The statement that when a point (x, y) is rotated 270 degrees about the origin, the resulting point is (y, -x) is true. This can be calculated using the formula (x cos θ – y sin θ, x sin θ + y cos θ), where θ is the angle of rotation.
When point (x, y) is rotated 270 degrees about the origin, the coordinates of the resulting point can be calculated using the following formula: (x cos 270° – y sin 270°, x sin 270° + y cos 270°).
Plugging in the values, we get (y, -x). Therefore, the statement is true.
When rotating a point (x, y) around the origin, the coordinates of the resulting point can be calculated using the following formula: (x cos θ – y sin θ, x sin θ + y cos θ). Here, θ is the angle of rotation. In this case, when the point is rotated 270 degrees about the origin, the resulting point is (y, -x).
The statement that when a point (x, y) is rotated 270 degrees about the origin, the resulting point is (y, -x) is true. This can be calculated using the formula (x cos θ – y sin θ, x sin θ + y cos θ), where θ is the angle of rotation.
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Solve the differential equation by variation of parameters. y" + y = CSC X y(x) =sin(x)ln(|sin(x)|) + C2cos(x) + C1sin(x) + xcos(x)
To solve the differential equation y" + y = csc(x) using variation of parameters, we first need to find a particular solution.
Since the non-homogeneous term is csc(x), we can try a particular solution of the form yp = u(x) csc(x), where u(x) is a function to be determined.
Substituting yp into the differential equation:
u''(x)csc(x) + u(x)csc(x) = csc(x)
To find u(x), we can multiply both sides by csc(x) and integrate with respect to x:
∫u''(x)csc(x) dx + ∫u(x)csc^2(x) dx = ∫csc(x) dx
Integrating the first term by parts:
u'(x) = ∫csc(x) dx = ln|cot(x/2)| + C1
Integrating the second term by parts:
u(x) = -∫csc(x)cot(x) dx = -ln|sin(x)| + C2
So, the particular solution for yp is:
yp = u(x)csc(x) = -ln|sin(x)|csc(x) + C1csc(x) + C2
Now we need to find the general solution y = yc + yp
where yc is the general solution for the complementary homogeneous equation y" + y = 0
yc = C1cos(x) + C2sin(x)
Now we can use the method of variation of parameters to find the general solution for the non-homogeneous equation
By this method, we need to find two functions v1(x) and v2(x) such that W(yc, yp) = v1(x)cos(x) + v2(x)sin(x)
W(yc, yp) = (yc * yp') - (yp * yc')
W(yc, yp) = (C1cos(x) + C2sin(x)) * (-cot(x)csc(x) + C1) - (-ln|sin(x)|csc(x) + C1csc(x) + C2) * (-sin(x)cos(x) + cos(x)sin(x))
W(yc, yp) = -C1cot(x)csc(x) + C1^2 + C2csc(x)
As W(yc, yp) is not identically zero, we can proceed to find v1(x) and v2(x)
v1'(x) = -cot(x)csc(x) + C1
v2'(x) = csc(x)
Integrating both sides by parts:
v1(x) = ln|cot(x/2)| - cot(x) + C3
v2(x) = -cot(x) + C4
The general solution for the non-homogeneous equation y" + y = csc(x) is:
y = yc + yp = (C1cos(x) + C2sin(x)) + (sin(x)ln|sin(x)|
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In AOPQ, 0 = 4.3 cm, p = 4.5 cm and q-5.6 cm. Find the area of AOPQ to the
nearest square centimeter.
Answer:
Step-by-step explanation:
You need to give more information. There is nothing you can tell from the information you gave. Nothing is fixed.
if h(x)=x^2-1 and f(x)=3x+5 , what is h(f(x))?
