The center of gravity of the combination of the two circles is at (x, y) = (0, 4/5).
The center of gravity, or the center of mass, of a two-dimensional object can be found by taking the weighted average of the x-coordinates and y-coordinates of the individual masses making up the object.
In this case, the two circles can be treated as point masses, with the mass of each circle being proportional to its area. The area of a circle with radius r is given by pi * r^2.
So, for circle c1 with radius 2, its mass is given by:
m1 = pi * 2^2 = 4 * pi
And for circle c2 with radius 1, its mass is given by:
m2 = pi * 1^2 = pi
The x-coordinate of the center of gravity is given by the weighted average of the x-coordinates of the two masses:
x = (m1 * 0 + m2 * 0) / (m1 + m2) = 0
Similarly, the y-coordinate of the center of gravity is given by the weighted average of the y-coordinates of the two masses:
y = (m1 * 0 + m2 * 4) / (m1 + m2) = 4 * (m2 / (m1 + m2)) = 4 * (pi / (4 * pi + pi)) = 4 * (pi / 5 * pi) = 4/5
So, the center of gravity of the combination of the two circles is at (x, y) = (0, 4/5).
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Pls pls pls Help I suck at math
Write an appropriate number in the cage
(5²)³ = 5□
and
Evaluate. log₃9
Answer:The appropriate number in the cage for the first equation is:
(5²)³ = 5³
The evaluation for log₃9 is:
log₃9 = 2
Step-by-step explanation:
Solve the inequality: four times a number increased by five is at least 33
Answer:
x [tex]\geq[/tex] 7
Explanation:
4x + 5 [tex]\geq[/tex] 33
4x + 5-5 [tex]\geq[/tex] 33 - 5
4x [tex]\geq[/tex] 28
[tex]\frac{4x}{4} \geq \frac{28}{4}[/tex]
x [tex]\geq[/tex] 7
HOPE IT HELPED, PLEASE MARK BRAINLIEST, THANK AND RATE!
I need help on this question
(-3/4) - 2/5
Answer:
Step-by-step explanation:
-1.15
Answer:
-1.15
The answer is -1.15
alicia paid 1.32 for a bag of pino beans the beans cost .55 per lb how much did the bag of pinto beans weigh
Answer:
2.4 lb
Step-by-step explanation:
We know
Alicia paid 1.32 for a bag of pinto beans
The beans cost .55 per lb
How much did the bag of pinto beans weigh?
1.32 / .55 = 2.4 lb
So, the bag of pinto beans weighs 2.4 lb.
Some other person’s sales tax is $1. 61. How much was their subtotal? and the sales tax rate is 9. 5%
If the tax rate at this restaurant is 9. 5% and some other person’s sales tax is $1. 61 then their subtotal is $18.56
Here, some other person’s sales tax is $1. 61
Let us assume that for the amount of 'p' dollars, the sales tax is is $1. 61
Here, the tax rate at this restaurant is 9. 5%
This means, 9.5 percent of m dollars is $1.61
Using percentage formula,
m × (9.5 / 100) = 1.61
m × 9.5 = 1.61 × 100
m × 9.5 = 161
m = 16.95 dollars
So, their subtotal would be,
m + sales tax
= 16.95 + 1.61
= 18.56 dollars
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The complete question is:
The tax rate at this restaurant is 9. 5%. Some other person’s sales tax is $1. 61. How much was their subtotal?
what are the rules for surds
With examples
in the photo
Find the common ratior for the geometric sequence and user to find the next three terms.
Enter your answer to six decimal places if necessary.
7, 4. 2, 2. 52, 1. 512,.
The next three terms are:
0.9072, 0.54432, 0.326592
So, the sequence is:
7, 4. 2, 2. 52, 1. 512, 0.9072, 0.54432, 0.326592
Geometric sequenceA geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. Its general term is. a n= a 1 r n – 1. The value r is called the common ratio. It is found by taking any term in the sequence and dividing it by its preceding term.
The sequence is:
7, 4. 2, 2. 52, 1. 512,.
We have to find the next three terms.
