Find the center of mass of the areas formed by x+3=(y-1)^2; y=2, in coordinate axes
Answers
The center of mass of the region is (21/20, 10/3).
To find the center of mass of the area formed by the curve \(x+3=(y-1)^2\) ans the line y=2, we need to first find the area of the region and then find the coordinates of the center of mass.
To find the area , we integrate the curve between the y-values of 2 and 3:
\(A = \int\limits^3_2 [(y-1)^2 - 3] dy \\ = > \int\limits^3_2 (y^2 - 2y - 2) dy \\ = > [\frac{1}{3} y^3 - y^2 - 2y]_2^3\\ = > \frac{1}{3} (27 - 4 - 6) - \frac{1}{3} (8 - 4 - 4) = \frac{5}{3}\)
So , the area of the region is 5/3 square units.
To find the coordinates of the center of mass , we need to compute the moments about the x and y axes and divide by the total area:
\(Mx = \int\limits^3_2[(y-1)^2 - 3] * y dy \\ = > \int\limits^3_2 (y^3 - 3y^2 + 2y) dy \\ = > [1/4 y^4 - y^3 + y^2]_2^3 \\ = > 1/4 (81 - 27 + 9) - 1/4 (16 - 8 + 4) = 7/4My = 1/2 \int\limits^3_2 [(y-1)^2 - 3] dx \\\\= > 1/2 \int\limits^3_2 [(y-1)^2 - 3] (dy/dx) dx \\\\\)
\({using dx = (dy/dx) dy}\\ = 1/2 \int\limits^3_2 [(y-1)^2 - 3] (2(y-1)) dx \\ {using dy/dx = 2(y-1)} \\ = \int\limits^3_2 (y-1)^2 (y-2) dx \\ = \int\limits^2_1u^2 (u+1) du \\ {using[ u = y-1], and[ dx = (1/2(y-1)) dy]} \\ = [1/3 u^3 + 1/4 u^4]_1^2 \\ = 1/3 (8 + 4) - 1/3 (1 + 1) = 7/3X = Mx / A = (7/4) / (5/3) = 21/20Y = My / A = (7/3) / (5/3) + 1 = 10/3\)
Therefore , the center of mass of the region is (21/20, 10/3).
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Related Questions
how can I find this answer
Answers
Answer:
No
Yes
No
Step-by-step explanation:
8 glitter wands for $50. 50/8 = $6.25 for each glitter wand.
1) 4 sparkle wands for $20. 20/5 = $4 for each sparkle wand.
Does NOT have same price per wand as glitter wands.
2) 6 fairy wands for $37.50. 37.5/6 = $6.25 for each fairy wand.
Has the same price per wand as glitter wands.
3) 10 glow wands for $65. 65/10 = $6.50 for each glow wand.
Does NOT have same price per want as glitter wands.
Hope that helps!
x=5 y = 3, x² + 3(x +y)=
HELP FAST
Answers
9514 1404 393
Answer:
49
Step-by-step explanation:
Put the variable values in place of the corresponding variables, and do the arithmetic.
x² +3(x +y) =
5² +3(5 +3) = 25 +3(8) = 25 +24 = 49
Given P(A) = 0.46, P(B) = 0.35 and P(B|A) = 0.45, find the value of
P(A and B), rounding to the nearest thousandth, if necessary.
Answers
So to find P(A and B) just multiply P(B|A) by P(A)
P(A and B) = 0.45*0.46 = 0.207
The solution is, the value of P(A and B) is 0.207.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
given that,
Given P(A) = 0.46, P(B) = 0.35 and P(B|A) = 0.45,
we know that,
P(B|A) = P(A and B)/P(A)
so, P(A and B) = P(B|A) * P(A)
i.e. we get,
So to find P(A and B) just multiply P(B|A) by P(A)
now, we have,
P(A) = 0.46, and P(B|A) = 0.45,
substituting the values, we get,
P(A and B)
= P(B|A) * P(A)
= 0.45*0.46
= 0.207
Hence, The solution is, the value of P(A and B) is 0.207.
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'SOMEBODY PLEASE HELP I WILL GIVE YOU A BRAINLIEST
PROP/CONSTANT
A factory makes 36 cookies in 12 mins. How many cookies can they make in ONE minute?
