The center of the circle lies on the x-axis. The radius of the circle is 3 units. The radius of this circle is the same as the radius of the circle whose equation is x² + y² is 9.
What is radius of a circle?The radius of a circle is the distance between the circle's centre and any point on its circumference. It is usually represented by the letters 'R' or 'r'. This number is significant in almost all circle-related formulas. A circle's area and circumference are also measured in terms of radius.
The standard equation of a circle is expressed as:
x² + y²+2gx+2fy+C=0
Centre is (-g, -f)
radius = √g²+f²-C
Given a circle whose equation is 2+ y²-2x-8=0.
Get the centre of the circle
2gx = -2x
2g=-2
g=-1
Similarly, 2fy = 0
f=0
Centre = (-(-1), 0) = (1, 0)
This shows that the center of the circle lies on the x-axis
r = radius = √g²+f²-C
radius = √1²+02-(-8)
radius =√9 = 3 units
The radius of the circle is 3 units.
For the circle x² + y² = 9, the radius is expressed as:
r² = 9
r = 3 units
Hence the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
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What is the common angle of APOT and ARSQ?
OZ POT
OZSPT
OZ SRO
OZSUT
P
R
S
Q
From the given options the common angle of ΔPQT and ΔRSQ is ∠PQT.
What is a common angle:When an angle appears simultaneously in multiple geometric figures, it is referred regarded as being a common angle. Two figures with shared vertices points and angle edges are said to have a common angle.
Here we have
ΔPQT and ΔRSQ
The internal angles of ΔPQT are
=> ∠PQT, ∠PTQ, and ∠QPT
The internal angles of ΔRSQ are
=> ∠SRQ, ∠RSQ, and ∠SQR
Where ∠PQT = ∠SQR
From above information
The common angles of ΔPQT and ΔRSQ are ∠PQT and ∠SQR
Therefore,
From the given options the common angle of ΔPQT and ΔRSQ is ∠PQT
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Complete Question:
What is the common angle of ΔPQT and ΔRSQ from the given figure?
Someone please help me I’m dying hereThank you so muchhh!
By using the formula for area of rectangle, it can be calculated that-
a) Expression for total area = [tex]6^2 + 2 \times 6 + 24[/tex]
Total area = 72 square inches
b) Length of the figure = 9 inches
Breadth of the figure = 8 inches
What is area of a rectangle?
Area of a rectangle is the total space taken by the rectangle.
If l is the length of the rectangle and b is the breadth of the rectangle, then area of the rectangle is calculated by
Area = l [tex]\times[/tex] b
Side of the square = 6 inches
Area of the square = [tex]6^2[/tex] square inches
Length of white rectangle = 2 inches
Breadth of white rectangle = 6 inches
Area of white rectangle = [tex]2 \times 6 =[/tex] 12 square inches
Area of blue rectangle = 24 square inches
Total area = [tex]6^2 + 2 \times 6 + 24[/tex] =
36 + 12 + 24 =
72 sq. inches
b) Let the breadth of the blue rectangle be b inches
Length of the blue rectangle = 2 + 6 = 8 inches
Total area = 8b square inches
By the problem,
[tex]8b = 24 \\b = \frac{24}{8}\\[/tex]
b = 3 inches
Length of the figure = 6 + 3 = 9 inches
Breadth of the figure = 2 + 6 = 8 inches
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PLEASE HELPPP ASAP I REALLY NEED MATH HELPPPP
The graph of the odd-degree polynomial reaches positive and negative infinity.
What is the end behavior of a polynomial?A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.
The graph's final behavior is determined by a polynomial function's degree and leading coefficient.
The given polynomial is shifted towards the left it reaches negative infinity quicker than positive infinity.
Also, the graph of the polynomial is of odd degree as it is symmetric about the origin shifted towards left.
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Find the monthly payment R needed to have a sinking fund accumulate the future value A. The yearly interest rater and the time t in years are given below. Interest
is compounded monthly.
