The 32nd term of the arithmetic sequence AP is calculated to be 240.
What basically is an AP arithmetic sequence?In mathematics, an arithmetic progression (AP) is a list and possibly sequence of numbers where each term is collected by adding a sequence towards the term before it.
The fixed number, without regard to arithmetic progression, is signified by the letter 'd.'Common difference => d = a2 - a1 = a3 - a2 = a4 - a3 =...... = a - an-1.nth term of AP: an = a + (n - 1) dThe sum of n terms of an AP's => Sn = n/2(2a+(n-1)d) = n/2(a + l), where l = last term of the AP.Finally, here is the answer to the question:
The following are the numbers with in displayed sequence:
23,30,37,44, ...........
The 32nd number in the series must be investigated because it contains 32 terms.
The common difference between two consecutive terms of an AP that are equal is denoted by the letter 'd.'
Let's consider the first term is'a₁' = 23.
Let's consider 'a₂' = 30 is the second term.
Let's consider the third term is 'a₃' = 37.
Substitute the values the above obtained equation; the 32nd term is-
d = a₂ - a₁
Estimate the common difference;
d = 30 - 23
d = 7
Substitute the values in the next formula; the 32nd term is
The formula given will estimate the nth term equation;
nth term of an AP: an = a + (n - 1) d
Total number of terms ; n = 32
Initial term is a = 23
Common difference d = 7
Substitute the given values in nth term formula;
a₃₂ = a + (n - 1) d
a₃₂ = 23 + (32 - 1)(7)
a₃₂ = 23 + 217
a₃₂ = 240
Thus, the 32nd term value of the given arithmetic sequence is estimated to be 240.
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Andrew ran 5 miles less than two times the number of miles Bernadette ran. Andrew ran a total of 13 miles. Write an equation to determine how many miles Bernadette ran.
13 = 2x − 5
x − 5 = 2(13)
x/13 = 2(5)
13 + 2x = 5
Answer:
a) 13 = 2x - 5
Step-by-step explanation:
Given that,
→ Andrew ran 5 miles less than 2 times the no. of miles Bernadette ran.
→ Andrew ran a total of 13 miles.
Then the equation will be,
→ 13 = 2 times - 5
→ 13 = 2x - 5
Hence, option (a) is correct.
Copy and complete the proof.
Given: C is the midpoint of AE.
C is the midpoint of BD.
AE ≅ BD
Prove: AC ≅ CD
Proof:
Statements Reasons
a. _______ a. Given
b. A C=C E, B C=C D b. _______
c. A E=B D c. _______
d. _______ d. Segment Addition Postulate
e. A C+C E=B C+C D e. _______
f. A C+A C=C D+C D f. _______
g. _______ g. Simplify.
h. _______ h. Division Property
i. AC ≅ CD i. _______
The words that are needed to complete the proof has been added below:
a. AE ≅ BD a. Given
b. A C=C E, B C=C D b. definition of midpoint
c. A E = B D c. definition of congruent segments
d. A C + C E = A E d. Segment Addition Postulate
e. A C + C E = B C + C D e. definition of congruent segments
f. A C + A C = C D + C D f. substitution
g. 2 A C = 2 C D g. Simplify.
h. A C = C D h. Division Property
i. AC ≅ CD i. definition of congruent segments
step I is the required proof
What are congruent segments?This is a term to compare segments that they are have similar properties such as equality in length. For instance using the line asked in the question, line AC is congruent to line CD means that the two lines are equal in length
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Find the coordinates of the midpoint of a segment with the given endpoints. A(0,0), C(3,-4)
The coordinates of the midpoint of a segment with the given endpoints will be (1.5, -2).
What is the mid-point of the line segment?Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).
Then the coordinate of the mid-point of the line segment is given as,
(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]
The endpoints are A(0, 0) and C(3, -4).
