Answer:
(a)The position of the particle after a time t is
[tex]S(t)=\frac{t^3}3+9t+c[/tex]
(b)The position of the particle after a time t is
[tex]S(t)=\frac{t^3}3+9t+3[/tex]
Step-by-step explanation:
We know that, the first order derivative of the position of an object is the velocity of the object.
(a)
Given that, the velocity of a particle moving in straight line is
[tex]V(t)=t^2+9[/tex]
[tex]\Rightarrow \frac{dS(t)}{dt}=t^2+9[/tex]
[tex]\Rightarrow {dS(t)}=t^2dt+9\ dt[/tex]
Integrating both sides
[tex]\int {dS(t)}=\int t^2dt+\int9\ dt[/tex]
[tex]\Rightarrow S(t)=\frac{t^3}3+9t+c[/tex] [ c is an arbitrary]
The position of the particle after a time t is
[tex]S(t)=\frac{t^3}3+9t+c[/tex]
(b)
Given that S= 3 at time t=0
[tex]\therefore 3=S(t)=\frac{0^3}3+9.0+c[/tex]
[tex]\Rightarrow c=3[/tex]
The position of the particle after a time t is
[tex]S(t)=\frac{t^3}3+9t+3[/tex]
The position function is computed by integrating the given velocity function v(t) = t^2 + 9. The constant of integration C was found to be 3 using the given initial condition of s(0) = 3. Thus, the position function without any unknown constants is S(t) = (1/3)t^3 + 9t + 3.
Explanation:The velocity function given for the particle moving in a straight line is v(t) = t2 + 9. This function can be used to find the position function using integral calculus.
hen t=0 the position function S(t) = (1/3)*03 + 9*0 + C = C = 3.
Thus, using the constant of integration we found, we can write the position function without any unknown constants as S(t) = (1/3)t3 + 9t + 3.
(a) Finding the Position Function
To find an expression for the position, we integrate the velocity function. Here, the integral of the given velocity function v(t) = t2 + 9 is S(t) = ∫(t2 + 9)dt = (1/3)t3 + 9t + C, where C is the constant of integration.
(b) Finding the Constant of Integration
Given that s(0) = 3, w
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Factor completely 16x^2-81
Answer:
(4x-9) times (4x+9)
Step-by-step explanation:
A certain medication comes in the form of a capsule, as shown below. The fluid inside the capsule contains several ingredients, including the active medication.
What is the volume of the capsule? Round to the nearest tenth.
V =
mm3
If the density of the active medication in the liquid is
0.7 mg/mm3, how many milligrams of the active medication are in one capsule? Round to the nearest tenth.
mg
Answer:
volume: 103.9 mm³medication: 72.7 mgStep-by-step explanation:
You want the volume of a medicine capsule and the mass of active ingredient if the capsule is a cylinder 4 mm in diameter and 5.6 mm long, capped on either end by a hemisphere, and the active ingredient has a density of 0.7 mg/mm³.
(a) VolumeThe volume of a cylinder is given by ...
V = πr²h
and the volume of a sphere is given by ...
V = 4/3πr³
The two hemispheres have a total volume equal to that of a sphere, and the radii of the cylinder and sphere are the same. This means the volume of the capsule can be found as ...
V = πr²h +4/3πr³
V = πr²(h +4/3r)
The radius is half the diameter, so we have ...
V = π(2 mm)²(5.6 mm +4/3(2 mm)) ≈ 103.882 mm³
The volume of the capsule is about 103.9 mm³.
(b) MilligramsMultiplying the volume by the density gives the mass of active ingredient:
m = ρV
m = (0.7 mg/mm³)·(103.882 mm³) ≈ 72.72 mg
There are about 72.7 mg of active medication in one capsule.
Points D, E, and F are on circle C and EF ≅ DF. Circle C is shown. Line segments D C and E C are radii. Point F is on the opposite side. Lines are drawn from points D and E to point F. Tangents D G and E G intersect at point G. Angle D G E is 76 degrees and angles G D C and G E C are 90 degrees. D F and E F are congruent. What is the measure of ∠CDF? 14° 19° 26° 38°
Answer:
Letter C: 26
Step-by-step explanation:
Just took the test e2020
Answer:
c
Step-by-step explanation:
derek wants to determine the height of the top of the backboard on the basketball goal at the playground. he places a standard 12 inch ruler next to the goal post and measures the shadow of the ruler and the background. if the ruler had a shadow of 10 inches and the backboard has a shadow of 7.25 feet, then how high is the top of the backboard
Answer:
7.91
Step-by-step explanaton:
Derek wants to determine the height of the top of the backboard on the basketball goal at the playground. He places a standard 12-inch ruler next to the goal post and measures the shadow of the ruler and the backboard. If the ruler has a shadow of 11 inches and the backboard has a shadow of 7.25 feet, then about how high is the top of the backboard?
A.
