The area of the circular DVD is given by A = 111.33 cm²
What is a Circle?A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the area of the circular DVD be A
Let the diameter of the DVD = 12 cm
So , the radius of the DVD = 6 cm
Now , the diameter of the hole = 1.5 cm
So , the radius of the hole = 0.75 cm
And , area of the circular DVD be A = π [ ( 6 )² - ( 0.75 )² ]
On simplifying , we get
The area of circular DVD is A = π ( 36 - 0.5625 )
The area of circular DVD is A = π ( 35.4375 )
The area of circular DVD is A = 111.33 cm²
Hence , the area of the circular DVD is 111.33 cm²
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can someone plz help me.
PLEASSEE HELP i really dont get this math and this is due today so can some please help me with this asap!!!!
help I can't figure this out
What is the slope of the line? 6x + 2y= -14
is the relation a function? Why or why not?
(-3, -2) (-1, 0) (1, 0) (5, -2)
A. no- to domain values exist for range value -2
B- yes- only one range value exists for each domain value
C- yes- to domain values exist for range value -2
D- no- the relation passes the vertical line test
Final answer:
A relation where each domain value is mapped to a single, unique range value is considered a function. The relation in question is indeed a function because each domain value corresponds to only one range value, and its correctness is supported by the distinct pairs of the domain and range. The correct answer is option (B)
Explanation:
To determine whether a given relation is a function, we check if each element of the domain maps to exactly one element of the range. The relation in question is composed of the following ordered pairs: (-3, -2), (-1, 0), (1, 0), (5, -2). The domain (which consists of the first elements of the ordered pairs) includes -3, -1, 1, and 5, and the range (the second elements) includes -2, 0.
A crucial aspect of a function is that each domain value is paired with a unique range value. Here, we see that no domain value is repeated; hence, none of them map to more than one range value. This satisfies the criterion for a function. However, it is not a problem that a range value, like -2, appears more than once in the relation as long as it corresponds to different domain values.
Based on this, the correct answer would be "B. yes- only one range value exists for each domain value" because each domain value is associated with one and only one range value, which is the definition of a function.
Aaron bought a large basket of 59 apples for $22.95. He also bought a small basket of 18 apples for 8.95. Which amount is the closest estimate of the cost per apple?
Which number is closest to V65 A. 8 B. 9 C. 32 D.64
The symbol 'V' before a number usually implies the square root in mathematics. Therefore, the square root of 65 (V65) is approximately 8.06. Hence, the closest number to V65 is 8.
Explanation:The symbol 'V' before a number often denotes the square root in mathematics. Thus, 'V65' implies the square root of 65. Calculating this gives an approximate value of 8.06. When you compare this value to the options provided: A. 8, B. 9, C. 32 and D. 64, you can see that the closest number to V65 (the square root of 65) is A. 8.
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How do you solve for x??
Steve bought a total of 6 packages of pens, and each package contained either 3 or 7 pens. If exactly 4 of the packages Steve bought a package that contained 7 pens, how many pens did Steve buy?
A) 21
B) 28
C) 30
D) 34
E) 42
A circle with center (-2,6) passes through the point (-2,10). Which of the following is the equation of the circle?
First option is correct. The equation of the is [tex](x-2)^{2} +(y-6)^{2} =16[/tex].
What is circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called "center".
General equation for circle[tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]
where,
(h, k) is the coordinate of the center of a circle
(x, y) are the coordinate points
r is the radius of circle.
According to the question
we have
the center of the circle, (h, k) = (-2, 6)
and the circle passes through the point (-2, 10)
since, the circle passes through point (-2, 10), the radius(r) of the circle is the distance between the points (-2, 6) and (-2, 10)
⇒ [tex]r =\sqrt{(-2+2)^{2 }+ (6-10)^{2} }[/tex]
⇒ r = [tex]\sqrt{0^{2}+(-4)^{2} }[/tex]
⇒[tex]r = \sqrt{16}[/tex]
⇒[tex]r = 4unit[/tex]
therefore,
the equation of the circle is given by
[tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]
[tex](x-(-2))^{2} +(y-6)^{2} =16[/tex]
[tex](x+2)^{2} +(y-6)^{2} =16[/tex] ..... (1)
[tex]x^{2} +4+4x+y^{2} +12y+36 = 16[/tex]
[tex]x^{2} +y^{2} +4x+12y+24=0[/tex]
Hence, equation 1 represent the equation of circle i.e. [tex](x+2)^{2} + (y-6)^{2} =16[/tex]
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The length of a rectangular prism is 5 feet and its height is 6 feet. Find the width of the prism if the surface area is 126 square feet.
Point x starts at -4 on a number line. Pint x then goes through a series of moves; +3 units, -2 units, +6 units and -5 units. What is the final position of Point x?
Starting from -4 and applying a series of moves (+3, -2, +6, -5) sequentially on the number line, the final position of Point x is -2.
Explanation:The question involves finding the final position of Point x after a series of moves on a number line. Starting from -4, we apply the moves in sequence: adding 3, subtracting 2, adding 6, and finally subtracting 5. The operations are as follows:
Start: -4After adding 3: -4 + 3 = -1After subtracting 2: -1 - 2 = -3After adding 6: -3 + 6 = 3After subtracting 5: 3 - 5 = -2Therefore, the final position of Point x on the number line is -2.
Which stem of equation should Omar use?
PLEASE HELP ME!! HURRY PLEASE
plz answer my multiple choice question
Which of the following statements is false? a. Every chord is a part of a secant b. Every diameterbis a part of secant c. Every chord is a diameter d. Every diameter is a chord
The wrong statement about a circle is c. Every chord is a diameter
Further explanationCircles are two-dimensional builds which are sets of equidistant points at a point called the center point
The distance of these points to the center is called the radius of the circle. While the circle field is an area which is bounded by a circle
There are terms - terms commonly used in circles:
1. The center point2. Radius3. Arc4. Circumference5. Segment6. Chord7. Annulus8. Diameter9. Disc10. LensA diameter is a line that passes through the center of a circle and divides the circle into two equal partsA Secant is a plotline that intersects a circle at two points on a circleA chord is a line that cuts a circle at 2 points located on the arcLet we see the answer choices :
a. Every chord is a part of a secantRight, because secant itself is an extension of the chord
b. Every diameter is a part of secantRight, because the diameter itself also intersects the circle at two points on the circle, just like secant
c. Every chord is a diameterIncorrect, because the diameter itself must pass through the center point while the chord does not have to
d. Every diameter is a chordRight, because each diameter intersects a circle at two different points
So the wrong statement is C. Every chord is a diameter
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Keywords: circle, secant, diameter, chord
Every chord is a diameter is false. Option (c) is false.
Further explanation:
Given:
The statements are as follows,
(a). Every chord is a part of a secant
(b). Every diameter is a part of secant
(c). Every chord is a diameter
(d). Every diameter is a chord
Explanation:
Diameter is a distance between the points that passes through the center of the circle.
The distance between the two points on the circle is known as the chord. The longest chord is the diameter of the circle.
Radius is line segment to a point from the center of the circle and the radius is half of the diameter.
Secant is a straight line that intersects two points on the circle.
Every chord is a diameter is false. Option (c) is false.
Statement (a) is true.
Statement (b) is true.
Statement (c) is false.
Statement (d) is true.
Learn more:
Learn more about inverse of the functionhttps://brainly.com/question/1632445. Learn more about equation of circle brainly.com/question/1506955. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Triangles
Keywords: false, chord, part, secant, radius, diameter, Every chord is a part of a secant, Every diameter is a part of secant, Every chord is a diameter, Every diameter is a chord.
Number 9. I was guessing helppp plssss
What is the next number in the sequence 3,7,15,31,63,
Answer:
The next number is 127
Step-by-step explanation:
The sequence is the previous number times 2 plus one.
10. Write an inverse variation to model the situation and answer the question. Two rectangular fields have the same area. One measures 75 yd by 60 yd. If the other has a length of 72 yd, what is its width?. show your work
Suppose 540 people visit the zoo.Predict how many people will choose the monkey exhibit as their favorite
Answer:
162
Step-by-step explanation:
There are 21 out of 70 people that like the monkey exhibit. So you divide that and get 0.3 or 3/10. Then you have to multiply that by 540. This gets you to 162 which is the answer to your problem.
Gabe went to the amusement pasrk with $40 to spend. His tickets cost $26.50. Write and solve an inequality to show how much he might spend on souvenirs and snacks.
what did the horse say when it fell down
True or false- "All quadrilaterals polygons."
the answer is true hope this helps :)
how do i solve this ? :')
Penny has 3 friends over after school, and they are hungry for an after school snack! They find 2/3 of a pie left over from dessert lastnight. If they split up the leftover pie evenly between the 4 girls, how much pie does each girls get to eat?
In the triangle below,
1) Find the length of BC
2) Find the are area of Δ ABC
A1. Since we have two sides (AC and AB) and the included angle (60°), we are going to use the law of cosines to find the length of BC:
We can conclude that the length of the side BC is .
2. To find the area of triangle ABC we are going to use Heron's formula:
where
is the area of the triangle
is the semi-perimeter of the triangle
But first, we are going to find the semi-perimeter of our triangle using the formula:
We can infer for our triangle and from our previous calculation that , , and . Lets replace those values to find the semi-perimeter of our triangle:
Ms. Coleman's class has already collected 403 cans for a food drive, but the class wants to collect a total of at least 1,000 cans. If each of the 28 students in the class brings an equal number of cans, how many more cans should each student bring for the class to have collected at least 1,000 cans?
Variable x is 7 more than variable y. Variable x is also 1 less than y. Which of the following pairs of equations best models the relationship between x and y? (4 points)
x = 1y
x = y + 7
x = y + 7
x = y – 1
y = x + 8
y = x – 1
y = 7x
y = x + 1
Answer:
1. x is 7 more than y
meaning
x=y+7
2. x is 1 less than y
meaning
x=y-1
so
the answer:
x = y + 7
x = y – 1
Consider the following system of equations:
2x + 3y = 45
x + y =10
What is the x-value of the solution for this system?
Yesterday's low temperature was − 2 . 5 ∘ C −2.5 ∘ Cminus, 2, point, 5, degree, C. Today's low temperature is 5 55 times as low as yesterday's low temperature.