To find r divide the 2nd term by the first:
4.2/7 = 0.6
To check if this is the same ratio for each number divide it by the ratio to get the number before it:
2.52/4.2 = 0.6
1.512/ 2.52 = 0.6
To find the next three terms multiply the last number by the ratio then repeat
(1.512)(0.6) = 0.9072
(0.9072)(0.6) = 0.54432
(0.54432)(0.6) = 0.326592
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What is the volume of a rectangular prism with the dimensions: base 3 1/4
cm, height 2 1/2
cm, and length 4 1/2
cm?
Answer:
V=whl=3.25·2.5·4.5=36.5625 cm
Step-by-step explanation:
Formula: V=whl
Width and base are interchangeable words so all you do is plug the base into (w).
Turn the fractions into decimals and multiply.
3 1/4 = 3.25
2 1/2 = 2.5
4 1/2 = 4.5
3.25*2.5*4.5 = V
V = 36.5625 cm
8 a and b are integers. a+b = 800 b is 250 greater than a. Work out the values of a and b
Answer:a=275 b =525
Step-by-step explanation:
Hi there, here's your answer:
Given:
a and b are integers
a + b = 800 ....(i)
b = a + 250
Putting value of b in (i)
a + (a + 250) = 800
2a + 250 = 800
2a = 800 - 250
Or
2a = 550
Therefore, a = [tex]\frac{550}{2}[/tex] = 275
Since b is 250 greater than a,
b = 250 + 275 = 525
Hope it helps!
Which equation has a slope of 6 and intercepts the y-axis at -4?
Answer:
The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept.
If the slope of the line is 6 and the y-intercept is -4, the equation of the line is y = 6x - 4. This equation describes a line with a slope of 6 that intercepts the y-axis at the point (0, -4).
How many groups of 1 2/3 are in each of these quantities? I’ll mark u as brainliest helppp
a. 1 5/6
b. 4 1/3
c. 5/6
Answer:
The answer is a ( 1 5/6 )
Step-by-step explanation:
.................
Graph the equation y = x² - 14x + 48 on the accompanying set of
axes. You must plot 5 points including the roots and the vertex.
Answer:
Below
Step-by-step explanation:
Here is a sample:
Joey is selling tickets for his new play. He sold 15 more adult tickets than children tickets. He sold 3 times as many senior tickets as children tickets.
Define the variables: _________________________________________________ Write an expression to represent the number of adult tickets sold ________________ Write an expression to represent the number of children’s tickets sold _____________
Variables: A = Adult tickets, C = Children tickets, S = Senior tickets
Expression for number of adult tickets sold: A = 15 + 3C
Expression for number of children's tickets sold: C = S/3
Let's define our variables:
A = Adult tickets
C = Children tickets
S = Senior tickets
We know that Joey sold 15 more adult tickets than children tickets. This means that the number of adult tickets (A) is 15 more than the number of children tickets (C). We can write this as an expression: A = 15 + C
We also know that Joey sold 3 times as many senior tickets as children tickets. This means that the number of senior tickets (S) is 3 times the number of children tickets (C). We can write this as an expression: S = 3C
Now, we can combine these two expressions to solve for the number of adult tickets sold. We can substitute the expression for S (3C) into the expression for A (15 + C) and solve for C.
Substituting 3C for S in A = 15 + C, we get: A = 15 + 3C
This expression tells us that the number of adult tickets sold (A) is equal to 15 plus 3 times the number of children tickets sold (C).
To solve for the number of children tickets sold (C), we can use the expression for S (3C). We can divide both sides of the equation by 3 to solve for C.
Dividing both sides by 3, we get: C = S/3
This expression tells us that the number of children tickets sold (C) is equal to the number of senior tickets sold (S) divided by 3.
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Define the variables: Let x be the number of children's tickets sold.
Write an expression to represent the number of adult tickets sold: The number of adult tickets sold can be represented as x + 15.
Write an expression to represent the number of children's tickets sold: The number of children's tickets sold can be represented as x.
In this problem, we are asked to represent the number of adult and children's tickets sold in terms of a single variable, x. The given information is that Joey sold 15 more adult tickets than children's tickets, and he sold 3 times as many senior tickets as children's tickets. Hence, we can represent the number of adult tickets sold as x + 15 and the number of children's tickets sold as x.
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The number of units produced does not affect net operating income when using _____ costing.
The number of units produced does not affect net operating income when using absorption costing.
All production expenses, including direct materials, direct labour, and both variable and fixed overhead costs, are included in the cost of each unit produced in absorption costing. This means that as more units are manufactured, the total manufacturing cost is distributed over a greater number of units, resulting in a reduced cost per unit.
