The ratio of the circumference of a circle with radius r to its area is 2:r or 2 to r.
Define circleA circle is a two-dimensional shape that is defined as the set of all points in a plane that are at a fixed distance, called the radius, from a given point, called the center. The distance around the circle is called the circumference, and the distance across the circle passing through the center is called the diameter.
The circumference of a circle with radius r is given by the formula:
C = 2πr
The area of a circle with radius r is given by the formula:
A = π×r²
Therefore, the ratio of the circumference of a circle with radius r to its area is:
C/A = (2πr) / (πr²)
Simplifying the expression by canceling out π and r from the numerator and denominator, we get:
C/A = 2/r
Therefore, the ratio of the circumference of a circle with radius r to its area is 2:r or 2 to r.
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The complete question is:
Find the following ratio.
The ratio of circumference of circle with radius r to its area.
PLEASE HELP ASAP TY IN ADVANCE!!
1. The Lifetime of the Sun. When the Sun formed 70% of its mass was hydrogen. 13% of that mass is at the Sun’s core where it is available for the nuclear fusion reaction that powers the Sun.
a. Given the mass of the Sun ms = 1.99 × 1030 kg, calculate the total mass of hydrogen at the Sun’s core available for nuclear fusion over its lifetime.
b. Given that the Sun fuses about 600 billion kg of hydrogen every second, calculate how long the Sun’s original supply of hydrogen can last. Express your answer in billions of years.
c. Given that the Sun is now 4.6 billion years old, how much longer will it take before it runs out of fuel?
Step-by-step explanation:
I think you mean the sun's mass is 1.99 × 10³⁰ kg.
70% of that is hydrogen :
1.99 × 10³⁰ × 0.7 = 1.393 × 10³⁰ kg
a.
13% of that is in the core :
1.393 × 10³⁰ × 0.13 = 0.18109 × 10³⁰ = 1.8109 × 10²⁹ kg
b.
600 000 000 000 kg = 6.0 × 10¹¹ kg/s
so, 1.8109 × 10²⁹ kg will last
1.8109 × 10²⁹ / (6.0 × 10¹¹) = 0.301816666... × 10¹⁸ =
= 3.01816666... × 10¹⁷ seconds
60 seconds per minute.
60 minutes per hour.
24 hours per day.
365 days per year.
1 000 000 000 years.
that is
31,536,000,000,000,000 seconds in 1 billion years =
= 3.1536 × 10¹⁶ seconds in 1 billion years
so, this will go on for
3.018166666... × 10¹⁷ / 3.1536 × 10¹⁶ billion years =
= 0.957054372... × 10¹ = 9.57054372... billion years.
c.
the sun has already "spent" 4.6 billion years, so, that leaves about
9.6 - 4.6 = 5 billion years
According to the information, the total mass of hydrogen available for nuclear fusion in the Sun's core is 10^29 kg, the duration of the oroginal supply of hydrogen of the sun is 3.02 × 10^17 seconds, and the left time of the sun is 4.98 billion years.
How to calculate the total avaliable mass of hydrogen at the Sun's core?a. The total mass of hydrogen available for nuclear fusion in the Sun's core is:
0.7 × 1.99 × 10^30 kg × 0.13 = 1.81 × 10^29 kg
How long the sun's original suply of hydrogen can last?
b. To find how long the Sun's original supply of hydrogen can last, we need to divide the total mass of hydrogen available for nuclear fusion by the rate at which the Sun fuses hydrogen:t = (1.81 × 10^29 kg) / (6 × 10^11 kg/s) = 3.02 × 10^17 seconds
Converting to billions of years:
t = (3.02 × 10^17 s) / (3.15 × 10^16 s/billion years) = 9.58 billion years
How to calculate how much longer will it take before it runs ouut out fuel?c. The Sun has already burned for 4.6 billion years, so the amount of time it has left before it runs out of fuel is:
9.58 billion years - 4.6 billion years = 4.98 billion years
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In the diagram below, BE intersects AD at C, AB | DE. If CD = 4.2 and AB = 9.6, what is the length of
BC to the nearest tenth of a centimeter?
Dont mind the writing
The length of BC, to the nearest tenth of a centimeter, is calculated as: 12.6 centimeter.