A=$4,000; r = 5.5%; t=1
R=$
(Round up to the nearest cent.)
Clear all
Check answer
2:21 PM
The monthly payment (R) needed to have a sinking fund accumulate the future value (A) is equal to $325.08
What is Future Value?
Future value (FV) is the value of an asset now based on an anticipated rate of increase in the future. Investors and financial planners use the future value to project how much an investment made now will be worth in the future.The formula for future value (A) is given as, [tex]A=\frac{R[(1+\frac{r}{n})^{nt}-1] }{\frac{r}{n}}[/tex], where R is the monthly payment, r is the yearly interest rate, t is the time (in years) and n is the number of compounding (monthly).Here, the given values are:
A=$4,000;
r=5.5%=0.055
t=1 year
And it is given that the interest is compounded monthly.
So, n=12
Using the formula for Future Value, [tex]A=\frac{R[(1+\frac{r}{n})^{nt}-1] }{\frac{r}{n}}[/tex]
Substituting the given values in the above equation, we get
[tex]4000=\frac{R[(1+\frac{0.055}{12})^{12 \times 1}-1] }{\frac{0.055}{12}}\\\implies 4000=\frac{R[(1+0.0046)^{12}-1] }{0.0046}\\\implies 4000=\frac{R \times 0.0566 }{0.0046}\\[/tex]
Rearranging the above expression in terms of the monthly payment, we get
[tex]R=\frac{4000 \times 0.0046}{0.0566} \\\implies R=325.08[/tex]
Therefore, the monthly payment (R) needed to have a sinking fund accumulate the future value (A) is $325.08
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Peter has collision insurance with $1000 deductible. He backs his car into a lamppost and causes $4300 worth of damage to the car. How much will his insurance company have to pay (assuming he is covered).
On a bicycle, Na'estse rides for 8 hours and s 42 miles from her house. After riding for 10 hours, she is 52
miles away.
What is Na'estse's rate?
miles per hour
Answer:5 miles per hour
Step-by-step explanation:
By subtraction, we can see that the second time was 10-8=2 hours and covered 52-42=10 miles. 10 miles/2hours = 5 miles per hour. So that was her constant (or average) speed throughout the trip.
I’ll mark BRAINLIST Can someone please help please
Jenny has c charms on her bracelet her older sister has five more charms than Jenny write an expression that
The expression that shows how many charms Jenny's older sister has is
c + 5.
What are algebraic expressions?
An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).
Expressions are made up of terms.
According to the given question:
Jenny has c charms on her bracelet.
Her older sister has 5 more charms than Jenny.
To write an expression that shows the number of charms her older sister has. we simply add 5 extra charms to the number of charms Jenny has
Therefore, Jenny's older sister has c + 5 charms.
In this expression c represents the number of charms Jenny has.
The complete question is as follows:
Jenny has c charms on her bracelet. Her older sister has 5 more charms than Jenny. Write an expression that shows how many charms her older sister has.
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Enter the equation of the circle described below.
Center (0, 8), radius = 8
x2 + (y -
)2 =
The equation of the circle described in the problem is x² + (y - 8)² = 64.
What is the equation of a circle?
The general equation of any type of circle is represented by: x2 + y2 + 2gx + 2fy + c = 0, for all values of g, f, and c.
The general equation of a circle is (x – h)2 + (y – k)2 = r2, where (h, k) represents the location of the circle's center, and r represents the length of its radius.
The standard form equation of a circle with center at (h, k) and radius r is given by:
(x - h)² + (y - k)² = r²
Substituting the given values into this equation, we get:
(x - 0)² + (y - 8)² = (8)²
Simplifying this equation gives:
x² + (y - 8)² = 64
Hence, This is the equation of the circle described in the problem.
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This season, the probability that the Yankees will win a game a is 0.53 and the
probability that the Yankees will
score 5 or more runs in a game is 0.48. The
probability that the Yankees win and score
and score 5 or more runs is 0.42. What is the
probability that the Yankees will lose when they score 5 or more runs? Round
your answer to the nearest thousandth.