6 cookies
4 cookies
3 cookies
2. A bathtub leaks 1/2 cup of water every 1/4 minute. How many cups of water leak every minute?
3 1/2 cups
1 cup
2 cups
3. 5 glazed donut has 750 calories altogether. How many calories are in TWO donuts?
300 calories
150 calories
450 calories
4. A cell phone company charges $70 for 2 months of service, and $210 for 6 months of service. What is the constant rate (per month) for the service?
$40 per month
$35 per month
$55 per month
5. Which is the formula to find the constant of a chart?
k = y/x
y = kx
x = k/y
6. A chart is not considered proportional if...
the chart has too many large numbers
the x values are bigger than the y values
if the y values are bigger than the x values
if there is no constant (k)
Use the chart below for questions 7 and 8
7. Is the chart above proportional?
Yes
No
8. Determine the constant(k) of the chart.
k = .75
k = 1.75
k = 2.15
Doesn't have a constant
Use the chart below to answer questions 9 - 12.
9. Is the chart above proportional?
8 points
Yes
No
10. Determine the constant(k) of the chart?
10 points
k = 5
k = 4
k = .25
11. Which formula satisfies an equation for Y.
y = 4x
y = .25x
y = 5x
12. Find the value of y when x is 49.
12.25
196
80
18
Answers
Answer:
1. 3 cookies
2. 2 cups
3. 300 calories
4. $35 per month
5. k = y/x
6. If there is no constant (k)
Step-by-step explanation:
1. The number of cookies the factory makes in one minute = (The number of cookies the factory makes in 12 minutes)/(12 minutes)
∴ The number of cookies the factory makes in one minute = 36 cookies/(12 minutes) = 3 cookies/minute
The correct answer is 3 cookies
2. The number of cups of water that leak every minute = (The number of cups of water that leak in 1/4 minute) × (The number of 1/4 minute per minute)
The number of cups of water that leak every minute = 1/2 cup per 1/4 minute × 4_1/4 minute per minute
The number of cups of water that leak every minute = 1/2 × 4 = 2
The number of cups of water that leak every minute = 2 cups
3. 5 glazed donuts contains 750 calories
∴ 1 glazed donuts contains 750/5 = 150 calories
2 = 2 × 1 glazed donuts will contain 2 × 150 = 300 calories
4. The charge of the cell phone company for 2 months = $70
The charge of the cell phone company for 6 months = $210
The constant rate per month = The rate of change of the cell phones companys charges
∴ The constant rate per month = (210 - 70)/(6 - 2) = 140/4 = 35
The constant rate (per month) for the service = $35 per month
5. The formula to find the constant of a chart, k = y/x
6. A chart is not considered proportional if there is no constant (k)
how do i solve this? I need proper assistance
Answers
Answer:
25
Step-by-step explanation:
(33 + 2z)^2 when z = -19
substitute in -19 in place of z:
(33 + 2(-19))^2
(33 + (-38))^2
(33 -38)^2
(-5)^2
= 25
A BASKETBALL PLAYER MAKES A BASKET THROUGH A TEN FOOT HIGH BASKET FROM 20 FEET AWAY. IF THE SHOOTER RELEASES THE BALL FROM 8 FEET ABOVE THE GROUND AND THE BALL HAS A HORIZONTAL VELOCITY OF 10 FEET/SECOND. WHAT IS THE VERTICAL VELOCITY OF THE BASKET BALL?
Answers
Answer:
The vertical velocity of the ball when released = 10.81 m/s
The vertical velocity of the ball in the basket = 8.81 m/s
Step-by-step explanation:
The given parameters are;
The height of the basket = 10 feet
The horizontal location of the shooter from the basket = 20 feet
The height from which the shooter releases the ball = 8 feet
The horizontal velocity of the ball = 10 ft/s
Therefore, we have;
Time, t = Horizontal distance/(Horizontal velocity)
t = 20/10 = 2 seconds
The vertical velocity is given as follows;
s = u·t - 1/2·g·t²
Where;
u = The vertical velocity
s = The height above the initial height from which the ball is released
s = y - y₀
Where;
y = The final height of the ball in the calculation = The height of the basket = 10 foot
y₀ = The initial height from which the ball is released = 8 feet
∴ s = 10 - 8 = 2 feet
g = The acceleration due to gravity = 9.81 m/s²
Substituting gives;
2 = u × 2 - 1/2 × 9.81× 2²
u = (2 + 1/2 × 9.81× 2²)/2 = 10.81 m/s
The vertical velocity of the ball when released = 10.81 m/s.