Answer:
3x^2−2
Step-by-step explanation:
Given f(x)=3x−5 and g(x)=x^2+1
∴f(g(x))=f(x^2+1)
=3(x^2+1)−5
=3x^2−2
Solve the system. {4x^2+4y^2=36 {2x+3y=6
Substitute 2x+3y=6 into the first equation:
4x^2+4y^2=(2x+3y)^2
4x^2+4y^2=4x^2+12xy+9y^2
0=12xy+5y^2
Divide both sides by 5:
0=2.4xy+y^2
Subtract 2.4xy from both sides:
-2.4xy=y^2
Take the square root of both sides:
y=±√-2.4xy
Substitute y=±√-2.4xy into the equation 2x+3y=6:
2x+3(±√-2.4xy)=6
2x±3√-2.4xy=6
Add 2x to both sides:
4x±3√-2.4xy=6+2x
Subtract 4x from both sides:
±3√-2.4xy=6-4x
Divide both sides by 3:
±√-2.4xy=2-4/3x
Square both sides:
-2.4xy=(2-4/3x)^2
-2.4xy=4-16/3x+8/9x^2
8/9x^2-16/3x+4+2.4xy=0
Use the quadratic equation to solve for x:
x= (16 ± √(256+192y^2))/18
Substitute this back into the equation 2x+3y=6 to solve for y:
2(16 ± √(256+192y^2))/18 + 3y = 6
3y = 6 - 32 ± √(256+192y^2))/9
3y = -26 ± √(256+192y^2))/9
y = (-26 ± √(256+192y^2))/27
Therefore, the solution is:
x = (16 ± √(256+192y^2))/18
y = (-26 ± √(256+192y^2))/27
Type the correct answer in each box. Write your answers as fractions, using / as the fraction bar, and write the greater value first.if log3 (8x-3)-log 4 = 2, the value of x is
The value of x 1/2 or 3/2.
The logarithm of any number N if interpreted as an exponential form, is the exponent to which the base of the logarithm should be raised, to obtain the number N. Here we shall aim at knowing more about logarithmic functions, types of logarithms, the graph of the logarithmic function, and the properties of logarithms.
The basic logarithmic function is of the form f(x) = logax (r) y = logax, where a > 0. It is the inverse of the exponential function ay = x. Log functions include natural logarithm (ln) or common logarithm (log). Logarithmic function properties are helpful to work across complex log functions. All the general arithmetic operations across numbers are transformed into a different set of operations within logarithms. The product of two numbers, when taken within the logarithmic functions is equal to the sum of the logarithmic values of the two functions. Similarly, the operations of division are transformed into the difference of the logarithms of the two numbers.
Here, we use:
1) loga/b = log a - log b
2) logba = (logc a)/(logc b)
Given logarithmic equation:
logₓ(8x-3) - logₓ4 = 2
logₓ (8x-3/4) = 2
(8x-3/4) = x²
8x - 3 = 4x²
4x² - 8x + 3 = 0
x = 1/2 or 3/2
Thus, the value of x 1/2 or 3/2.
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i took a borrowed 2500$ from the bank
if the loan is for two years and the amount of interest for those two years is 175$ what is the simple interest rate will i charged
The simple interest rate that you are charged, based on the loan amount and the period of the loan, is 3. 5 %
How to find the simple interest rate ?Borrowers must pay lenders simple interest as a fee in exchange for a loan. Compound interest is excluded from the calculation and just the original principal is used. Simple interest applies to all loans, not just specific ones. Additionally, it refers to the kind of interest that banks give their customers on their savings accounts.
Simple interest is the amount of interest charged on a specific principal amount at a specific interest rate. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.
To find the simple interest rate, find the simple interest charged per year to be:
= 175 / 2
= $ 87. 50
Then , the simple interest rate would be:
= Simple interest per year / Loan amount
= 87. 50 / 2, 500
= 3. 5 %
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i have b right i just don’t know how to find a
The value of a is 16 and b is 18 by similarity of triangles.
What are similar triangles ?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
If the respective sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are comparable (or proportion). Triangles that are similar will have the same form but may not be the exact same size.
Two triangles are said to be similar if their corresponding angles are equal. Equiangular triangles are what they are called. Two equiangular triangles were the subject of a significant finding made by the well-known Greek mathematician Thales. He applied the Basic Proportionality Theorem, sometimes known as the Thales Theorem, as a conclusion.