Variable costing, on the other hand, includes only variable production expenses, such as direct materials, direct labor, and variable overhead costs, in the cost of each unit produced. Fixed manufacturing overhead costs are considered period expenses and are not included in the product cost.
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Cuando pablo compra su auto, este le costo 35000000 pesos, si ahora vale el 45% de su precio original, entonces, su valor actual en pesos corresponde a
The current value of Pablo's car in pesos corresponds to 15,750,000 pesos.
This is calculated by multiplying the original price of 35,000,000 by the discount percentage of 45%, which corresponds to 15,750,000. To calculate the current price, the discount percentage (45%) is first determined and then multiplied by the original price (35,000,000). This is done to determine the discount in pesos (15,750,000) and is then subtracted from the original price to get the current price of 15,750,000.
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Complete Question:
When Pablo buys his car, it cost him 3,500,000 pesos. If it is now worth 45% of its original price, then what is its current value in pesos?
WILL GIVE brainliest ASAP HELPP
An expression that represents the total area of Meiling's new deck is 4.3x + 29.67.
What is rectangular shape?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle.
Given:
An architect plans to build an extension to Meiling's rectangular deck.
Let x represent the increase, in meters, of her deck's length.
The expression 4.3(x+ 6.9) represents the area of the deck,
where 4.3 is the width in meters and (x + 6.9) represents the extended length in meters.
Using the Distributive Property to write an expression that represents the total area of Meiling's new deck.
A = 4.3(x+ 6.9)
A = 4.3x + 29.67
An expression that represents the total area of Meiling's new deck is 4.3x + 29.67.
Hence, area is 4.3x + 29.67 square meters.
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A ball is dropped from 2 meters and rises up by 75%
The height of ball which is droped from 2m and rises to 75% after third bounce is equals to the 0.843 meters.
If an object is thrown from high and has a bouncing feature, each bouncing is less than the initial height until it stops. Each bounce reduces the growth rate until it reaches zero. In order to calculate the height of each bounce, so we can estimate what percentage the object will reach after each bounce. If we get the percentage of each bounce, we can easily determine the height of each bounce. We have, a ball is droped from 2 meters and bounce up to 75%. That is height of first bounce is determined by using percentage, height is 2 m × 75% = 2 m×0.75 = 1.5 m
In second bounce, height is 1.5 m × 75%
= 1.5 m×0.75 = 1.12 m
In third bounce, 1.12 m× 75%
= 1.12 m×0.75 = 0.843 m
The height the ball reaches on its third bounce is 0.843 m.
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Complete question :
A ball is dropped from a height of 2 meters and rises up by 75% of its height on each bounce. How high would the third bounce be?
Find the quotient.
(2x4 – 3x3 – 6x2 + 11x + 8) ÷ (x – 2)
The division of the polynomial 2x⁴ - 3x³ - 6x² + 11x + 8 by x - 2 will give a quotient of 2x³ + x² - 4x + 3 +(14 / x - 2)
What is the quotientThe quotient of polynomials is the result of dividing one polynomial by another. It is a mathematical expression representing the ratio of two polynomials, often written as a fraction. The numerator of the fraction is the dividend polynomial, and the denominator is the divisor polynomial. The quotient of polynomials can be found using long division or synthetic division methods.
In the polynomial division between 2x⁴ - 3x³ - 6x² + 11x + 8 and x - 2
2x⁴ - 3x³ - 6x² + 11x + 8 ÷ x - 2 = 2x³ + x² - 4x + 3 +(14 / x - 2)
The quotient of the division is 2x³ + x² - 4x + 3 +(14 / x - 2) while the divisor is x - 2.
The remainder of the polynomial division is 14
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we colored all points of r2 with integer coordinates by one of six colors. prove that there is a rectangle whose vertices are monochro- matic. can we make the statement stronger by limiting the size of the purported monochromatic rectangle?
Yes, we can make the rectangle has sides of length n and n, and all four vertices have the same color
A rectangle is a two-dimensional shape with four sides, two of which are parallel and equal in length, and the other two sides are also parallel and equal in length.
In this case, the objects are the points in the plane with integer coordinates, and the available spaces are the six colors.
Since there are an infinite number of points with integer coordinates and only six colors, it follows that there must be a color that appears at the vertices of a rectangle.