The vertical velocity of the ball in the basket is given by the following relation;
v² = u² - 2·g·s
v² = 10.81² - 2×9.81×2 = 77.6161
v = √(77.6161) = 8.81 m/s
The vertical velocity of the ball in the basket = 8.81 m/s
The map shows the location of the mall, library, and school in the city; Brittany travels from the school to the mall and then from the mall to the library. Alice traveled directly from the school to the library. How many more miles to Britney travel than Alice? A. 8 miles B. 9 miles C. 10 miles D. 12 miles
Answers
Answer:A) 8 miles
Step-by-step explanation:
8 miles
What is the measure of
In ABC as shown, AC 1 BC , AB = 11.4, and
BC = 7.
degrees
А
11.4
B
С
7
Answers
hope it helps. , good afternoon , have a great day .
5x + 2(-3x) = *
A)-11x
B) -x
C) -x^2
D) 11x
Answers
Answer:
B) -x
Step-by-step explanation:
distribute the 2 to -3x to get 5x + (-6x)
combine terms to get -x
In the circus, a lion has been trained to jump through a ring of fire that has a radius of 1 meter. What is the ring's circumference?
Answers
A circle is a curve sketched out by a point moving in a plane. The circumference of the ring of fire is 6.2831 meters.
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
The circumference of the ring if the radius is 1 meter is,
Circumference of the ring = 2πr = 2 × π × 1 = 6.2831 meters
Hence, the circumference of the ring of fire is 6.2831 meters.
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4+1/2=
me ayudan plis
Answers
Answer:
9/2 or 4 1/2 or 4.5
Step-by-step explanation:
4+1/2=8/2+1/2=9/2
Answer:
es 4 1/2 creo
Step-by-step explanation:brainliest plis
Solve the following basic one step equation:x12=3
Answers
Answer:
x=1/4
Step-by-step explanation:
x12=3 (I would treat it as 12x=3 since the 12 is still attached with multiplication)
x=3/12 (simplify your fraction)
x=1/4
Which figures have a volume greater than 500 cubic inches? Choose all that apply.
How many times greater is the volume of the sphere than the volume of cone #1? Round your answer to the neared tenth. Use 3.14 for pi.
Answers
Answer:
All shapes except the cone with 5in radius and 8in height
Step-by-step explanation:
Volume of the cylinder with radius 5in and height 8in is expressed as;
V = πr²h
V = 3.14*5²*8
V = 3.14*25*8
V = 628 square inches
The volume of the cylinder is greater than 500in³
Volume of the cone with radius 5in and height 24in is expressed as;
V = 1/3πr²h
V = 1/3*3.14*5²*24
V = 3.14*25*8
V = 628 square inches
The volume of the cone is greater than 500in³
Volume of the spheree with radius 5in is expressed as;
V = 4/3πr³
V = 4/3π(5)³
V = 4/3 * 3.14 * 125
V = 523.33 square inches
The volume of the sphere is greater than 500in³
the average number of shoppers at a particular grocery store in one day is 505, and the standard deviation is 115. the number of shoppers is normally distributed. for a random day, what is the probability that there are between 250 and 450 shoppers at the grocery store?
Answers
For a random day with the standard deviation, the probability that there are less than 300 shoppers on a random day, is 0.00585.
Probability is a measure of the likelihood that an event will occur.
Many events cannot be predicted with absolute certainty. We can only predict the probability that an event will occur, i.e. how likely it is to occur, using it.The average total number of shoppers on a grocery store in 1 day is 505; the standard deviation is 115.
Let, X be the random variable denoting the number of shoppers on a random day.
Then, X follows normal with mean 505 and standard deviation of 115.
Then, we can say that,
Z=(X-505)/115 follows standard normal with mean 0 and standard deviation of 1.
We have to find
P (250 <X< 450)
= P {(250-505)/155} < Z < {(450-505)/155}
= P (-1.64 <Z< -0.03)
Where, Z is the standard normal variate.
ρ = -1.64 <ρ< -0.03
Where, ρ is the distribution function of the standard normal variate.