In triangle OXY and ONM
[tex]\frac{4}{16} = \frac{6}{6 + b}[/tex]
⇒ 24 + 4b = 96
⇒ 4b = 72
⇒ b = 18
again ,
[tex]\frac{4}{16} = \frac{4}{a}[/tex]
⇒ a = 16
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003 (part 1 of 2) 10.0 points
a 0.58 kg object is at rest. a 2.65 n force
to the right acts on the object during a time
interval of 1.51 s.
a) what is the velocity of the object at the
end of this time interval?
answer in units of m/s.
004 (part 2 of 2) 10.0 points
at the end of this interval, a constant force of
3.60 n to the left is applied for 2.86 s.
b) what is the velocity at the end of the
2.86 s?
answer in units of m/s.
At the end of 1.51 seconds, the velocity is 6.9 m/s, and at the end of 2.86 seconds, it is 24.64 m/s.
What is the basic meaning of velocity?The dislocation that an article of particle experiences with regard to the time is expressed vectorially as velocity. The meter per moment (m/s) is the accepted unit of velocity profiles (also known as speed).
A. F = ma, where F is force, m is mass and a is acceleration.
a = 2.65/0.58
Performing division
a = 4.57 m/s²
With respect to final and starting velocities, acceleration, and time, the formula is v = u + at.
v = 4.57×1.51
The act of multiplying
v = 6.9 m/s.
B). New acceleration = 3.60/0.58
The act of multiplying
New acceleration = 6.2 m/s²
v = u + at
v = 6.9 + 6.2×2.86
Performing multiplication
v = 6.9 + 17.75
Performing addition
v = 24.64 m/s.
At two different locations, the velocities are 6.9 m/s or 24.64 m/s.
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last week, juan drove b miles. This week, he drove 164 miles. Using b write an expression for the total number of miles he drove in the two weeks.
Answer: b+164
Step-by-step explanation:
Answer: B + 164 = T
Step-by-step explanation:
T = TOTAL
B = LAST WEEK
Hunter is 1. 75 meters tall. At 12 noon, he measures the length of a tree's shadow to be 30. 85 meters. He stands 26. 8 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter
The height of the tree to the nearest hundredth of a meter is 29.1m.
We can use the concept of similar triangles to find the height of the tree. The ratio of the height of the tree to the length of its shadow is the same as the ratio of Hunter's height to the length of his shadow.
Let h be the height of the tree.
Hunter's height : h = 1.75m : x (where x is the height of the tree)
Hunter's shadow : Tree's shadow = 1.75m : 30.85m
We know that Hunter is 26.8 meters away from the tree, and the tip of his shadow meets the tip of the tree's shadow.
Hunter's shadow = Hunter's height + Tree's shadow
1.75 + x = 30.85
x = 29.1m
Therefore, the height of the tree to the nearest hundredth of a meter is 29.1m.
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-3(y + 2) = 2(y + 6) + 7
Answer:
y = -5
Step-by-step explanation:
-3(y+2) = 2(y+6)+ seven
-3y-6 = 2y+12+
-3y-6 = 2y + 19
-2 -2
-5y - 6 = 19
+6 +6
-5y 25
-5 -5
y = -5
Kristin spent $25 on a magazine and some notepads. If the magazine cost $5 and each notepad cost $4, then how many notepads did she buy?
Answer:
5 notepads
Step-by-step explanation:
We know
Kristin spent $25 on a magazine and some notepads
1 magazine = $5
1 notepad = $4
$25 - $5 = $20
How many notepads did she buy?
We take
$20 divided by $4 = 5 notepads
So, she bought 5 notepads
Answer:
5 notepads
Step-by-step explanation:
25=4x+5
subract 5 from 25 and cancel out old 5
20=4x
divide by 4
20/4 = 5
Please help ASAP i will give brainliest if they answer all the questions "100 points"
Thank you Have a good day :)!
How do i do this? I forgot
Scientific notation 295000 is 295×10³ and standard notation of 7.3×10⁻⁴ is 0.00073 and From least to greatest is 1, 3/2, π/2, √3, 9 and E is the best estimate of √3
What is Number system?A number system is defined as a system of writing to express numbers.
Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.
295000 is 295×10³
Now let us write 7.3×10⁻⁴ is standard notation
7.3/10000=0.00073
We have to arrange from least to greatest
1, 9, 3/2, √3, π/2
1, 9, 1.5, 1.732, 1.57
From least to greatest is 1, 3/2, π/2, √3, 9
E is the best estimate of √3
Hence, scientific notation 295000 is 295×10³ and standard notation of 7.3×10⁻⁴ is 0.00073 and From least to greatest is 1, 3/2, π/2, √3, 9
E is the best estimate of √3
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18. in a bag containing only red apples and green apples, the number of red apples is 3 4of the number of green apples. what fraction of the apples in the bag is red? express your answer as a common fraction.
The fraction of red apples in the bag is 3/ (4+x).
Let there be "x" number of green apples and "y" number of red apples in the bag.
According to the given information,
3/4 * x = y
Therefore, y = 3/4 * x
Since the fraction of red apples is y/ (x+y)
Therefore, fraction of red apples = 3/4 * x / (x+3/4 * x)
Simplifying,
Fraction of red apples = 3/ (4+x)
Therefore, the fraction of red apples in the bag is 3/ (4+x).
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A teacher would like to estimate the true mean amount of time her students spend completing a particular homework assignment. The day the homework is due, the teacher selects a random sample of 30 of her 75 students and records the amount of time that each of them spent completing the assignment. Are the conditions for constructing a t confidence interval met
The conditions for constructing a t-confidence interval are met.
In order to construct a t-confidence interval for the mean amount of time the students spend completing the homework assignment, the following conditions must be met:
The data must be a random sample from the population of interest
The sample size must be sufficiently large (typically, n > 30)
The data should be approximately normally distributed
The population standard deviation or variance must be unknown
From the information provided it can be inferred that the data is a random sample (30 students out of 75 students) and that the population standard deviation or variance is unknown. If the sample size is greater than 30, and the data is approximately normal or the sample size is large, then the conditions for constructing a t-confidence interval are met.
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An elephant weighs 1.1 * 10 to the 4th power pounds a giraffe weighs 2.1 * 10 to the third power pounds how much more does the elephant weigh than the giraffe
The elephant weighs 8.9 × 10³ pounds more than the giraffe.
What is weight?Weight is the gravitational pull of a large second object, like the Moon or the Earth, on a first object. Weight is a result of the universal law of gravitation, according to which any two objects will gravitationally attract one another with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Because of this, larger objects naturally weigh more when placed in the same location; however, the farther an object is from the Earth, the less weight it has.
Given that
Elephant weighs 1.1 × 10⁴ pounds
Giraffe weighs 2.2 × 10³ pounds
To find how much more elephant weighs than giraffe, we need to find the difference of their weights. i.e
1.1 × 10⁴ - 2.1 × 10³
= 11000 - 2100
= 8900
= 8.9 × 10³ pounds
Thus, the elephant weighs 8.9 × 10³ pounds more than the giraffe.
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x - 10 = √9x show steps
The solution of the equation is as follows;
x = -5How to solve equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
The equation can be solved as follows:
x - 10 = √9x
subtract x from both sides of the equation
x - x - 10 = √9x - x
-10 = √9 x - x
-10 = 3x - x
-10 = 2x
divide both sides by 2
x = -10 / 2
x = -5
Therefore,
x = -5
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How much Vanilla extract Will be needed to make 2 dozen cookies?
As you answer the following questions, write explanations for why your current answer is correct
The amount of vanilla extract that will be needed to be able to make 2 dozen cookies is 2 teaspoons of vanilla extract
How to find the amount of vanilla extract ?The recipe given will be able to yield 1 . 5 dozen of Oatmeal Raisin Cookies which means that the 1 . 5 teaspoons of vanilla extract will be needed for 1. 5 dozens of Oatmeal Raisin Cookies.