In other words, we can color the points in a manner such that there will be a rectangle in which all four vertices are the same color. This is because, if we divide the points into six different regions, there must be at least one region that contains more points than the others.
When we look for a rectangle, we look for two points in this region that are the farthest apart from each other. The rectangle that connects these two points will have all four vertices the same color.
In conclusion, we can make the statement stronger by limiting the size of the purported monochromatic rectangle.
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PLANETS The average distance d in astronomical units that a planet is from the Sun can be modeled by d=t^2/3, where t is the number of Earth years that it takes for the planet to orbit the Sun. Find the average distance a planet is from the Sun if the planet has an orbit of 27 Earth years.
The average distance a planet is from the Sun is 9.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
Given;
Sun can be modeled by d=t^2/3, where t is the number of Earth years that it takes for the planet to orbit the Sun.
The planet has an orbit of 27 Earth years.
Now,
d=27^2/3
d^3=27^2
d=9
Therefore, by unitary method the answer will be 9.
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PLS HELP THIS IS DUE TODAY
After the hole is cut, 248 square feet of blue feet of blue surface remain.
What is the surface area of the given cube?
The formula for surface area is equal to six times of square of the length of the sides of the cube. It is represented by 6a², where a is the side length of the cube. It is basically the total surface area.
We have given,
the cube of side length 6 ft,
the shape of a 2-by-4-by-6-foot rectangular prism is cut out of the cube,
to find: After the hole is cut, how many square feet of blue feet of blue surface remain?
area of an original cube is:
= 8 * 6 * 6
= 288 ft²
the area of the cube, after the hole, is cut.
remaining area = original cube area - 2 * 4 *4
= 288 - 32 ft²
= 248 ft²
Hence, After the hole is cut, 248 square feet of blue feet of blue surface remain.
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Given: AB=CB, CD=ED, Prove: AB // DE
The proofing of the triangle is shown below.
How to proof the triangleA triangle is a shape which has three sides and the sum of the three angles is equal to 180 degrees.
We have, Triangle ABC and Triangle CDE
Both triangles are equilateral. This means, three sides are equal and the angle opposite to the side is also equal.
Now, ∠ACB and ∠DCE are vertical angles.
Vertical angles are equal. If ∠ACB and ∠DCE are equal.
The sides opposite ∠ACB and ∠DCE are also equal.
This means, AB = DE
Now, If AB = DE
We can say that, AB is parallel to DE
Thus, AB // DE
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Find the area of the figure. It is formed by two congruent trapezoids
The total area formed by the two congruent trapezoids in this problem is given as follows:
48 m².
How to obtain the area of a trapezoid?The area of a trapezoid is obtained adding the bases, multiplying by the height, and dividing by 2.
For the two congruent trapezoids in this problem, the parameters are given as follows:
Bases 3 and 9.Height of 8/2 = 4.Considering that there are two trapezoids, teh total area is given as follows:
A = 2 x 1/2 x (3 + 9) x 4
A = 12 x 4
A = 48 m².
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A relay race team has 4 runners who run different parts of the race.
There are 16 students on your track team. How many ways can your coach
select students to compete in the race?
The number of ways coach can select students to compete in the race are 1820.
What is combination?The selections are another name for combinations. The choice of items from a predetermined group of items corresponds to combinations. We don't want to organize anything here. We are going to choose them. We use the notation nCr to indicate how many distinct r-selections or combinations there are among a set of n objects. A combination is distinct from an arrangement or a permutation. No matter how the objects are arranged, combinations are produced by choosing some or all of them.
Given;
There are 16 students on your track team with 4 runners who run different parts of the race.
Now, n=16 and r=4;
nCr = 16C4
=16*15*14*13/4*3*2*1
=4*5*7*13
=1820
Therefore, by combination there are 1820 ways.
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The difference , the sum and the product of two positive integers are in the ratio 1:2:6.Find the integers.
The integers are 12 & 4
How to find the integerThe difference , the sum and the product of two positive integers are in the ratio 1:2:6.Find the integers.
