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]
What is rotational inertia?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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1. Emily wants to make 1, 000 paper cranes. She can make
eight cranes a day. If she has already made 304 cranes, how
many days are left till she makes the rest of the 1,000 paper
cranes?
CA
3-4
Answer:
87 days
Step-by-step explanation:
First if she already made 304 cranes and she makes 8 a day. Simply divide 304 by 8. You would then get 38. Next divide 1,000 by 8. You would get 125. You would subtract the total from how many days you need; 125, to how many days you already spent; 38. 125 - 38 = 87. 87 days are needed to make paper cranes.
How many ways can you fold the square so one half? How many ways an you fold the letter G one half fits exactly on top of the other half?
There are four ways to fold the square into half and the number of ways to fold the letter G is 0
Folding a square?A square has 4 lines of symmetry.
Each line of symmetry divides the square into half
This means that the square can be folded in any of its line of symmetry to get one half
Hence, there are four ways to fold the square into half
Folding the letter GThe letter G has no line of symmetry.
This means that the letter cannot be folded so that the halves fit perfectly
Hence, the number of ways to fold the letter G is 0
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How many square feet of glass is used to create the window
Answer:108
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Step-by-step explanation:8 pieces of glass uses 1 sqft. glass window. 864 sqin. required = = 108 pieces. Number of pieces required for 864 sq.inches = 108 pieces.
The runways at an airport are arranged to intersect and are boarded by fencing a security guard needs to patrol the outside fence of the runways once per shift what is the estimated distance she walks every shift
The estimated distance she walks every shift will be 18000 feet.
How to calculate the distance?From the information given, it was stated that the
runways at an airport are arranged to intersect and are boarded by fencing a security guard.
The estimated distance she walks every shift from the complete information will be:
= 2(4000 + 5000)
= 2 × 9000
= 18000 feet.
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Answer:
the answer is 23,320 ft
Step-by-step explanation:
I hope it helps you
Sarah said, "There is only one possible third side for a right triangle with two sides measuring 9 units and 15 units.'
Sarah's claim is not true. Give the two possible answers for the third side of the right triangle. Leave your answer
as a square root unless it can be simplified
The two possible answers for the third side of the right triangle are 6 and 24.
What is the triangle inequality theorem?
The Triangle Inequality theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
So, a difference of two sides <x< sum of two sides, will give you the possible length of a triangle.
Sarah said, "There is only one possible third side for a right triangle with two sides measuring 9 units and 15 units.'
The two possible answers for the third side of the right triangle are;
[tex]\rm 15-9 < x < 15+9\\\\6 < x < 24[/tex]
The possible length of the third side of a triangle.
For checking the possible length:
15 + 9 > 7 (a+b>c)
9 + 7 > 15 (b+c>a)
7+ 15 >9(a+c>b)
Which satisfy the triangle inequality theorem.
Hence, the two possible answers for the third side of the right triangle are 6 and 24.
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6. Allie used the $1,200 she got from her
graduation party to open a savings account.
If the account earns 1% interest each
month and she makes no additional deposits,
how much money will be in the account in 5
years?
URGENT:!!!!!!!!!!!
Answer:
$1261.21
Step-by-step explanation:
Stephanie spent $96 on trash cans, if each trash can was $24. How many trash cans did she get
i need help pleaseeeeee
Answer:
answer is X= 175
Step-by-step explanation:
all you had to do is to get rid off both 5 on left which would leave you with x and on right side the answer to 35×5 is 175
what’s the area and perimeter for this problem?
Answer:
the area of the triangle is 41
the perimiter of the triangle is 33.25
Step-by-step explanation:
Hi Help me with this please :)
Answer:
4
Step-by-step explanation:
to find the mean you add up all of the numbers and then divide by the numbr of numbers there are. So to add them all up that will be 3+5+0+4+7+5+5+3=32
so then you divide 32 by 8 which equals 4.
So therefore your answer is 4.
Please give me brainliest.