If you are to make 2 dozen cookies therefore, it means that the recipe would require a higher amount of vanilla extract which can be found by the formula:
= ( Dozen cookies needed x teaspoons in 1 .5 dozen ) / 1 . 5 dozen
= ( 2 x 1 . 5 ) / 1 . 5
= 2 teaspoons of vanilla extract
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in the geometric sequence with a first term of $6$ and a second term of $-6$, what is the $205^{th}$ term?
The 205th term of the given geometric sequence is given by 6
What is a Geometric Sequence?A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.
Given here: The first term of a given geometric sequence as 6 and second term -6.
Thus clearly we can deduce that the common ratio of the sequence is given by -1
Therefore the geometric sequence has two elements that are alternating sequence of the form 6,-6,6,-6,6.........
Therefore the 205th term of the sequence will be given by
T₂₀₅=6×-1²⁰⁵⁻¹
=6×1
=6
Hence, The 205th term of the given geometric sequence is given by 6
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PLEASE HELP ASAP!!! It's a math problem I can't figure out and i don't want to get it wrong.
Thank you so much, it's appreciated!
nevermind yall
i figured it out you don't have to answer, claim ur points in the answer idc
Answer: 21 boxes are needed
Step-by-step explanation:
Total area: length = 1.5 + 6.25 + 1.5 = 9.25 height = 1.5 + 6.25 = 7.75
Total Area = 9.25 x 7.75 = 71.6875
Area of the patio = 6.25 x 6.25 = 39.0625
Area of the extension = Total Area - Area of the patio = 71.6875 - 39.0625 = 32.625
Area covered by one box of tiles: 25 x 0.25 x 0.25 = 1.5625
Number of boxes needed: 32.625 / 1.5625 = 20.88 = 21 boxes
I hope this helps even though you already figured it out!
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What is the area of ΔABC given m∠B = 95°, a = 22 feet, and c = 17 feet?
34.23 feet2
128.54 feet2
188.29 feet2
34680.46 feet2
Answer:
Given m∠B = 95°, a = 22 feet, and c = 17 feet, we can use the Law of Cosines to find the value of b and then use Heron's formula to find the area of ΔABC.
The Law of Cosines states:
c^2 = a^2 + b^2 - 2ab * cos(C)
Since ∠B = 95° , angle C = 180 - 95 = 85
Therefore,
c^2 = a^2 + b^2 - 2ab * cos(85)
so,
b = sqrt(c^2 - a^2 + 2ab * cos(85))
We can substitute the given values of a and c to find b:
b = sqrt(17^2 - 22^2 + 2 * 22 * 17 * cos(85))
Once we have the value of b, we can use Heron's formula to find the area of the triangle:
Area = sqrt(p*(p-a)(p-b)(p-c))
where p is the semiperimeter of the triangle: p = (a + b + c) / 2
Area = sqrt(((22 + b + 17) / 2)((22 + b + 17) / 2 - 22)((22 + b + 17) / 2 - b)*((22 + b + 17) / 2 - 17))
The only option that matches this area is 128.54 feet^2, so the area of ΔABC is 128.54 feet^2.
Find The Range of y-x=3
a shipping service restricts the dimensions of the boxes it will ship for a certain type of service. the restriction states that for boxes shaped like rectangular prisms, the sum of the perimeter of the base of the box and the height of the box cannot exceed 130130130 inches. the perimeter of the base is determined using the width and length of the box. if a box has a height of 606060 inches and its length is 2.52.52, point, 5 times the width, which inequality shows the allowable width xxx, in inches, of the box?
The inequality 60 + 5x ≤ 130 shows the maximum width, in inches, of the box that meets the restrictions of the shipping service, given that the box has a height of 60 inches and a length of 2.5 times the width.
1. Let x = the width of the box, in inches.
2. The perimeter of the base of the box is calculated by the following formula: Perimeter = 2(Width) + 2(Length)
3. Therefore, the equation is: 60 + 5x + 2(2.5x) = 130
4. Simplify the equation by expanding the parentheses and combining like terms: 60 + 5x + 5x = 130
5. Solve for x: 5x = 130 - 60
6. Simplify: 5x = 70
7. Divide both sides by 5 to find x: x = 70/5
8. Simplify: x = 14
9. Therefore, the inequality 60 + 5x ≤ 130 shows the maximum width, in inches, of the box that meets the restrictions of the shipping service is 14 inches
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What is the type of a triangle with sides measuring 5 cm 6 cm and 4 cm?