Then the coordinates of the midpoint of a segment with the given endpoints will be
(x, y) = [(0 + 3) / 2, (0 - 4) / 2]
(x, y) = (3/2, -4/2)
(x, y) = (1.5, -2)
The coordinates of the midpoint of a segment with the given endpoints will be (1.5, -2).
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If in ∆ABC, the bisectors of ∠B and ∠C intersect each other at O. Prove that ∠BOC = 90° + 1/2∠ A.
ps- pls help istg
It has been proved that if the bisectors of ∠B and ∠C intersect each other at O, then; ∠BOC = 90°+ ¹/₂∠A
How to prove angles?A △ ABC such that the bisectors of ∠ ABC and ∠ ACB meet at a point O.
To prove :
∠BOC = 90° + ¹/₂∠A
Proof :
In △BOC, we have
∠1 + ∠2 + ∠BOC = 180°
In △ ABC, we have, ∠A + ∠B + ∠C = 180°
∠A + 2(∠1) + 2(∠2) = 180°
¹/₂∠A + ∠1 + ∠2 = 90°
∠1 + ∠2 = 90° - ¹/₂∠A
Therefore, in equation 1,
90° - ¹/₂∠A + ∠BOC = 180°
∠BOC = 90°+ ¹/₂∠A
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A truck can be rented from Company A for $40 a day plus $0.7 per mile. Company B charges $20 a day plus $0.9 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
Answer:
100 milesStep-by-step explanation:
Let the number of miles be x.
Company ATotal amount of rental is:
A = 40 + 0.7xCompany BTotal amount of rental is:
B = 20 + 0.9xSince A = B, substitute the values and solve the equation:
40 + 0.7x = 20 + 0.9x0.9x - 0.7x = 40 - 200.2x = 20x = 20/0.2x = 100What is 905.255 round to
Answer:
No decimal: 905
One decimal: 905.3
If 9(x) = x-2 and h(x) = 4- x, what is the value of (go h) (- 3) ?
Answer: 8/5
Step-by-step explanation:
Two friends are sharing one half of a pizza that is divided into three pieces, as shown in the figure.
A
B
O
C
D
If mZAOB = (2x - 4) and mZBOD= (14x+12)°, what is the value of x?
Using supplementary angles, it is found that the value of x is of x = 10.75.
What are supplementary angles?Supplementary angles are angles whose measures add to 180º.
An entire pizza is 360º, hence half the pizza is 180º, meaning that angles AOB and BOD are supplementary.
Their measures are given as follows:
m<AOB = 2x - 4.m<BOD = 14x + 12.Since they are supplementary, they add to 180º and we can add their measures and solve for x as follows:
2x - 4 + 14x + 12 = 180
16x = 172
x = 172/16
x = 10.75.
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Draw an isospeles right triangle on the coondinate plane so that the midpoint of its hypotenuse is the origin. Label the coordinates of each vertex.
The isosceles right triangle on the coordinate plane so that the midpoint of its hypotenuse is the origin is shown in the picture.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
It is given that:
Draw an isosceles right triangle on the coordinate plane so that the midpoint of its hypotenuse is the origin.
The coordinate of the origin is (0, 0)
We can take the coordinate of point A and B as (-1, 1) and (1, -1)
The right angle triangle is shown in the attahced picture.
Thus, the isosceles right triangle on the coordinate plane so that the midpoint of its hypotenuse is the origin is shown in the picture.
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L
1. If M is between L and N, find MN given:
LN = 6x-5, LM = x + 7, and MN = 3x + 20
M
N
The length of MN is 68.
what is Algebra?Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.
Given:
LN = 6x-5, LM = x + 7, and MN = 3x + 20
As, M is in between L and N.
LM + MN = LN
x+7 + 3x+ 20 = 6x-5
4x + 27 = 6x -5
-2x = -32
x= 16
So, the length of MN = 3x + 20 = 3 * 16 + 20 = 68
Hence, the length of MN is 68.