Solve the system of the linear equations with three variables:
6x + 4y + z = 12
6x + 4y + 2z = 12
6x + 4y + 3z = 12
Answer:
z = 0
y = -3x/2 + 3
Step-by-step explanation:
6x + 4y + z = 12
6x + 4y + 2z = 12
6x + 4y + 3z = 12
Second equation minus first equation:
z = 0
If you plug in z = 0 in all the original equations, you get a single equation:
3x + 2y = 6
The best you can do is to solve for y in terms of x.
y = -3x/2 + 3
Answer:
z = 0
y = -3x/2 + 3
Español Use the equation below to find y, if m=4, x=8, and b=12. y=mx-b
Answer
[tex]y=4* 8 -12\\[/tex]
Step-by-step explanation:
4 x 8 = 32
y=32-12
y=20
Find the unknown dimension or volume of each rectangular prism.
V = _______
l = 4 cm
w = 4 cm
h = 11 cm
Answer:
176
Step-by-step explanation:
you multiply the numbers 4 4 and 11 to get 176
help me pleaseee >:)
Answer:
Cylinder: [tex]V_c = 80 \pi \approx 251.33[/tex]
Rectangular prism: [tex]V_r = 384[/tex]
Total: [tex]V = 80\pi + 384 \approx 635.33[/tex]
Step-by-step explanation:
The volume of the cylinder:
[tex]V_c = \pi r^2 h\\V_c =\pi4^2 \times 5\\V_c = 80\pi\\V_c \approx 251.33[/tex]
The volume of the rectangular prism:
[tex]V_r = lwh\\V_r = 12 \times 8 \times 4\\V_r = 384[/tex]
The total volume:
[tex]V = V_c + V_r\\V = 80\pi + 384\\V \approx 635.33[/tex]
Please help me.
I will give you Brainliest, if you answer correctly
Answer:
9(5x^3-1)
Please Vote Me Brainliest. Thank You.
Can someone please help?? This is sooooo hard!!!
Answer:
Step-by-step explanation:
1) [tex]\overline{AC}[/tex] bisects [tex]\overline{BD}[/tex] and [tex]\overline{BC} \parallel \overline{AD}[/tex] (given)
2) [tex]\overline{AE} \cong \overline{EC}[/tex] (a bisector splits a segment into two congruent parts)
3) [tex]\angle BCE \cong \angle EAD[/tex] (if two parallel lines are cut by a transversal, the alternate interior angles are congruent)
4) [tex]\angle CBE \cong \angle EDA[/tex] (if two parallel lines are cut by a transversal, the alternate interior angles are congruent)
5) [tex]\triangle BEC \cong \triangle DEA[/tex] (AAS)
I need help to find the measures and equation pls.
Answer:
Equation: 7x + 8x = 180
x = 12
∠CBA = 84
∠CFH = 96
Step-by-step explanation:
We can see that ∠CBA = ∠CFE and ∠CBD = ∠CFH.
We know that the sums of two angles on a straight line are going to be equal to 180.
∠CBA = 7x
∠CFH = 8x
To find the value of x, we must do the following:
7x + 8x = 180
15x = 180
15x/15 = 180/15
x = 12
Now we just substitute to find the angle measures:
∠CBA = 7 · 12 = 84
∠ CFH = 8 · 12 = 96
If you are at school 8 out of the 24 hours every weekday what percent of the time are yoou at home every weekday
Answer:
Rounded it is 66.7%
Step-by-step explanation:
24-8=16
Then find the percentage of 16 out of 24.
Answer:
33.33333%
Step-by-step explanation:
24 divided by 8=3
4 days out of the past 20 days. What is the
estimated probability, based on relative frequency, that her ride will be late
tomorrow?
O A. 80%
B. 40%
O c. 20%
O D. 60%
Answer quickly please and thank you
Find the mistake in the following set of steps in a student’s attempt to solve 5x+2≥x+2/5, for x. What is the correct solution set?