The probability that the Yankees will lose when they score 5 or more runs is equal to 0.2766.
What is Conditional Probability?
Conditional probability, or P(A/B), denotes the likelihood of event A that is dependent on event B.The chance of an event occurring given that another event has already occurred (via assumption, supposition, assertion, or evidence) is known as conditional probability in the field of probability theory.This particular approach assumes that event B occurs in some way related to event A. A conditional probability analysis with respect to event B in this scenario can be performed.The conditional probability formula is given as, [tex]P(M/N)=\frac{P(M\cap N)}{P(N)}[/tex]From the question, we know that the probability that the Yankees will win a game is 0.53.
[tex]\implies P(W)=0.53[/tex]
Also, then the probability that the Yankees will lose a game is given as,
[tex]P(L)=1-P(W)\\\implies P(L)=1-0.53\\\implies P(L)=0.47[/tex]
It is also given that, the probability that the Yankees will score 5 or more runs is 0.48.
[tex]\implies P(A)=0.48[/tex] -----(1)
So, the probability that the Yankees will score less than 5 runs is,
[tex]P(S)=1-P(A)\\\implies P(S)=1-0.5\\\implies P(S)=0.5[/tex]------(2)
We also know the probability that the Yankees will win and score 5 or more runs is 0.42.
[tex]\implies P(B)=0.42[/tex]
Also, then the probability that the Yankees will lose or score less than 5 runs is given as,
[tex]P(C)=1-P(B)\\\implies P(C)=1-0.42\\\implies P(C)=0.58[/tex]
Next, the probability that the Yankees will lose and score less than 5 runs is,
[tex]P(D)=0.42+0.5-0.58\\\implies P(D)=0.34[/tex]
Now, the required probability is the probability that the Yankees will lose and score 5 or more runs.
It can be calculated using the conditional probability formula, [tex]P(M/N)=\frac{P(M\cap N)}{P(N)}[/tex]
So, the required probability that the Yankees will lose and score 5 or more runs is given as,
P(they score 5 or more runs / probability that they lose game) = P(they lose and score 5 or more runs) / P(they lose the game)
[tex]\implies P(E)=\frac{0.47-0.38}{0.47} \\\implies P(E)=0.2766[/tex]
Therefore, the probability that the Yankees will lose when they score 5 or more runs is equal to 0.2766.
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what times 7 equals 3.5
Answer:
Step-by-step explanation:
Answer 2
You would divide 7 by 3.5 and you get 2 If the equation was what times 3.5 =7
Select the expression that represents the ADDITION of
the two number lines.
O-10x+ 5x - 30x
O-10x-5x + 30x
O 10x + 5x - 30x
An expression that represents the ADDITION of the two number lines is: B. -10x - 5x + 30x.
Each segment equals 5x and the first arrow is 30x long.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
Based on the number line shown above, we can reasonably infer and logically deduce that each of its segment is equal to 5x with the longest arrow measuring 30x on the number line.
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Consider a student loan of $25,000 at a fixed APR of 9% for 20 years.
a. Calculate the monthly payment.
b. Determine the total amount paid over the term of the loan.
c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.
The monthly payment will be $161.20.The total amount paid over the term of the loan is $38,688 and 58.2% is paid toward the principal while 41.8% is paid toward interest.
What is compound interest?Compound interest is applicable when there will be a change in principal amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount.
As per the given,
Principle amount P = $25,000
APR = 9% = 0.09
Time period T = 20 years
a) Monthly payment will be given as,
⇒ P(r/12)/(1 -(1 +r/12)^(-12t))
⇒ 22500·(0.06/12)/(1 -(1 +0.06/12)^(-12·20))
⇒ $161.20
b) After 20 years the amount as,
$161.20 x 240 = $38,688
c) (22500/38688)·100% = 58.2% is paid toward principal
The remaining amount, 41.8% is paid toward interest.