From the standard normal table, this becomes
=0.00585
For a random day, the probability that there are less than 300 shoppers on a random day, is 0.00585.
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A single card is drawn from a standard 52 card deck.
Work out the probability of choosing "a club".
Give your answer in its simplest form.
Help pleaseee
Answers
13/52
.25
Or 25% of drawing a club
Graph and find the area of the figure with the given vertices. 5. (−1, 4), (−4, −3), (4, −3)
Answers
Answer:
28 units^2
Step-by-step explanation:
A=1/2bh
base is 8
height is 7
A=1/2*56
A=28 units^2
Haydn makes $10 for every 2 glasses of lemonade he sales. Which graph Models a relationship with the same unit rate?
Answers
Answer: 20
Step-by-step explanation:
multiply 10 times 2 and get an answer of 20
Answer: 20
Step-by-step explanation:
If the measure of arc CE is 9x+5 degrees the measure of arc ED is 4x+1 degrees and the measure of arc CD is 101 degrees what is the value of x? Round your answer to the nearest hundredth. Pls answer
Answers
Answer: 2.436. 2.44.
Step-by-step explanation:X is an algebraic variable which has no defined value. X is kind of universe variable taken in most of the equations. If X is any question or an equation then we may solve the equation and get the desired value that would satisfy the given equation.
Evaluate the following integral. dx (441-x²) What substitution will be the most helpful for evaluating this integral? O A. x=21 sin 0 O B. x=21 sec 0 O C. x=21 tan 0 Find dx. dx= de Rewrite the given
Answers
To evaluate the integral ∫dx/(441-x²), the substitution x=21 sinθ will be the most helpful and appropriate.
Using this substitution, we can rewrite the integral as ∫dθ/(cos²θ), and then use the identity cos²θ = 1-sin²θ to obtain ∫dθ/(1-sin²θ).
We can then use partial fractions to decompose this expression into a sum of simpler integrals, namely:
∫dθ/[(1+sinθ)(1-sinθ)] = 1/2 ∫[1/(1+sinθ) + 1/(1-sinθ)] dθ
We can evaluate each of these integrals using the substitution u=tan(θ/2), which leads to:
∫dx/(441-x²) = 1/42 ∫[dx/(21+x) + dx/(21-x)] = 1/42 ln|(21+x)/(21-x)| + C
where C is an arbitrary constant of integration.
However, the substitution x=21 sinθ will be the most helpful and appropriate to evaluate the integral ∫dx/(441-x²).
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What is the slope of the line?
Answers
the slope of the line on the graph is 3 .
What is slope of a line ?Slope is calculated by dividing the "vertical change" by the "horizontal change" between any two distinct points on a line. The ratio can alternatively be expressed as a quotient, which yields the same result for any two separate locations on the same line ("rise over run"). A negative "rise" indicates a falling line. A road surveyor may judge that the line is useful, or it may show up in a diagram of a road or a roof as a description or a design. The steepness, incline, or grade of a line can be measured using the slope's absolute value. A slope with a larger absolute value denotes a steeper line.
Calculationto find the slope of the graph we will take two points which lies on the same line i.e. they must be collinear .
the points i m choosing is (-2,0) and (-1,3)
now for finding the slope we will use the formula
m = (y2-y1)/(x2-x1)
m = (3 - 0 ) / (-1+2)
m = 3 / 1
m = 3
so the slope of the line on the graph is 3 .
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What is the value of x to the nearest tenth?
In a triangle, acute angle is 28 degree and the obtuse angle is 126 degree. The adjacent side of 28 degree angle is 8. 2 and opposite side is x.
A. 4. 8
B. 7. 7
C. 8. 8
D. 14. 1
Answers
Answer:
8.8
Step-by-step explanation:
jus did da math
what distance is between -5,3 and 7,3 i need it for a dba
Answers
Answer: d=\(\sqrt{x1-x2)2+(y1-y2)2}\)
Step-by-step explanation:
i will love uu forever if uu answer dis for me
Answers
#15 is 11 and
#16 is adding 3
Answer:
the answer is 2...........jpjpjp ion knowwwwwwwww
Step-by-step explanation:
An equilateral triangle has the area of 36 √3 square units. What is the side length?