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Find the slope of the line through each pair of points. (1,2) and (2,3)
The slope of the line through each pair of points (1,2) and (2,3) is 1.
How can we determine slope?
Find the coordinates of two points along the selected line.
Find the difference in these two locations' y-coordinates (rise).
Find the difference in these two locations' x coordinates (run). Add the difference in x-coordinates (rise/run or slope) to the difference in y-coordinates.
The formula to calculate slope is -
m = y2 - y1 / x2 - x1
m = 3 - 2 / 2 - 1
m = 1
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I need this answered please
Each face of a cube is a square with a side length of 2 feet. What is the total area of all the faces of the cube?
The total area of all the faces of the cube is square feet
How to determine what is the total area of all the faces of the cube?The given parameter is
Side length, l = 2 feet
The total area of all the faces of the cube is calculated as
So, we have
Total area = 6 * Side length^2
This gives
So, we have
Total area = 6 * 2^2
Evaluate the exponent
So, we have
Total area = 6 * 4
Evaluate the product
So, we have
Total area = 24
Hence, the total area of all the faces of the cube is 24 square feet
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A bouncy ball is dropped such that the height of its first bounce is 6.5 feet and each successive bounce is 78% of the previous bounce's height. What would be the height of the 10th bounce of the ball? Round to the nearest tenth (if necessary).
Answer:
Approximately [tex]0.7\; {\rm ft}[/tex].
Step-by-step explanation:
If the current bounce is of height [tex]h\; {\rm ft}[/tex], the next bounce would be of height [tex](78\%\, h)\; {\rm ft}[/tex], which is equal to [tex](0.78\, h)\; {\rm ft}[/tex].
It is given that the first bounce is of height [tex]6.5\; {\rm ft}[/tex]. Relative to this first bounce:
The [tex]n = 2[/tex] bounce is dampened [tex](2 - 1) = 1[/tex] time. The height of this bounce would be [tex]((0.78)\, 6.5)\; {\rm ft} = ((0.78)^{2 - 1} \, 6.5)\; {\rm ft}[/tex].The [tex]n = 3[/tex] bounce is dampened [tex](3 - 1) = 2[/tex] times. The height of this bounce would be [tex](0.78)\, ((0.78)\, 6.5)\; {\rm ft} = ((0.78)^{3 - 1} \, 6.5)\: {\rm ft}[/tex].In general, the [tex]n[/tex]th bounce would have been dampened [tex](n - 1)[/tex] times. The height of that bounce would be [tex]((0.78)^{n - 1}\, 6.5)\; {\rm ft}[/tex].
Thus, the [tex]10[/tex]th bounce would have been dampened [tex](10 - 1) = 9[/tex] times. The height of that bounce would be [tex]((0.78)^{10 - 1} \, 6.5)\; {\rm ft} \approx 0.7\; {\rm ft}[/tex] (rounded to the nearest tenth, one digit after the decimal point.)
PLEASE HELP ME ASAP! Find the approximate side length of a square game board with an area of 205 in2
Answer:
Side length of a square game board is 11.916 inches. Explanation: If the area is 142 ∈2 , as area is square of side length of a square,
Step-by-step explanation:
Solve 2y + xy = 6for y. Then find the value of y when x = -3
Christine got a prepaid debit card with $20 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 9 cents per yard. If after that purchase there was $17.75 left on the card, how many yards of ribbon did Christine buy?
Write an explicit formula for each geometric sequence. Then find the first three terms.a₁ =3, r= 3/2
A recursive function allows us to find the value of any term in a geometric sequence by using the previous term in that exact sequence. If the common ratio of that geometric sequence is 9, then each term is nine times the previous term.
The general term for the geometric sequence is
an= a1 * r ^ (n-1)
where an is the nth term, a₁ is the first term, r is the common ratio, and n is its position or number. The term.
where a₁ = 3 and r = 3/2
Sequence: 3, 4.5, 6.75, 10.125, 15.1875, 22.78125, 34.171875, 51.2578125, 76.88671875 ...