Hence "The monthly payment will be $161.20.The total amount paid over the term of the loan is $38,688 and 58.2% is paid toward the principal while 41.8% is paid toward interest".
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Principal: $225, Interest Rate: 6%, Time: 2 years.
What is simple interest? I know it is something related to PxRxT or something like that.
Answer:
$27
Step-by-step explanation:
Simple interest is a way of calculating the interest charge on a loan or investment. It is calculated by multiplying the principal amount by the interest rate and the time period. In your example, the simple interest calculation would be $225 * 6% * 2 years = $27.
Answer:
Simple interest is a type of interest that is calculated only on the principal amount of a loan or investment, without taking into account any additional interest that has been earned on the principal. To calculate simple interest, you multiply the principal amount by the interest rate and the length of time the interest is being applied. For example, if you have a principal of $225, an interest rate of 6%, and a time of 2 years, the simple interest would be calculated as follows:
$225 x 6% x 2 years = $27.
In this case, the simple interest on the $225 principal would be $27. This means that after 2 years, you would owe $252 in total, including the original principal and the interest that has been earned on it. Simple interest is typically used for short-term loans or investments, where the interest is paid or earned at regular intervals, such as monthly or annually.
An object placed on a conveyor belt can move 9 feet every 18 seconds.
Plot two points that represent the distance an object would travel in different amounts of time at that rate.
Select two points on the coordinate grid. A line will connect the points.
A graph of the two (2) points (-0.5, 0) and (9, 0) that represent the distance which this object would travel in different amounts of time at that rate is shown in the image attached below.
How to write a linear function for the distance and time?Mathematically, a linear function is sometimes referred to as the slope-intercept form of a straight line and it can be modeled (represented) by this mathematical expression;
d = mt + b
Where:
d represents the distance.t represents the rate of change (slope).b represents the y-intercept.Therefore, the required linear function that relates the distance (d) and speed (s) at time (t) seconds is given by this mathematical expression;
d(t) = 18t + 9
For instance when time (t) = -0.5 seconds, the distance traveled by this object placed on a conveyor belt is given by;
d(t) = 18t + 9
d(-0.5) = 18(-0.5) + 9
d(-0.5) = -9 + 9
d(-0.5) = 0 feet.
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Given the value: 47.728
a. Write the word name of the value.
b. Write the expanded form of the value
c. Use a number line to round this value to the nearest hundredth.
Your knowledge of the percentage 47.728 is already complete.4772.8% is the percentage equivalent of 47 7 2 8.
What is 47.728 as a Percent?To compute 47.728 as a percentage of a given number x, divide 47.728 by x and multiply the result by 100.
For instance, the ratio of 47.728 to 10 is equal to (47.728 / 10) times 100%, or 477.28%.
Use the decimals to percents converter found below at your convenience.
Place your value in the "% of" area after entering 47.728 in the number field.
Press reset first if you want to restart.
At this point, an automatic conversion to 47.728 in percent will take place.
The answer has been rounded to ten decimal places, as you can see.
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PLEASE HELP WILL MARK BRAINLIEST..Write a polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots.
x= -2, x=7
P(x)=
A polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots is P(x)=x²-5x-14
What is a polynomial function?A function is said to as polynomial when a variable in an equation, such as a quadratic equation or cubic equation, etc., has only positive integer exponents or non-negative integer powers. One polynomial with an exponent of 1 is 2x+5, for instance. One that has more than two algebraic terms is referred to as a polynomial expression. Polynomial is a monomial or binomial that is repeatedly added, as the name suggests.
A mathematical expression containing one or more algebraic terms, where each algebraic term is made up of a constant multiplied by one or more variables raised to a nonnegative integral power.
x= -2, x=7
Given,
P(x) = 0
This polynomial function has the roots,
x= -2, x=7
So,
(x+2)(x-7)
We have to multiply both of them we get,
P(x)=(x+2)(x-7)
0=x²-5x-14
x²-5x-14=0
Therefore, P(x)=x²-5x-14 is the polynomial function.