How to Find the Length of the Indicated Side?Recall that two similar triangles will always have side lengths that are proportional in length. The triangles shown are similar to each other, therefore, the proportion below would be true:
AC/CE = BC/CD
Given the following:
AC = 7.2 units
CE = 2.4 units
CD = 4.2 units
BC = ?
Plug in the values:
7.2/2.4 = BC/4.2
Cross multiply:
BC = 7.2 * 4.2 / 2.4
BC = 12.6 cm
Thus, the length of side BC in the similar triangles shown is approximately 12.6 cm.
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A framed picture has a total area y, in square inches. The thickness of the frame is
represented by x, in inches. The equation y = (8+2x)(10 + 2x) relates these two
variables.
1. What are the length and width of the picture without the frame?
2. What would a solution to the equation 100 = (8+2x)(10+2x) mean in this
situation?
The given total area including the frame is y = (8+2x)(10+2x).
As per the question the thickness of the frame is x.
The area of a rectangle is given by A=L*B
For a picture with frame it will be A=(L+2t)*(B+2t)
1. Comparing the above equation with the given equation it can be concluded that the Length is 10 and the width is 8.
2. The given equation is 100=(8+2x)(10+2x)
Upon solving it simplifies to [tex]x^2+9x-5=0[/tex]
x=0.525.
Thus the thickness x=0.525.
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where should the linear inequality y ≤ 1/4 x- 3 be shaded?
The required direction of the inequality is below the line.
How to find the direction of inequality in graph?If you're not graphing a vertical line, the inequality's sign will tell you which half-plane to shade. Shade above the line when using the or > sign. Shade below the line if the symbol or is used. Larger solutions are to the right and smaller solutions are to the left, respectively, for a vertical line.
According to question:To check the direction, we will take points from the graph and put in the given inequality.
At point (2, 0)
y ≤ x/4 - 3
0 ≤ 2/4 - 3
0 ≤ -25
It is false
Again
At (2, -4)
y ≤ x/4 - 3
-4 ≤ 2/4 - 3
-4 ≤ -2.5
It is true,
Thus, we can say the direction of the inequality is below the line.
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Confusing
Kerrin is making an input-output table for the rule "add 5." What is the output value for an input value of 5?
Options:
A: 0
B :5
C: 10
D: 25
The calculated output value for an input value of 5 is (c) 10
What is the output value for an input value of 5?From the question, we have the following parameters that can be used in our computation:
Kerrin is making an input-output table for the rule "add 5."
This means that
Output = input + 5
In this case, we have
input = 5
substitute the known values in the above equation, so, we have the following representation
Output = 5 + 5
Evaluate
Output =10
Hence, the output is 10
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Can someone help me please
here is the picture
The result of adding -4 (row 1) to row 3 is determined as (0 - 9 2)|12.
What is the result of the row multiplication?The resultant of the row multiplication in the Matrice is calculated by applying the following method;
row 1 in the given matrices = [1 2 1] | -5
To multiply row by -4, we will multiply each entity by 4 as shown below;
= -4(1 2 1) | -5
= (-4 -8 - 4) |20
To add the result to 3;
(-4 -8 - 4)|20 + (4 - 1 6) | -8
= (0 - 9 2)|12
Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 4.
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MN=3X+2 AND NP=X+4 WHAT IS THE VALUE OF X
Answer:
N = M + 10/3P
Step-by-step explanation:
Write the equation of the line in slope-intercept form.
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-1}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-4)}}} \implies \cfrac{-5}{0 +4} \implies \cfrac{ -5 }{ 4 } \implies - \cfrac{ 5 }{ 4 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- \cfrac{ 5 }{ 4 }}(x-\stackrel{x_1}{(-4)}) \implies y -4 = - \cfrac{ 5 }{ 4 } ( x +4) \\\\\\ y-4=- \cfrac{ 5 }{ 4 }x-5\implies {\Large \begin{array}{llll} y=- \cfrac{ 5 }{ 4 }x-1 \end{array}}[/tex]
Given Circle C, calculate the length of PQ (Thx for any help!)
Answer:
3π
Step-by-step explanation:
Given
Radius=9
Angle=60°
Since PQ is an arc
Perimeter of an Arc =(θ/360)×2πr
60/360×2π(9)
1/6×18π
3π
The temperature is dropping at 3 degrees per hour. At noon it was 0 degrees, what was the temperature at 1pm? 2pm? 3pm? 6pm? What was the temperature t hours after noon?
