, -4).

First, we can see that our function is a quadratic function of positive leading coefficient. So it opens upwards.

Then we will only have a minima, which is located in the vertex of the parabola.

Remember that for:

y = a*x^2 + b*x + c

The x-value of the vertex is h = -b/2a

Then for g(x) = x^2 - 4x we have:

h = -(-4)/2*1 = 2

And the y-value of the vertex is:

g(2) = 2^2 - 4*2 = -4

Meaning that the minima of the function g(x) is (2, -4).

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The exact location of all the relative and absolute extrema of the function is (2, -4).

First, we can see that our function is a quadratic function of the positive leading coefficient.

Then we will only have a minimum, which is located in the vertex of the parabola.

The equation of the parabola is;

[tex]\rm y = ax^2 + bx + c[/tex]

The x-value of the vertex is h = -b/2a

Then for g(x) = x^2 - 4x we have:

h = -(-4)/2*1 = 2

And the y-value of the vertex is:

g(2) = 2^2 - 4*2 = -4

Meaning that the minima of the function g(x) are (2, -4).

Hence, the exact location of all the relative and absolute extrema of the function is (2, -4).

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Answer:

B

Step-by-step explanation:

[tex]9 \frac{7}{12} - 4 \frac{3}{12} = 5\frac{4}{12} = 5 \frac{1}{3} [/tex]

The system of equations which is represented the equivalent single equation without the y variable in it is x-1=0.

A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.

The system of equations as an equivalent single equation without the y variable has to be found out for the given equation.

The first equation given in the problem is,

[tex]x + y = 10[/tex]

Subtract x from both sides and solve it for y,

[tex]x + y -x= 10-x\\y=10-x[/tex]                    .........1

The second equation given in the problem is,

[tex]y = 4x + 5[/tex]

Put the value of y in this equation from equation 1 as,

[tex]y = 4x + 5\\10-x = 4x + 5\\10-5=4x+x\\5=5x\\5x-5=0[/tex]

Divide both side with number 5,

[tex]x-1=0[/tex]

Thus, the system of equations which is represented the equivalent single equation without the y variable in it is x-1=0.

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Answer:

152

Step-by-step explanation:

Substitute 6 in for x since x = 6:

8(3(6) + 1)

8(18 + 1)

8(19)

= 152

hope this helps!

Answer:

Do you have weight

Step-by-step explanation:

Are these tests weight the same or different?

Answer:

Angle B = 120.5°

Step-by-step explanation:

When two angles are supplementary, it means that they add up to 180°. Therefore, you can find the measure of Angle B by doing the following:

Angle B = 180 - 59.5

Angle B = 120.5°

Hope this helps

Answer:

see the attachment!

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Answer:

B

Step-by-step explanation:

Answer:

-44

Step-by-step explanation:

The slope of the line passing through two points (x₁, y₁) and (x₂, y₂) is given by (y₂ -  y₁)/(x₂ - x₁)

Therefore the slope of the given line k = (10-4)/(9-8) = 6

In the slope intercept equation, y = mx + b, m is the slope and b is the y intercept

Substituting for m we get the line equation as

y = 6x + b

Substitute any one of the points in this equation. Let's use point(8,4) ie x= 8, y =4

we get

4 = 6 x 8 + b

which gives b = 4-48 = -44

Answer:

i dont know if im correct cause i know nothing about math

Step-by-step explanation:

18.6? my answer

Answer:

The answer is 24.8

Step-by-step explanation:

after you add the total ans subtract it gives you 24.8

Answer:

[tex]\frac{2}{cos(x)}[/tex]

Step-by-step explanation:

Key facts you will need to know to solve this

[tex]tan(x) = \frac{sin(x)}{cos(x)}[/tex]

[tex]sin^2 + cos^2 = 1[/tex]    so [tex]1-sin^2= cos^2[/tex]

The equation can also simplify by cross multiplying the fraction to make:
[tex]\frac{cosx-sincosx}{(1+sinx)(1-sinx)} + \frac{cosx+sincosx}{(1-sinx)(1+sinx)}[/tex]

[tex]\frac{cosx-sincosx}{1-sin^2(x)} + \frac{cosx+sincosx}{1-sin^2(x)}[/tex] = [tex]\frac{2cos(x)}{1-sin^2(x)}[/tex]

Using the equation [tex]1-sin^2= cos^2[/tex] that we established earlier, the fraction is also:

[tex]\frac{2cos(x)}{cos^2(x)}[/tex] = [tex]\frac{2}{cos(x)}[/tex]

Therefore, the answer is [tex]\frac{2}{cos(x)}[/tex]

The volume of the cone with the given parameters is calculated as approximately: 19.17 cubic units.