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Use the image to answer the question.
What is the surface area of the figure in square centimeters?
Enter your answer as a number, like this: 42
Answer:
66 [tex]cm^{2}[/tex]
Step-by-step explanation:
Front: 6 x 5 = 30
Back: 6 x 4 = 24
Left side: 1/2 (3 x 4) =6
Right side: 1/2 ( 3 x 4) 6
Add
30 + 24 + 6 + 6 = 66
I AM ON A TEST HELP WHAT IS THE MAXIMUM OR MINIMUM VALUE AND WHAT ARE THE COORDINATES OF THE VERTEX y=2x^2+12x+5
The parabola's vertex is (-3/2, -22). Because this is the lowest point on the parabola, the function's minimum value is -22.
To determine the maximum or minimum value of the quadratic function y = 2x² + 12x + 5, you need to find the vertex of the parabola formed by this function.
To find the vertex of the parabola, you can use the formula x = -b / (2a), where x is the x-coordinate of the vertex, a is the coefficient of the x² term, and b is the coefficient of the x term.
In this case, the coefficient of the x² term is 2, and the coefficient of the x term is 12. Therefore, the x-coordinate of the vertex is x = -12 / (2×2) = -6 / 4 = -3/2.
To find the y-coordinate of the vertex, you can substitute the x-coordinate back into the original equation:
y = 2(-3/2)² + 12(-3/2) + 5 = 2(-9/4) + (-18) + 5 = -9 + (-18) + 5 = -22.
Therefore, the vertex of the parabola is (-3/2, -22). This is the lowest point on the parabola, so the minimum value of the function is -22.
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Processing for result of 3/4+5/4=
Answer:
8/4, or 2
Step-by-step explanation:
Brainliest, Please!
Like fractions are fractions that have the same denominator.
To add like fractions, you must add the numerators and keep the same denominator. Finally, the result is simplified if possible.
The procedure for this addition of fractions is as follows:
[tex]\begin{gathered} \sf \frac{3}{4} + \frac{5}{4} = \\ \\ \sf \frac{3 + 5}{4} = \\ \\ \boxed{ \sf\frac{ \red8}{ \red4} }= \sf \blue2\end{gathered}[/tex]
Therefore, the result of the sum of fractions is two.
in forming a 95% confidence interval for a population mean from a sample size of 20, we can proceed with large sample inference. True or False ?
As per the given confidence interval, the given statement "in forming a 95% confidence interval for a population mean from a sample size of 20, we can proceed with large sample inference" is false.
Confidence interval,
in probability , confidence interval refers the probability that a population parameter will fall between a set of values for a certain proportion of times.
Given,
in forming a 95% confidence interval for a population mean from a sample size of 20, we can proceed with large sample inference.
Here we need to find the given statement is true or false.
While we looking into the given question, we have identified that the value of
Confidence interval = 95%
Sample size = 20
Then the sample inference is calculated as, if we were to take 20 different samples and compute a 95% confidence interval for each sample, then approximately 95 of the 100 confidence intervals will contain the true mean value (μ).
Therefore, the statement is in correct.
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367 Times 10 -3
Express the following numbers in scientific notation
Answer:
To express a number in scientific notation, you need to write it as a number between 1 and 10, multiplied by a power of 10.
In this case, 367 can be written as 3.67 x 100, and 10-3 can be written as 0.001.
Therefore, 367 x 10-3 can be expressed in scientific notation as:
3.67 x 0.001 = 0.00367
This can also be written as 3.67 x 10^-3. The ^ symbol indicates an exponent, and in this case, it means that the base number (3.67) is multiplied by 10 to the power of -3.
Step-by-step explanation:
Work out the volume of this half-cylinder.
Give your answer in terms of π.
The diagram is not drawn to scale.