Answer:
scalene
Step-by-step explanation:
It is a scalene triangle, meaning all sides are different lengths. It is NOT a right triangle because the 6 cm side is "too short" to be a hypotenuse.
The angles of a quadrilateral are $x$, $5x + 15^\circ $, $3x - 25^\circ$, and $4x - 20^\circ $. Find the measure of the largest angle of the angle
The measure of the largest angle of the quadrilateral is 88 degrees.
The sum of the angles of a quadrilateral is 360 Degrees. This is derived from the property named Angle Sum property of quadrilateral. We can use this fact to set up an equation using the given information:
x + (5x + 15) + (3x - 25) + (4x - 20) = 360
Simplifying this equation:
13x = 350
x = 27^
Now we can substitute this value of x back into the equation for any of the four angles to find the largest angle:
4x - 20 = 4(27) - 20 = 108 - 20 = 88
Therefore, the measure of the largest angle of the quadrilateral is 88 degrees.
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a) Two workers laid 250 bricks. If Ram had laid twice as many as he did and Shyam had laid half as many as Ram did, there would have been 50 bricks left over. How many bricks did each lay?
Step-by-step explanation:
Let x be the number of bricks Ram laid.
Shyam laid x/2 bricks.
Therefore, x + x/2 + 250 = x(3/2) + 250 = x(3/2) = 300
x = (2*300)/3 = 200
Ram laid 200 bricks.
Shyam laid 200/2 = 100 bricks.
a fair die is rolled three times. what’s the probability that it will land on a 2 on the first roll, a 3 on the second roll, and a 4 on the third roll?
1/216
1/6
1/18
1/24
The probability of having a 2 on first roll, 3 on second roll and 4 on third roll is 1 / 216
What is probability of a fair diceA fair dice is a dice that is equally likely to land on any of its faces, meaning that each face has the same probability of facing up after a roll. The probability of getting a specific face on a fair dice is represented by the number of ways that face can appear divided by the total number of possible outcomes.
For a standard six-sided fair dice, the total number of possible outcomes is 6, since there are six faces on the dice. The probability of getting a specific face (for example, the number 4) is 1/6, because there is only one way to get that number out of the six possible outcomes.
The probability of landing 2 on first roll, 3 on second roll and 4 on third roll is given as;
P = (1/6 * 1/6 * 1/6)
P = 1 / 216
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Determine the volume of a sphere with a great circle of radius 12 cm. Question 7 options:A) 7,238.2 cm3 B) 3,216.9 cm3 C) 1,024 cm3 D) 21,714.7 cm3
The volume of the sphere with a great circle of radius 12 cm is 7238.2 cm³. The correct option is A) 7,238.2 cm3
Calculating the volume of a sphereFrom the question, we are to calculate the volume of the sphere with the given radius.
From the formula for calculating the volume of a sphere, we have that
V = 4/3πr³
Where V is the volume
and r is the radius
From the given information,
The sphere has a great circle of radius 12 cm
Thus,
r = 12 cm
Substitute the value of r into the equation,
V = 4/3πr³
That is,
V = 4/3 × π × 12³
V = 4/3 × π × 1728
V = 4 × π × 576
V = 4 × 576 × π
V = 2304π
V = 7238.2 cm³
Hence, the volume is 7238.2 cm³
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Steadman Bailey's bank account shows a previous balance of $65.00. He
made $756.00 in deposits. He wrote $44.10 in checks. He had a service
charge of $4.90 and earned $10.00 in interest. What is his present
balance?
VEGHER
PEREKONNAN
FRECEN
CAFETERA
FREETING
Answer:
present balance=782
Step-by-step explanation:
65+756=821
now has 821 in account
821-44.10=776.9
now has 776.9
776.9-4.90=772
now has 772 in account
772+10=782
he now has 782 in his account