The temperature at 1pm is -3°C, at 2pm it's -6°C, at 3pm it's -9°C, and at 6pm it's -18°C. The temperature t hours after noon is T = 0 - 3t
If the temperature is dropping at a rate of 3 degrees per hour, then the temperature t hours after noon can be represented by the equation T = 0 - 3t, where T is the temperature in degrees Celsius.
To find the temperature at a specific time after noon, we need to substitute the corresponding value of t into the equation and solve for T. For example:
At 1pm (t = 1), T = 0 - 3(1) = -3°C
At 2pm (t = 2), T = 0 - 3(2) = -6°C
At 3pm (t = 3), T = 0 - 3(3) = -9°C
At 6pm (t = 6), T = 0 - 3(6) = -18°C
To find the temperature t hours after noon, we can use the same equation: T = 0 - 3t. For example, if we want to find the temperature 4 hours after noon, we can substitute t = 4 into the equation: T = 0 - 3(4) = -12°C. So the temperature 4 hours after noon is -12°C.
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HELP PLEASE I REALLY NEED HELP ON THIS QUESTION HELP!
Answer:
Step-by-step explanation:
To determine which flight will have the most no-shows, we need to compare the probabilities of no-shows for each flight.
The probability of a no-show for the afternoon flight is 1/10, which means that on average, 1 out of every 10 passengers on the afternoon flight will not show up.
The probability of a no-show for the morning flight is 1/20, which means that on average, 1 out of every 20 passengers on the morning flight will not show up.
Since 1/10 is greater than 1/20, the afternoon flight will have a higher number of no-shows, on average. Therefore, the afternoon flight is more likely to have the most no-shows.
Working with Formulas
HELP PLS
.
the rate of interest is 11.25%.we can use simple interest formula get answer as above
what is simple interest ?
Simple interest is a type of interest that is calculated as a percentage of the principal amount of a loan or investment, and is based only on the original amount of money that was borrowed or invested.
In the given question,
We can use the formula for simple interest to solve for the rate:
Simple Interest = (Principal x Rate x Time) / 100
Substituting the given values, we get:
$900 = (400 x Rate x 20) / 100
Multiplying both sides by 100 and dividing by 400 x 20, we get:
Rate = $900 / (400 x 20) = 0.1125 or 11.25%
Therefore, the rate of interest is 11.25%.
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The volume of a juice box is about 24 cubic inches.
helpppp
in the figure below, m WXZ=72 degrees, and m 2 is three times m 1. Find m 1
Answer:
Step-by-step explanation:
Sonji went to a sandwich shop for lunch with 8 of her friends. Part of the group ordered only a sandwich for $5, and the
rest of the group ordered à combo for $8. The bill for all 9 people totaled $66.00. Which system of equations represents
the number of meals of each type that Sonji and her friends purchased?
Answer:
x+y=9
5x+8y=66
Step-by-step explanation:
At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $1.80 and the cost of a large greeting card is $3.85. How much would it cost to get 4 small greeting cards and 3 large greeting cards? How much would it cost to get
�
x small greeting cards and
�
y large greeting cards?
Answer: 18.75
Step-by-step explanation:
small greeting cards = 1.80
large greeting cards = 3.85
1.80 x 4 = 7.20
3.85 x 3 = 11.55
7.20 + 11.55 = 18.75
What is the meaning of "Finally [tex]s _{i}\circ s_{i}=s _{j}\circ s_{i}=1[/tex] hence [tex]s _{j}=s_{i}\circ r_{i-j}[/tex] and [tex]s _{i}=r_{i-j}\circ s_{j}[/tex]?
This statement describes the relationship between symmetries and rotations
Explaining the meaning of the statement as statedThis statement describes a relation between two symmetry operations, denoted by [tex]s_i[/tex] and [tex]s_j[/tex], and a rotation operation denoted by [tex]r_{i-j}[/tex]. The notation [tex]"s_i \circ s_i"[/tex] and [tex]"s_j \circ s_i"[/tex] denotes the composition of these operations, which means applying one operation after the other.
The statement says that [tex]s_i[/tex] and [tex]s_j[/tex] are both symmetries, and that they have a specific relationship with each other: when [tex]s_i[/tex] is composed with itself, it gives the identity operation (denoted by 1), and when [tex]s_j[/tex] is composed with [tex]s_i[/tex], it also gives the identity operation.
Then the statement concludes that this relationship implies that [tex]s_j[/tex] can be obtained by first applying [tex]s_i[/tex] and then applying a rotation operation [tex]r_{i-j}[/tex], and that [tex]s_i[/tex] can be obtained by first applying a rotation operation [tex]r_{i-j}[/tex] and then applying [tex]s_j[/tex].
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9 belongs to the set N
Answer:
9 belongs to set N, natural, whole, integer, rational, and real number
Step-by-step explanation:
* Natural number: use for counting
* Whole number: includes natural number and zero
* Integer : are whole numbers and their opposite
*Rational number:come from fraction, and their results can be positive integer
*Real number: includes all numbers
This is for precalc can someone help please
What is the value of y in the solution to the system of equations shown?
y = 3x − 1
y = −x − 5
Answer:{y,x}={-4,-1}
Step-by-step explanation:
One number is 6 3/4 while another number is 2 1/6 smaller. Find the sum of these numbers.
The sum of both numbers is 107/12
How to calculate the sum of both numbers ?One number is 6 3/4
The other smaller number is 2 1/6
The sum of both numbers can be calculated as follows
= 6 3/4 + 2 1/6
= 27/4 + 13/6
= 162 + 52/24
= 214/24
= 107/12
Hence the sum of both numbers is 107/12
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Select the correct location on the table.
Darian knows the area of a ring-shaped figure, and wants to determine the radius of the outer circle. His teacher tells him the following formula for finding the area of a ring based on the radius of the smaller circle, r, and the radius of the outer ring, R.
An illustration of two concentric circles. The radius of the inner circle is lower case r and the radius of the outer circle is upper case R.
Darian decides to rewrite the equation to solve for the radius of the outer ring. His work is shown below. Determine if Darian made a mistake when rewriting the equation, and if so, select the step where Darian made his first error.
There was no error in the procedure as we can see below.
What is the change of subject in a formula?In algebra, a formula expresses a relationship between two or more variables. Changing the subject of a formula means isolating a specific variable on one side of the equation. This is done by applying inverse operations in a specific order to eliminate all other variables and isolate the desired one.
We have the formula as;
[tex]A = \pi R^2 - \pi r^2\\A = \pi(R^2 - r^2)\\A/ \pi = R^2 - r^2\\R^2 = A/ \pi + r^2\\R = \sqrt{} A/ \pi + √r^2\\R = \sqrt{} A/ \pi + r[/tex]
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Factor the polynomial completely. If the polynomial is prime, so state.
15y2 - 19y + 6
Answer: 15y2 - 19y + 6 = 0
Step-by-step explanation:
The first term is, 15y2 its coefficient is 15 .The middle term is, -19y its coefficient is -19 .The last term, "the constant", is +6 Step-1 : Multiply the coefficient of the first term by the constant 15 • 6 = 90 Step-2 : Find two factors of 90 whose sum equals the coefficient of the middle term, which is -19 .
A total of $5550 is plit into
Awo investments. Part of the money.
is invested at 4%, and the reminder
is invested at 5"%.. If the total annual
interest from the two investments is
$259, how much is invested at each rate?
a = amount invested at 4%
how much is 4% of "a"? (4/100) * "a", namely 0.04a.
b = amount invested at 5%
how much is 5% of "b"? (5/100) * "b", namely 0.05b.
we know the total amount invested is 5550, so whatever "a" and "b" might be, we know that a + b = 5550.
we also know that the yielded amount in interest is 259, so if we simply add their interest, that'd be 0.04a + 0.05b = 259.
[tex]a+b=5550\implies b=5550-a \\\\[-0.35em] ~\dotfill\\\\ 0.04a+0.05b=259\implies \stackrel{\textit{substituting from above}}{0.04a+0.05(5550-a)~~ = ~~259} \\\\\\ 0.04a+277.5-0.05a=259\implies 277.5-0.01a=259\implies -0.01a=-18.5 \\\\\\ a=\cfrac{-18.5}{-0.01}\implies \boxed{a=1850}\hspace{9em}\stackrel{ 5550~~ - ~~1850 }{\boxed{b=3700}}[/tex]
I Need help with this question
Answer:
The answer is A.
Step-by-step explanation:
For this graph, you are using the linear equation formula: y = mx + b
m is the slope (rise/run)b is the y-intercept (where the line crosses zero at the y-intercept)using calculations show that the height of the barrel of oil is 96.82cm
The use of calculations to show that the height of the barrel of oil is 96.82cm is given below:
The volume is given as V = 42 gal
The radius is given as r = 18/2 = 9 in
The height is given as h= 96.83 cm
How to solveUsing the formula:
V = πr²h
h = V/(πr²)
The volume is given as V = 42 gal
42 gal x 3.7854 l/gal = 158.987 l
158.987 l = 158,987 ml = 158,987 cm³
The radius is given as r = 18/2 = 9 in
9 in x 2.54 cm/in = 22.86 cm
The height is given as h = (158987 cm³) / π(22.86 cm)² ≈ 96.82 cm
depending on how you round, the more precise answer is 96.8285 ≈ 96.83 cm
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En un grupo de 60 alumnos, 12 sacaron 10 en el examen de matemáticas. ¿Cuál es el porcentaje de alumnos que sacaron 10?
We can see that the percentage is 20%, then 20 percent of the students got a 10.
Which percentage of the students got a 10?To find this, we need to use the formula:
Percentage = 100%(number of students with a 10)/(total number of students)
Here we know the that the revelant numbers are:
Number of students with a 10 = 12
total number of students in the class = 60
Replacing that in the formula we will get the percentage:
P = 100%*(12/60)
P = 20%
So 20% of the total number of students got a 10.
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I have no idea how to solve this problem.
(a) The domain of f of g is {1, 8}.
(b) The range of f of g is {0, 1}.
What is the domain and range of f of g?The domain of f of g consists of all the inputs in the domain of g that are also in the domain of f.
(a) Domain of f of g:
The inputs in the domain of g that are also in the domain of f are 1, and 8. Therefore, the domain of f of g is {1, 8}.
To find the range of f of g, we need to apply the function composition f(g(x)) to each input in the domain of f of g, and collect all the outputs.
(b) Range of f of g:
The range of f of g consists of all the outputs obtained by applying f(g(x)) to each input in the domain of f of g.
We have:
f(g(1)) = f(8) = 0
f(g(4)) = f(2) = 1
f(g(8)) = f(0) = 1
Therefore, the range of f of g is {0, 1}.
Thus, in set notation, the domain of f of g is {1, 8}, and the range of f of g is {0, 1}.
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Help please!!!!
Whoever answers right gets brainliest!
Answer:
its 112.7
Step-by-step explanation:
x+2x=3x. 3x = 338
divide 3x and 338 by 3 three is cancelled and x equals to 112.7
[tex]\sf x=13.[/tex]
Step-by-step explanation:1. Formula for area.Assuming that the canvas has a standard rectangle shape, the area should be given by: [tex]\sf A= bh[/tex], where "b" is the base length of the rectangle, and "h" its heignt.
2. Form an equation.We're told that the canvas is "x" inches wide, and that the length of it is "twice as long as the width", thus it is "2x". Now, let's take width as the base, and length as the height.
Since the formula for area is just a product between width and length, and those values are "x" and "2x", respectively, the formula for the area of this canvas is:
[tex]\sf (x)(2x)=338(in^{2} )[/tex]
3. Solve the equation.a) Solve the product.
[tex]\sf (x)(2x)=338(in^{2} )\\ \\\sf 2x^{2} =338(in^{2} )[/tex]
b) Divide by "2" on both sides of the equation.
[tex]\sf \dfrac{2x^{2}}{2} =\dfrac{338(in^{2} )}{2} \\ \\x^{2} =169[/tex]
c) Take the square root of both sides.
[tex]\sf \sqrt{x^{2}} =\sqrt{169} \\ \\x=13[/tex]
4) Final answer.[tex]\sf x=13.[/tex]
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What integer is closest to the radius of a circle with a circumference of 50.27?
The integer which is closest to the radius of a circle with a circumference of 50.27 as required is; Choice A; 8.
Which answer choice is closest to the radius of the circle?It follows from the task content that the integer which is closest to the radius of the circle whose circumference is; 50.27 is to be determined.
Recall; Circumference, C = 2πr
r = C / 2π
r = 50.27 / 2π
r = 8.000718989
Ultimately, the integer which is closest to the radius is; Choice A; 8.
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