3rd value: 6.75.
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For most people, the cost of a subscription to streaming music services is definitely a
discretionary expense. Marshal researched subscription costs and found the following monthly
rates for streaming services:
$10
$5 $10 $4 $12 $5
which is?
$6 $2.75 $3
a. What is the mean subscription fee?
303
of numbers
b. What is the median subscription fee?
c. What is the mode subscription fee?
d. If Marshal is looking to add another subscription how much would it have to be so the mean
$2.0.cdcas!
subscription is exactly $7 per month?
For the given subscriptions, we have that:
a) The mean is of $6.42.
b) The median is of $5.
c) The modes are of 5 and 10.
d) Marshall would have to add a subscription of $12.25.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
For this problem, the observations are given as follows:
10, 5, 10, 4, 12, 5, 6, 2.75, 3.
Hence the mean is:
M = (10 + 5 + 10 + 4 + 12 + 5 + 6 + 2.75 + 3)/9 = $6.42.
With another observation, we want a mean of $7, hence:
(10 + 5 + 10 + 4 + 12 + 5 + 6 + 2.75 + 3 + x)/10 = 7
57.75 + x = 70
x = 12.25.
Hence, for item d:
Marshall would have to add a subscription of $12.25.
What is the median?The median of a data-set is the middle value, which is the value that 50% of the data-set is greater and 50% is lesser.
The ordered data-set in this problem is:
2.75, 3, 4, 5, 5, 6, 10, 10, 12.
The middle value is of 5, which is the median.
What is the mode of a distribution?The mode of a distribution is the observation that appears the most times in the distribution.
In this problem, those observations are 5 and 10, both of which appears twice, hence the distribution is bimodal.
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16) Long John had 100 bags of silver. Each bag contained 9 3/4 lb. How much silver did he
have altogether?
Answer:
975 lbs.
Step-by-step explanation:
9 3/4 = 9.75
9.75 × 100 = 975
Which equation demonstrates the distributive property? Responses
A.(3 + 8)5 = 5(3 + 8)
B.15 x 40 = 40 x 15
C.15 + 40 = 55
D.15 + 40 = 5(3 + 8)
The option D.15 + 40 = 5(3 + 8); demonstrates the distributive property.
What is the meant by the term distributive property?To "distribute" something means to divide it or give a fraction or portion of it.The distributive property corresponds to the distributive law of multiplication over basic arithmetic operations such as addition and subtraction.This property states that multiplying a sum of two or even more addends by a number produces the same outcome as multiplying each addend separately by the number and afterwards adding the products together.In other words, the distributive property requires an expression of the form: A (B + C) can be written as AB + BC.This property also applies to subtraction: A (B - C) can be written as AB - BC.This indicates that other two operands share operand A.From the given options;
Consider option D; 15 + 40 = 5(3 + 8).
It is the case of distributive addition.
where
5(3 + 8) = 5×3 + 5×8
5(3 + 8) = 15 + 40
Thus, the option D is the correct representation of the distributive law.
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Find the geometric mean between pair of numbers.
14 and 21
To calculate the geometric mean, we take their product instead: 1 x 5 x 10 x 13 x 30 = 19,500 and then calculate the 5-th root of 19,500 = 7.21. This is equivalent to raising 19,500 to the 1/5-th power. Another way to calculate the geometric mean is with logarithms, as it is also the average of logarithmic values converted back to base 10.
Evaluate the expression when a=7 and b=5 . 6a+b
Answer:
47
Step-by-step explanation:
6(7)+5=42+5=47
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The numbers of seats in the first 16 rows in a curved section of another arena form an arithmetic sequence. If there are 20 seats in Row 1-23 seats in Row 2, how many seats are in Row 16?
The total number of seats are there is row 16 is 65.