Answers
Step 1
Given;
\(An\text{ equilateral triangle with area 36}\sqrt[]{3}unit^2\)Required; To find the side length.
Step 2
State the area(A) of an equilateral triangle.
\(\begin{gathered} A=\frac{\sqrt[]{3}}{4}a^2 \\ \text{where a= side length} \end{gathered}\)Step 3
Find the side length
\(\begin{gathered} A=36\sqrt[]{3}unit^2 \\ 36\sqrt[]{3}=\frac{\sqrt[]{3}}{4}a^2 \\ 144\sqrt[]{3}=\sqrt[]{3}a^2 \end{gathered}\)\(\begin{gathered} \frac{\sqrt[]{3}a^2}{\sqrt[]{3}}=\frac{144\sqrt[]{3}}{\sqrt[]{3}} \\ a^2=144 \\ \sqrt[]{a^2}=\pm\sqrt[]{144} \\ a=\pm12\text{ units} \end{gathered}\)But, the side length cannot be negative, therefore, the side length of the equilateral triangle = 12 units
Suppose you want to figure out how likely it would be to spin red and flip tails. We call red and tails the event.
Answers
Answer with Explanation: We need to find the probability of obtaining the red and tails when the two are flipped at the same time:
\(\begin{gathered} P\left(R\right)=\frac{1}{2} \\ P\left(T\right)=\frac{1}{2} \end{gathered}\)The probability of the red and tails or P(Red and Tails) is as follows:
\(\begin{gathered} P\left(R\text{ and }T\right?=P\left(R\right)\times P\left(T\right) \\ \therefore\rightarrow \\ P\left(R\text{ and }T\right?=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4} \\ P\left(R\text{ and }T\right?=\frac{1}{4} \end{gathered}\)Conclusion: Therefore the probability is (1/4) or 25%.
xavier writes the expression y+7x2\5 which expression is equivalent to the one xavier writes
Answers
Answer:
bhkhbkb bkhjgjvbhbhhhtfdik gfjkbfg
Step-by-step explanation:
a cleaning service orders 7 large bottles and 14 small bottles of a cleaning product.Each large bottle has 124 ounces.Each small bottle has 64 ounces. which is the best estimate of the total amount of cleaning product the cleaning service orders?
I need help please!!
Answers
Answer: small bottles
Step-by-step explanation:
124 * 7 =868 ounces
14 * 64 = 896 ounces
to investigate whether the consumption of beetroot juice enhances exercise performance, a researcher selected a random sample of 50 student athletes from all the student athletes at a college. the athletes in the sample were randomly assigned to one of two groups. in one group, 25 athletes were given a daily dose of beetroot juice, and in the other group, the remaining athletes were given a daily dose of a placebo. at the end of six weeks of exercise training, the researcher compared the performances of the two groups. based on the design of the investigation, which of the following is the largest population to which the results can be generalized?
(A) The 25 student athletes assigned to the beetroot juice group (B) The 50 student athletes in the sample (C) All student athletes at the college (D) All students at the college (E) All people who exercise
Answers
The largest population to which the results can be generalized is in option C i.e. All student-athletes at the college.
Population: A population can be described as a complete group with at least one characteristic in common and a sample of the population can be used to get the features of the population.
We were told that a random sample of 50 student-athletes from all the student-athletes at a college, even though the population can be used to have an idea about how the consumption of beetroot juice enhances exercise performance, and it can not be used to get the results that can be generalized as more than 50 students-athletes is required which is chosen randomly.
All the other options are wrong because of this reason.
Therefore, option C is correct.
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Convert 7/8 into a decimal
Answers
Answer:
0.875
Step by step explanation:
The perimeter of a rectangle is 90 feet. The width is 15 feet. What is the perimeter?
Answers
=
15
feet
Breadth of the rectangle
=
30
feet.
Explanation:
Let the breadth of the rectangle
=
x
So, the length of the rectangle
=
2
×
x
The perimeter given
=
90
feet
As per the formula for perimeter of a rectangle
Perimeter
=
2
×
(length + breadth )
90
=
2
×
(
x
+
2
x
)
90
=
2
×
(
3
x
)
90
=
6
x
x
=
90
6
x
=
15
So the length of the rectangle
=
15
feet, breadth of the rectangle
=
30
feet.