Answer:
Vhc = 401.92 cm3
Step-by-step explanation:
Vcylender = Pi*r2*h
Vhalfcyldr = (Pi*r2*h)/2
then
h= 16cm
r = 8cm/2 = 4cm
then
Vhalfcylinder = ((3.14)*(4)2*16) / 2
Vhc = 401.92 cm3
Solve (x + 1)2 – 4(x + 1) + 2 = 0 using substitution. u = x 4(x +1) x +1 (x + 1)2 Select the solution(s) of the original equation. x = 1 +
The solutions for the given equation are x=-3 and x=1.
The given equation is (x + 1)² - 4(x + 1) + 2 = 0.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
(x + 1)² - 4(x + 1) + 2 = 0
⇒ (x + 1)² - 4(x + 1)=-2
⇒ (x+1)[(x+1)-4]=-2
⇒ x+1=-2, (x+1)-4=-2
⇒ x=-2-1, x+1=-2+4
⇒ x=-3, x+1=2
⇒ x=-3, x=1
Therefore, the solutions for the given equation are x=-3 and x=1.
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What is the RANGE of the cluster shown on this graph?
The range of the cluster shown in the graph is [1, 6]
What is range of a graph?
The range is all the values of the graph from down to up or on the x-axis.
Solution :
∵ Range is calculated from x-axis
∴ Range {1,2,3,4,5,6} = 6-1
= 5
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The range of the cluster shown in the graph is [1, 6]
What is range of a graph?The range is all the values of the graph from down to up or on the x-axis. The possible output values are displayed on the y-axis and make up the range. Remember that the domain and range of the graph could be larger than the visible values if it extends beyond the area that can be seen.
Solution :
∵ Range is calculated from x-axis
∴ Range {1,2,3,4,5,6} = 6-1
= 5
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Determine a series of transformations that would map polygon ABCD onto poly
A'B'C'D'?
The polygon ABCD is transformed 4 units to the left after being reflected across the x-axis.
How does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
Reflect the polygon ABCD across the x-axis as;
A(x, y) → A'(x, -y) (x, -y) (x, -y)
According to this rule, A's coordinates are
A(1, -5) → A'(1, 5) (1, 5) (1, 5)
ABCD is shifted 4 units further to the left.
Now apply to the translation:
A"(x - 4, y) = A'(x, y) (x - 4, y)
A'(1, 5) → A"(1 - 4, 5) (1 - 4, 5) (1 - 4, 5)
→ A"(-3, 5) (-3, 5) (-3, 5)
Thus Polygon ABCD will eventually overlap Polygon A'B'C'D' through a series of transformations.
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How many solutions are there for the system of nonlinear equations represented by this graph?
Answer: A
Step-by-step explanation:
1,y=4 x+3
2.y=5/4 x+3
3.y=-4 x+3
4.y=-5/4 x+3
Answer:
the answer will be the option 2
g(x)=x-2/x+19 findg(-5)
Answer:
the functions domain is; x < -19 or x > -19
x= -19
Sorry otherwise im not sure what you need here :P
How far does a wheel travel in 4 rotations with a radius of 36 inches?
Round to the nearest hundredths
The wheel will travel 904.32 inch when it take 4 rotation
How do you calculate distance using radius and revolutions?
Hint: To calculate the wheel's circumference, use the formula 2πr, where r is the radius and π=3.14 , to first determine the distance covered in one revolution. To determine the distance traveled, multiply the distance covered in one revolution by 200. In the end, multiply it by 100 to get the distance in meters.
In mathematics, what is the circumference?
The distance between the center of the sphere and any plane passing through it is known as the circumference. Any large circle that passes through a point known as a pole is called a meridian.
The circle's circumference must be known in order to compute the distance covered during one rotation. C=2πr is the formula for the circumference.
The radius, designated as r, is 36 inches. As a result, C=2π36 = 72π. The distance covered in one rotation is 226.08 inches because (pi) =3.14159, C=226.08 inches. So when we rotate this 4 times the it travels 226.08 * 4 = 904.32 inch
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