Let x = first integer
y = second integer
Finding x and y;
(x - y): (x + y) : xy = 1:2:6
for : (x-y)/(x+y) = 1/2
cross multiply
2(x-y) = x+y (equation 1)
for: (x+y)/ xy = 2/6 = 1/3
cross multiply
3(x+y) = xy (equation 2)
solve for x and y using equation 1 and equation 2
equation 2: xy= 3(x+y)
xy = 3x + 3y
xy -3y = 3x
y(x-3) =3x
divide both sides by (x-3):
y= 3x/(x-3) (equation 3)
substitute equation 3 to equation 1:
2(x-y) =x+y
2[x-(3x/(x-3))] = (3x/(x-3)) +x
solve for x:
x = 12
using equation 3, solve for y:
y = 3(12)/ (12-3)
y = 4
Check:
difference: 12-4 =8
sum: 12+4 =16
product: 12(4) =48
8:16:48 (when reduce to lowest term; dive by 8)
1: 2: 6 (same with the given ratio of the difference, sum and product)
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Please help I’m bad at graphs
Answer:
Step-by-step explanation:
(0,8)
An engine has enough power to operate at full power for 20 minutes. For how long could the engine operate at 35% of full power.
The engine operates for 7 mins at 35% of the full power.
As we know that, full power of the engine refers to 100% capacity.
A/Q,
∵ 100% power of the engine operates for 20 mins
∴ 1% power of the engine operates for [tex]\frac{20}{100}[/tex] mins
∴ 35% power of the engine will operate for [tex]\frac{20}{100}[/tex] × [tex]35[/tex] mins
[tex]=\frac{1}{5}[/tex] × [tex]35[/tex] = 7 minutes (Ans.)
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Anna works in a department store selling clothing. She makes a guaranteed salary of $450 per week, but is paid a commission on top of her base salary equal to 15% of her total sales for the week. How much would Anna make in a week in which she made $2400 in sales? How much would Anna make in a week if she made
x dollars in sales?
Total earnings when selling $2400:
Total earnings when selling $x:
Anna's total earnings in a week with $2400 in sales would be $810. Her total earnings in a week with $x in sales would be $450 + ($x * 0.15).
Explanation:Anna makes a guaranteed salary of $450 per week, and she earns a commission of 15% on her total sales. To calculate her total earnings in a week when she made $2400 in sales, we need to find her commission and add it to her base salary. The commission can be calculated by multiplying her total sales by 15%, which is $2400 * 0.15 = $360. Therefore, Anna's total earnings for that week would be $450 + $360 = $810.
To calculate Anna's total earnings in a week when she made $x in sales, we would follow the same process. The commission would be $x * 0.15, and this amount would be added to the base salary of $450 to determine her total earnings.
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PLEASE HELP ME SOMEONE WITH THIS PLEASE SOMEEONE HELP ME ITS DUE TONIGHT PLEASEEE:(
The detail that best supports the inference that the auto manufacturing industry supports green solutions is -
"Pyrolysis generates low-cost energy that can be used in the automobile manufacturing industry".
What is Parabola?In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
Given is a graph as shown in the image attached.
We can write -
{ 1 } -
f{g(x)} = (x - 2)² - 2(x - 2) - 3
{ 2 } -
g{f(x)} = (x² - 2x - 3) - 2
Therefore, we can calculate f{g(x)} and g{f{x}) as -
f{g(x)} = (x - 2)² - 2(x - 2) - 3g{f(x)} = (x² - 2x - 3) - 2To solve more questions on Pyrolysis, visit the link -
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1 - cos² 15° - cos² 75°
Answer:
1 - cos² 15° - cos² 75° can be simplified as follows:
Using the identity cos² x = 1 - sin² x, we can write the expression as:
1 - (1 - sin² 15°) - (1 - sin² 75°)
= sin² 15° + sin² 75° - 1
Using the identity sin 2x = 2sin x cos x, we can write sin 15° and sin 75° in terms of sin 30° and sin 45°:
sin 15° = sin (30° - 15°) = (1/2) * sin 30°
sin 75° = sin (45° + 30°) = sin 45° + sin 30°
Substituting these values in the above expression, we get:
sin² 15° + sin² 75° = (1/4) * sin² 30° + sin² 45° + sin 30° * sin 45°
= (1/4) * (2 * (1/2)²) + (2 * (1/2) * (1/2)) + (1/2) * (1/2)
= (1/4) + 1/2 + 1/4 = 1
So, 1 - cos² 15° - cos² 75° = sin² 15° + sin² 75° - 1 = 1 - 1 = 0.
Step-by-step explanation: