Find the diameter of a circle that is 90 centimeters long and 28 centimeters from the center of the circle
Answer:
o Identify some basic parts of a circle, such as the radius and diameter
o Calculate the circumference of a circle
o Calculate the area of a circle
In this article, we will consider a geometric figure that does not involve line segments, but is instead curved: the circle. We will apply what we know about algebra to the study of circles and thereby determine some of the properties of these figures.
Introduction to Circles
Imagine a point P having a specific location; next, imagine all the possible points that are some fixed distance r from point P. A few of these points are illustrated below. If we were to draw all of the (infinite number of) points that are a distance r from P, we would end up with a circle, which is shown below as a solid line.
Thus, a circle is simply the set of all points equidistant (that is, all the same distance) from a center point (P in the example above). The distance r from the center of the circle to the circle itself is called the radius; twice the radius (2r) is called the diameter. The radius and diameter are illustrated below.
The Circumference of a Circle
As with triangles and rectangles, we can attempt to derive formulas for the area and "perimeter" of a circle. Unlike triangles, rectangles, and other such figures, the distance around the outside of the circle is called the circumference rather than the perimeter-the concept, however, is essentially the same. Calculating the circumference of a circle is not as easy as calculating the perimeter of a rectangle or triangle, however. Given an object in real life having the shape of a circle, one approach might be to wrap a string exactly once around the object and then straighten the string and measure its length. Such a process is illustrated below.
Obviously, as we increase the diameter (or radius) of a circle, the circle gets bigger, and hence, the circumference of the circle also gets bigger. We are led to think that there is therefore some relationship between the circumference and the diameter. As it turns out, if we measure the circumference and the diameter of any circle, we always find that the circumference is slightly more than three times the diameter. The two example circles below illustrate this point, where D is the diameter and C the circumference of each circle.
Again, in each case, the circumference is slightly more than three times the diameter of the circle. If we divide the circumference of any circle by its diameter, we end up with a constant number. This constant, which we label with the Greek symbol π (pi), is approximately 3.141593. The exact value of π is unknown, and it is suspected that pi is an irrational number (a non-repeating decimal, which therefore cannot be expressed as a fraction with an integer numerator and integer denominator). Let's write out the relationship mentioned above: the quotient of the circumference (C) divided by the diameter (D) is the constant number π.
We can derive an expression for the circumference in terms of the diameter by multiplying both sides of the expression above by D, thereby isolating C.
Because the diameter is twice the radius (in other words, D = 2r), we can substitute 2r for D in the above expression.
Thus, we can calculate the circumference of a circle if we know the circle's radius (or, consequently, its diameter). For most calculations that require a decimal answer, estimating π as 3.14 is often sufficient. For instance, if a circle has a radius of 3 meters, then its circumference C is the following.
The answer above is exact (even though it is written in terms of the symbol π). If we need an approximate numerical answer, we can estimate π as 3.14. Then,
Interested in learning more? Why not take an online class in Pre-Algebra?
The symbol ≈ simply means "approximately equal to."
Practice Problem: A circle has a radius of 15 inches. What is its circumference?
Solution: Let's start by drawing a diagram of the situation. This approach can be very helpful, especially in situations involving circles, where the radius and diameter can easily be confused.
Step-by-step explanation:
Answer:
56cm
Step-by-step explanation:
The radius is half the diameter so times the radius by two to find the width of the diameter. 28 x 2 = 56cm
correct solutions if identified to be incorrect
4a²-8ab³=2a(ab-4b³)
Answer:
sorry but there's nothing to be solve the the only thing that I know can be done is expansion expanding the equation
Step-by-step explanation:
I'm confused, I'm used to doing these problems with both coordinates :/
Answer:
{0, 1, 16, 81}
Step-by-step explanation:
If the domain of this function is the set {0, 1, 4, 9}, we find the set representing the range by evaluating the function at each of the four values in the domain.
f(0) = 0
f(1) = 1
f(4) = 16
f(9) = 81
and so the range is the set {0, 1, 16, 81}.
PLEASE ANSWER
What is the area of the parallelogram?
13.4 in
7.5 in
Answer:
area = 100.5 in²
Step-by-step explanation:
area = 13.4 x 7.5 = 100.5 in²
solve for x: x²+7x+45=0
Answer: x= -[tex]\frac{7-i\sqrt{131} }{2}[/tex],-[tex]\frac{7+i\sqrt{131} }{2}[/tex]
Step-by-step explanation:
Solve the equation by finding x, a, b, and c of the quadratic, then apply the quadratic formula.
A shipment of 12 television sets content to defective sets in how many ways can a hotel purchase five of these ads and receive at least two of the defective sets
Answer:
Total number of ways a hotel can purchase 5 of 12 sets and receive at least 2 defective sets = 288
Step-by-step explanation:
P.S - The exact question is -
Given - A shipment of 12 television sets contains 3 defective sets.
To find - In how many ways can a hotel purchase 5 of these sets and receive at least 2 of the defective sets?
Proof -
We know that The combination of n distinct objects taken k at a time is
[tex]^{n} C_{k} = \frac{n!}{k! (n-k)!}[/tex]
Now,
The number of ways hotel can receive 2 defective sets among 5 that can be purchased is
[tex]^{9} C_{3} * ^{3}C_{2} = \frac{9!}{3! (9-3)!} \frac{3!}{2! (3-2)!}[/tex]
⇒[tex]^{9} C_{3} * ^{3}C_{2}[/tex] = 84(3) = 252
Now,
The number of ways that hotel receives 3 defective sets among 5 that are purchased is
[tex]^{9} C_{2} * ^{3}C_{3} = \frac{9!}{2! (9-2)!} \frac{3!}{3! (3-3)!}[/tex]
⇒[tex]^{9} C_{2} * ^{3}C_{3}[/tex] = 36(1) = 36
Now,
Total number of ways a hotel can purchase 5 of 12 sets and receive at least 2 defective sets = 252 + 36 = 288
⇒Total number of ways a hotel can purchase 5 of 12 sets and receive at least 2 defective sets = 288
The isotope Herodium-100 decreases by half every minute, Herodium-100 is there
isotope that gives a super hero their strength. Once the amount depletes to 4 ml, a
superhero becomes tired and need to leave the fight. If Mathman has 2000mL in his
body, when will he have to rest and replenish, rounded to the nearest minute?
Answer:
After about 9 minutes.
Step-by-step explanation:
We can write an exponential function to model the decay of Herodium-100.
We are given that it decreases by half every minute.
The standard exponential function is given by:
[tex]f(m)=A(r)^m[/tex]
Where A is the initial amount, r is the rate, and m is the rate (in this case, in minutes).
Mathman initially has 2000 mL of Herodium-100. Therefore, A = 2000.
And since it decreases by half every minute, r = 1/2. Thus:
[tex]\displaystyle f(m)=2000\Big(\frac{1}{2}\Big)^m[/tex]
Mathman needs to rest when the Herodium-100 levels drop to 4 mL. Therefore, we can substitute 4 for f(m) and solve for m:
[tex]\displaystyle 4=2000\Big(\frac{1}{2}\Big)^m[/tex]
Solve for m. Divide both sides by 2000:
[tex]\displaystyle \frac{4}{2000}=\frac{1}{500}=\Big(\frac{1}{2}\Big)^m[/tex]
We can take the natural log of both sides:
[tex]\displaystyle \ln\Big(\frac{1}{500}\Big)=\ln\Big(\frac{1}{2}^m\Big)[/tex]
By logarithm properties:
[tex]\displaystyle \ln\Big(\frac{1}{500}\Big)=m\ln\Big(\frac{1}{2}\Big)[/tex]
Therefore:
[tex]\displaystyle m=\frac{\ln(1/500)}{\ln(1/2)}\approx 8.9657\approx 9\text{ minutes}[/tex]
Mathman will have to rest and replenish after 9 minutes.
carl bought a circular cake and ate 1/5 of it on monday and 0.25 on Tuesday what percent of the cake has carl not eaten yet
0.45 or %45 is left of the circular cake.
Hope this helps; have a great day!
The Great Pyramid in Giza, Egypt is a square-based pyramid. It was constructed in 2056 BC out of lime stone. The length of one side of the base was 755 feet, it had a height of 481 feet and a slant height of 610 feet. About how much interior space did the Egyptians have to place the tombs and worship their beloved leaders?
Answer:
i think its 274,182,025 cubic feet
Step-by-step explanation:
.
Which expressions are equivalent to the one below? Check all that apply. 49^x
Answer:
A,D,F
Step-by-step explanation:
Answer:
7^x•7^x, (7•7)^x, 7^2x
Step-by-step explanation:
Just took it, the other one is wrong
4x + 7 = ? (I'm not so good in math so please help)
Answer:
4(x+ 1.75)
Step-by-step explanation:
Answer: 4
i wish that helped
What is the definition of a tangent in math
Answer:
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. ... The word "tangent" comes from the Latin tangere, "to touch".
Step-by-step explanation:
A straight line touching a curve at a single point without crossing it there is tangent.
can someone plsss help me
Answer:
The equation for charge is = current x times
A vacation resort offers surfing lessons and parasailing. If a
person takes a surfing lesson and goes parasailing, she will pay
a total of $175. On Friday, the resort collects a total of $3,101 for
activities. How much does each activity cost?
After solving the equations, the cost of parasailing will be 99.75 and the cost of surfing will be equal to 75.25.
What is an Expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both.
Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
The given information in the question is,
Assume the cost of parasailing is x and the cost of surfing is y.
x + y = 175
Total number of people in Parasailing = 16 people
Total number of people in Surfing = 20 people
Total collection done by resort = $3,101
16x + 20y = 3,101
So, the equations will be,
16x+20y=3,101 (i)
x + y = 175 (ii)
Now, multiply the equation (ii) by 16 and solve the equation,
16x+20y=3,101
16x+16y= 2,800
4y = 301
Now, find the value of y,
y = 301/4
y = 75.25
Then, the value of x will be equal to,
x + y = 175
x+75.25 =175
Solve for x:
x=175-72.25
x = 99.75
To know more about expression:
https://brainly.com/question/14083225
#SPJ2
It seems that your question is not complete, the complete question should be:
A vacation resort offers surfing lessons and parasailing. If a person takes a surfing lesson and goes parasailing, she will pay $175. There are 16 people who go parasailing and 20 people who take surfing lessons. On a Friday, the resort collects a total of $3,101 for activities. How much does each activity cost?
HELP ME PLS IM AWARDING BRAINLIEST!
Answer:
(4th option) 254.34 cm
Step-by-step explanation:
Area of a circle = pi (r)^2
r=radius of circle which is half of diameter.
diameter=12+6=18
So, radius is half of 18 = 9
Plug it into the formula:
[tex]\pi (9)^{2}[/tex]
And you should get 254.34 cm^2
Answer:
Step-by-step explanation:
area of a circle is pi * r^2
r for the big circle is 1/2 of 18 or 9
pi * 9^2 = 254.469
¿Cuál es la medida del ángulo x?
A.-130°
B.-100°
C.-50°
D.-40°
Step-by-step explanation:
x+50 = 180 because asim circle
x =180-130
x=150
Pleaseee help! HELP NEEDED ASAP!
Does this graph show a function? Explain how you know.
Answer:
C
Step-by-step explanation:
It passes the vertical line test
the vertical line test is taking a vertical line and putting it anywhere on the graph, and if it passes 2 points, it fails, and since if you put the line anywhere, it only passes one point of the parabala, so it passes the line test
Answer: C
Step-by-step explanation: The easiest way to determine if a
relation is a function is to use the vertical line test.