What is the sequence of AP arithmetic progression?In Arithmetic Progression, the difference between two different arithmetic orders is a fixed number (AP). Arithmetic Sequence is another name for it.
We'd come along through a few specific terms in AP that had been labeled as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)As shown below, the AP can also be referred to in terms of common differences.
The following is the procedure for evaluating an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, as the values given in the question;
There are total 16 rows in the arena.
Thus, n = 16.
There are 20 seats present in row 1.
Consider the first term as 'a₁' = 20.
Similarly, there are 23 seats present at row 2.
Consider 'a₂' = 23 is the second term.
Now, calculate the common difference;
d = a₂ - a₁
Put the values in the 'd'.
d = 23 - 20 = 3.
Now, compute the total number of seats in 16th row bu nth formula.
n-th term: an = a + (n − 1) × d
a₁₆ = a₁ + (n - 1)d
a₁₆ = 20 + (16 - 1)3
a₁₆ = 20 + 45
a₁₆ = 65
Therefore, the total number of seats present in the 16th row is 65.
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(a³b¹²c²) × (a³c²) × (b³c¹) ⁰ =
12.4
O A. a¹5¹24
○ в. a³b¹¹c³
8
O c. a³b¹²4
OD. a¹4b¹5c9
Answer:
Answer C is correct
Step-by-step explanation:
We know that,
[tex] \sf \: {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \\ \sf \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \: \: \: \: \: \: \: \: [/tex]
[tex]\sf (x) ^{0} = 1 \rightarrow \: Any \: number \: to \: the \: power \: 0 \: is \: 1[/tex]
Let us solve it now.
[tex] \sf( {a}^{3} {b}^{12} {c}^{2} ) \times ( {a}^{5} {c}^{2} ) \times ( {b}^{5} {c}^{4} )^{0} \\ \sf( {a}^{3} {b}^{12} {c}^{2} ) \times ( {a}^{5} {c}^{2} ) \times 1 \: \: \: \: \: \: \: \: \: \: \: \\ \sf {a}^{3} \times {a}^{5} \times {b}^{12} \times {c}^{2} \times {c}^{2} \times 1\\ \sf {a}^{3 + 5} \times {b}^{12} \times {c}^{2 + 2} \times 1 \: \: \: \: \: \: \: \: \: \: \: \\ \sf {a}^{8} \times {b}^{12} \times {c}^{4} \times 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf {a}^{8} {b}^{12} {c}^{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
log_(2) (sqrt((2+14 )*(1+3))
The value of the expression is 3 using the concept of the logarithm.
A base must be raised to a certain exponent or power, or logarithm, to produce a specific number. If bˣ=n, then x is the logarithm of n to the base a, which is expressed mathematically as x = logₐ n.
Given the expression log₂√(2+14)(1+3)
Solving the square root we obtain,
[tex]log_{2} \sqrt{(16)(4)}\\[/tex]
Simplifying further we get,
[tex]=log_{2} (4)(2)[/tex]
[tex]=log_{2} (8)[/tex]
We know that the logarithm of 8 with base 2 is 3.
Hence, the given expression can be simplified as 3.
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I need this answered please
The phrase "54 less than twice Chrissy's age" is translated into an algebraic expression as 2x - 54.
What is the algebraic expression in the given phrase?Given the phrase in the question;
"54 less than twice Chrissy's age"
Let variable 'c' represent Chrissy's age
Translation
Chrissy's age ⇒ x
Twice Chrissy's age ⇒ 2 × x = 2x
54 less than ⇒ -54
Now combine terms
2x and - 54
2x - 54
Therefore, the phrase "54 less than twice Chrissy's age" is translated into an algebraic expression as 2x - 54.
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2.13 A weird density curve A line segment can be considered a density "curve" as shown
in Exercise 2.1A bekline graph can abe b ended a demiry curve. Figure 2.10
shows such a demity curve.