Volume = 1/3πr²h

Given the following:

Volume of the cone = 1/3π(2²)(4.58)

Volume of the cone = 19.17 cubic units.

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Answer:

12.56 edge

Step-by-step explanation:

Answer:

63.35

Step-by-step explanation:

1. Remember the sector formula which is Ø/360 x pi x radius squared

2. Square the radius (11 in this question)

3. 11 squared is 121

4. Get the answer from the squared radius and multiply it by pi

5. 121 times pi is 380.13

6. Mulitply the final number on that side by the degree over 360

7. 380.13 times 60/360 is 63.35

8. In the end you get 63.35 or if rounding to the nearest tenth 63.4

Hope this helps! Correct me if im wrong! :) Have a nice day!

The choices are equivalent to the expression correct choices are A, C, and D.

The given expression is

x^3 /5

The expression consists of numbers and arithmetic operators. It does not contain equality or inequality symbols.

[tex]a^{\frac{m}{n} =\sqrt[n]{a^m}[/tex]

Therefore the above power rule implies that,

[tex]x^{(\frac{3}{5}) }=\sqrt[5]{x^3}[/tex]

Also, we have the power rule

[tex](a^m)}^n=a^{mn}[/tex]

[tex]x^{\frac{3}5} =(x^3)^{\frac{1}{5}[/tex]

or it can be written as

[tex]x^{\frac{3}{5} =(\sqrt[5]{x})^3[/tex]

The correct choices are A, C, D.

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The weight Isaac and his workout partner lifting when they both lifting the same amount, after the 1 set and the weight they be lighting is 10 kg.

Unknown variables are used to find the unknown values of the problem using the algebraic expressions.

To find the values of unknown quantity, the statements of a problem is converted in the algebraic equation form using the variable in place of unknown numbers.

Isaac and his workout partner are lifting weights together, doing many sets of each exercise.

Isaac is using 5-kg bar, and increasing the amount of weight he lifts by 5 kg on each set. The weight he lifts after x set is,

5+5x

His partner, started out using a 7-kg bar and is upping the weight by adding 3 kg on every set. The weight his partner lift after x set is,

7+3x

Let after x sets, the weight lifted by both will be same. Thus,

[tex]5+5x=7+3x\\5x-3x=7-5\\2x=2\\x=\dfrac{2}{2}\\x=1[/tex]

Thus, the weight Isaac and his workout partner lifting when they both lifting the same amount, after the 1 set and the weight they be lighting is 10 kg.

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Answer:

average rate of change = 2

Step-by-step explanation:

since f(x) is a linear function, then the slope is the measure of the average rate of change of f(x).

note the average rate of change is constant over any closed interval.

the equation of a linear function in slope- intercept form is

f(x) = mx + c ( m is the slope and c the y- intercept )

f(x) = 2x + 4 ← is in slope- intercept form

with slope m = 2

then average rate of change = 2

Answer:

11.2 mm

Explanation:

Given a right angle triangle, In order to find the third side: Use Pythagoras Theorem: a² + b² = c²

Insert Values:

x² + 3.8² = 11.8²

x² + 14.44 = 139.24

x² = 139.24 - 14.44   (subtract)

x² = 124.8

x = √124.8              (square root)

x = 11.1714 ≈ 11.2     (rounded to 3 significant figures)

3.8 mm

11.8 mm

the unknown "x"

we'll have to use pythagoras theorem.

unknown value is x

[tex] {c}^{2} = {b}^{2} - {a}^{2} [/tex]

[tex] {x}^{2} = {11.8}^{2} - {3.8}^{2} [/tex]

[tex] {x}^{2} = 124.8[/tex]

[tex] {x}^{2} = \sqrt{124.8} [/tex]

[tex]x = 11.17139204[/tex]

[tex]x = 11.2 \: mm[/tex]

Answer:

0.09

Step-by-step explanation:

So if you use the Simple interest equation it will begin with:
Interest total = Initial Amount of money x Interest rate per year x Years money is invested for.

Then substitute the values you have been given so:

$6300 = 7000 x Interest rate per year x 10.

This is simplifies to 6300 = 70,000 x Annual Interest rate

You can rearrange this to find the annual interest rate by dividing by 70,000:
[tex]\frac{6300}{70000} = Interest\ rate[/tex]

Simplifying this would be:
[tex]\frac{63}{700}\\[/tex] = Interest rate.

The interest rate is 0.09.

41.6/2.6 = 16

therefore into 16 parts

hope it helps...!!!

Answer:

A & B

Step-by-step explanation:

the rest are incorrect because sinx = 8/15 and cscx = 15/8