The vertical line test tells us that if we can draw a vertical line
that intersects more than one point on the graph of a relation,
then the relation is not a function.
However, in this case, notice that there is no way to draw a
vertical line that intersects more than one point on the graph.
Therefore, this relation must be a function.
State whether or not each equation or situation represents direct variation.
give me time will think and say
Answer:
The new Yorker is a very different kind than the word
I WILL GIVE BRAINLIST EASY QUESTION
What was done to turn the parallelogram into a rectangle?
Hint (The length of the segment the figure was cut along is the height of the parallelogram)
Help me with this pls
Answer:
A & E
Step-by-step explanation:
Simone runs the 100m in 12 seconds.Hanno covers 2.5 km in 4minutes with his bicycle who moves fastest?
Answer:
Hanno moves faster than Simone.
Step-by-step explanation:
Simone: 25x100=2500m or 2.5km in 25x12=300 seconds or 5 minutes
Hanno- 2.5 km in 4minutes
So, Hanno moves 1 minute faster.
Please mark as brainliest.
If arc VY = 132° and ∠YUV = 41°, what is the measure of arc XV?
Answer:
50
Step-by-step explanation:
Use this equation
[tex] \frac{b - a}{2} = angle \: yuv[/tex]
where b is arc VY, A is arc XV.
Substitute the equation in
[tex] \frac{132 - a}{2} = 41[/tex]
[tex]132 - a = 82[/tex]
[tex] - a = - 50[/tex]
[tex]a = 50[/tex]
so our arc measure is 50
2) Solve the system of equations using substitution.
2x – 9y = 14
x= -6y +7
Answer:
(7,0) ---> (x = 7) and (y = 0)
Step-by-step explanation:
2x – 9y = 14
x= -6y +7 <-- (Substitute for x to above equation)
---------------------------------------------------------------------------------------------------------
2(-6y +7)– 9y = 14
-12y + 14 - 9y = 14 <-- combine like terms
-21y + 14 = 14
-14 = -14 <-- inverse operation on both sides
-21y = 0 <-- Divide
y = 0 <--- Substitute for y to get x ↓
-------------------------------------------------------------------------------------------------------
2x – 9y = 14
2x – 9(0) = 14 <-- Substituted y from above
2x = 14 <-- Divide
x = 7
The sum of three consecutive even integers is 30 more than the largest
Answer:
nljgdetbeybrybdtbrbrtbetbrynrynenehtnehymyrumeymryjmryj ryu
Is v = 12 a solution to the inequality below?
V> 7
Answer: Yes
Step-by-step explanation: If V=12
Then we plug in for the inequality and get 12>7
PLEASE HELP !! DUE SOON :(
Answer: your so bad
Step-by-step explanation:
hahahaahahahahahhahahahahahahaha
Answer:
A. Yes
B. yes
C. Yes
D. No
E. Yes
Step-by-step explanation:
Good luck!
Hi I need help please
Answer:
x = 9
Step-by-step explanation:
8x - 10 = 62
8x = 72
x = 9
Over the past few years, Mitchell has made 99 trips to visit the amusement park. He drove 6,870.1 kilometers in all. To the nearest hundredth of a kilometer, how far did Mitchell drive on each trip?
Answer:
69.39 kilometers
Step-by-step explanation:
total kilometres driven on each trip = total kilometres driven on all trips / total number of visits
6,870.1 / 99 = 69.394949
To the nearest hundredth means we are rounding off the third number after the decimal point. The second number after the decimal is the hundredth. The third number is less than 4, so zero would be added to the preceding number
69.39 kilometers
Help!!!!!!!!!!!!!!!!!?!?!??!!
Answer:
B
Step-by-step explanation:
I learned this a while ago, if you have the < symbol then you shade below the dotted line. You can get the rest.