Figure 2.10 An unusual broken-line" density curve, for Exercise 2.13
0.2
0.4
0.5
0.3
(a) Verify that the graph in Figure 2.10 is a valid density curve.
For each of the following, use areas under this density curve to find the proportion of
observations within the given interval
(b) 0.6 ≤ x ≤0.8
(c) 0≤x≤ 0.4
(d) 0≤x≤02
(e) The median of this density curve is a point between X=0.2 and X=0.4. Explain why.
Regarding the piecewise curve and probabilities, we have that:
a) The figure is a value density curve because the area under the figure is of 1.
b) The probability is: P(0.6 ≤ X ≤ 0.8) = 0.2.
c) The probability is: P(0 ≤ X ≤ 0.4) = 0.6.
d) The probability is: P(0 ≤ X ≤ 0.2) = 0.3.
e) The median is the value of a for which P(0 ≤ X ≤ a) = 0.5, P(0 ≤ X ≤ 0.2) = 0.3 and P(0 ≤ X ≤ 0.4) = 0.6, hence the median of this density curve is a point between X=0.2 and X=0.4.
What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
For this problem, to the left of x = 0.4, we have a linear curve with:
An intercept of 2.Slope of -2.5, as when x increases by 0.4, y decays by 1.Then, considering the constant:
y = -2.5x + 2, x ≤ 0.4.y = 1, 0.4 < x ≤ 0.8.To represent a distribution, it's area over the entire interval has to be of 1. The area is composed by.
A rectangle of dimensions 1 and 0.8.A right triangle with dimensions 1 and 0.4.Hence the total area is:
A = 0.8 x 1 + 0.5 x 0.4 x 1 = 1.
Hence:
The figure is a value density curve because the area under the figure is of 1.
For itens b to d, the probabilities are also given by areas, hence:
0.6 ≤ X ≤ 0.8 = 1 x 0.2 = 0.2.0 ≤ X ≤ 0.4 = 1 x 0.4 + 0.5 x 0.4 x 1 = 0.6.0 ≤ X ≤ 0.2 = 1 x 0.2 + 0.5 x 0.2 x 1 = 0.3.For item e, we have that:
The median is the value of a for which P(0 ≤ X ≤ a) = 0.5, P(0 ≤ X ≤ 0.2) = 0.3 and P(0 ≤ X ≤ 0.4) = 0.6, hence the median of this density curve is a point between X=0.2 and X=0.4.
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Write the equation of the circle that passes through the given point and has a center at the origin. (Hint: You can use the distance formula to find the radius.) (-6,-4)
The equation of the circle that passes through the point (-6 , -4) and has a center located at the origin is x^2 + y^2 = 52.
Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (-6 , -4).
radius = distance = √(x2 - x1)^2 + (y2 - y1)^2
radius = √(-6 - 0)^2 + (-4 - 0)^2
radius= √36 + 16
radius = √52
The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (0 , 0)
r = √52
(x - 0)^2 + (y - 0)^2 = (√52)^2
x^2 + y^2 = 52
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CodeHS
Using Graphics in JavaScript: Do Now Activity
1) Identify the parts of each circle below.
Answer ?
Parts of each Graph is,
a) Centre = C
Radius = CA = CB = CD
Diameter = BD
b) Centre = S
Radius = SP = SQ = SR
Diameter = PQ
The center of a circle is the center point in a circle from which all the distances to the points on the circle are equal. This distance is called the radius of the circle. Here, point P is the center of the circle.
The distance between the center of the circle to its circumference is the radius.
The diameter of a circle is the distance from a point on the circle to a point. radians away, and is the maximum distance from one point on a circle to another. The diameter of a sphere is the maximum distance between two antipodal points on the surface of the sphere.
Therefore,
Parts of each Graph is,
a) Centre = C
Radius = CA = CB = CD
Diameter = BD
b) Centre = S
Radius = SP = SQ = SR
Diameter = PQ.
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