5x+2≥x+2/5
5(x+2/5)≥x+2/5 (factoring out 5 on the left side)
5≥1 (dividing by (x+2/5))
So, the solution set is the empty set.
Answer: x ≥ [tex]\frac{-2}{5}[/tex]
Step-by-step explanation:
I cannot see what the student did wrong in your question, so I solved for x in the equation...
[tex]5x + 2[/tex] ≥ [tex]x + \frac{2}{5}[/tex]
1. subtract x from both sides
4x + 2 ≥ [tex]\frac{2}{5}[/tex]
2. subtract 2 from both sides to isolate 4x
4x ≥ [tex]\frac{-8}{5}[/tex]
3. divide both sides by 4
x ≥ [tex]\frac{-2}{5}[/tex]
round to the nearest hundreth
IXL percent of change
Answer:
What? I think you forgot to attach the picture.
how many 3 servings are in ounces
It depends on the size of the portion and you divide that size by 3 and the result comes out
In a 30-60-90 triangle what is the measure of the hypotenuse if the shorter leg measures 10cm?
Answer:
[tex]10\sqrt{5} [/tex]
Step-by-step explanation:
Tan(30) = 1/2
Longer leg = 20
Hypotenuse = 10*sqrt(5)
Ms. Sutton recorded the word counts and scores of the top ten essays in a timed writing contest. The table shows her data. A 3-row table with 10 columns. The first row is labeled essay rank with entries 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. The second row is labeled essay score with entries 9. 7, 9. 5, 9. 5, 9. 0, 8. 9, 8. 9, 8. 5, 8. 4, 8. 2, 7. 0. The third row is labeled word count with entries 324, 352, 337, 318, 299, 304, 290, 291, 278, 250. How does the word count of an essay relate to its score in the contest? Word count tends to decrease as the score decreases. Word count tends to increase as the score decreases. Word count tends to remain constant as the score decreases. Word count has no apparent relationship to the score of the essay.
Answer:
D. word count has no apparent relationship to the score of the essay
Step-by-step explanation:
ya its D ANYWAYSSSSSS
8x10^-3 is how many times as great as 4x10^-6
The value [tex]8\times 10^{-3}[/tex] is about 2000 times greatest as [tex]4\times 10^{-6}[/tex]
What are exponent values?Exponents, also known as powers, are values that show how many times to multiply a base number by itself.
Here we have the values [tex]8\times 10^{-3}[/tex] and [tex]4\times 10^{-6}[/tex]
Now to compare the value we will write [tex]4\times 10^{-6}[/tex] as [tex]0.004\times 10^{-3}[/tex]. We will divide the value [tex]8\times 10^{-3}[/tex] by the value [tex]4\times 10^{-6}[/tex] So it will give us 2000.That means that the value [tex]8\times 10^{-3}[/tex] is 2000 times them the value [tex]4\times 10^{-6}[/tex]
[tex]\dfrac{8\times 10^{-3}}{0.004\times 10^{-3}}=2000[/tex]
So value [tex]8\times 10^{-3}[/tex] is about 2000 times greatest as [tex]4\times 10^{-6}[/tex]
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PLSSSSSSSS HEEEELLPPP WITH THIS!!!!
WILL GIVE 100 POINTS AND BRAINIEST!!!!!!!!!
Answer:
Sorry, I don't have an answer but is this how hard math gets. My dad is an engineer and he says math is easy but....
PLEASE HELP i already asked this question but no one helped.
There are 12 players on a baseball team. In how many different ways can the coach choose players for left field, right field, and center field?
A) 36
B) 220
C) 1320
D) 1728
Martin ordered a pizza with a 16-inch diameter. Ricky ordered a pizza with a 20-inch diameter. What is the approximate difference in the area of the two pizzas?
Question 1 options:
50 inches2
113 inches2
201 inches 2
452 inches 2
Answer:
B: 113 inches2
Step-by-step explanation:
16inch diameter=201
20inch diameter=314
314-201=113