6.14 feet
B.
8.92 feet
C.
7.91 feet
D.
9.17 feet
i was looking for the answer and jess couldn't find it and so i answered it and it told me the answer was 7.91.
it also told me that the reason for this was:
Since the backboard and the ruler are both vertical and the sun is at the same position in the sky, the triangle made by the backboard and its shadow is similar to the triangle made by the ruler and its shadow.
The ratio of the corresponding sides of the triangles are equal and the height of the backboard can be determined by solving the following proportion.
Therefore, the top of the backboard is 7.91 feet high.
The diameter of a circle is 20 kilometers. What is the angle measure of an arc bounding a sector with an area 10 pi square kilometers. (Simplify fractions)
PLEASE ANSWER
Answer: I’m not sure
Step-by-step explanation: Good luck some one will answer soon i hope
Answer: The answer is 9.
Step-by-step explanation:
I didn't get a fraction. I plugged in the information. I got 10pi/400pi =x/360. After doing the calculations I then got 9 and it was correct when I plugged it into my assignment. Hope this helped.
London inherited $823,000. If she wants to donate a tenth of her inheritance to charities, how much should she donate?
$
Answer:
She donated 82,300
Step-by-step explanation:
She donated a tenth of 823,000. A tenth is 10% or .10. A tenth of 832,000 is just 832,000 * .10. Or if it's a tenth, you can take off a zero
Answer:
$82,300
Step-by-step explanation:
823,000 times 0.10
= 82,300
B -17 =-2 is what I cant
Answer:
Please make your question more clear
Step-by-step explanation:
We can not read your question.
please explain your question better
Answer:
15
Step-by-step explanation:
How do you know that 361 + 283 is greater than 500 without finding
the sum?
You would estimate first look at the 100's place 3+2=5 so we already have 500 so we know that the sumis greater than 500 because is you at 61+83 with 500 its a larger number than just 500
Final answer:
To see if 361 + 283 is greater than 500, round each number to the nearest hundred and add them. The rounded sum of 400 + 300 = 700 is clearly greater than 500, thus the actual sum must also be greater than 500.
Explanation:
To determine if the sum of 361 + 283 is greater than 500 without actually adding the numbers together, you can use estimation. You can round each number to its nearest hundred to make the math easier. 361 can be rounded to 400 and 283 can be rounded to 300. When you add these rounded numbers together, 400 + 300 = 700, which is clearly greater than 500. Since rounding each number up only increases the sum, the actual sum of 361 + 283 must also be greater than 500.
This concept is based on the understanding that the rules of mathematics are universally valid, as addition is commutative (A+B=B+A).
$83 giraffe; 17% markup
Answer:
$97.11
Step-by-step explanation:
17% of $83 = $14.11
$83 + $14.11 = $97.11
For similar light intensity, compact fluorescent bulbs use about 25% of the energy of incandescent bulbs. Let's say you replaced a bulb of 100 W with a fluorescent bulb and that your utility charges $0.15/kW-hour. How many dollars would you save in electricity in the 10,000−hour lifetime of the bulb?
Answer:
$112.50¢
Step-by-step explanation:
please kindly check the attached file for explanation
$112500 would be saved in electricity in the 10,000−hour lifetime of the Fluorescent bulb.
Given that compact fluorescent bulbs use about 25% of the energy of incandescent bulbs.
Hence, For a 100W bulb, the corresponding energy is:
Fluorescent bulb = 25% of 100W = 0.25 * 100 = 25W
Since the charges is $0.15/kW-hour, hence, for 10000 hour lifetime:
Total charges for Incandescent = 100W * 10000 hour * $0.15/kW-hour = $37500
Total charges for Fluorescent = 25W * 10000 hour * $0.15/kW-hour = $150000
Therefore the money saved in electricity = $150000 - $37500 = $112500
Hence $112500 would be saved in electricity in the 10,000−hour lifetime of the Fluorescent bulb.
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A cone has a base that is a shape of a circle. The length across is 16 feet. The height is 8 feet and the slant height is 10 feet. What is the lateral area of the cone using 3 for pi
Answer:
The answer to your question is Surface area = 432 ft²
Step-by-step explanation:
Data
diameter = 16 ft
height = 8 ft
slant height = 10 ft
pi = 3
Process
1.- Write the formula to calculate the surface area
Surface area = pi x radius x slant height + pi x radius²
2.- Substitution
Surface area = (3 x 16/2 x 10) + (3 x (16/2)²)
-Simplification
Surface area = 240 + 192
-Result
Surface area = 432 ft²
Find the midpoint of the line segment joining the points A=(-6,-4) and B=(-2,6)
Answer:
The midpoint is (-4,1)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates and divide by 2
(-6+-2)/2 = -8/2 = -4
To find the y coordinate of the midpoint, add the y coordinates and divide by 2
(-4+6)/2 = 2/2 =1
The midpoint is (-4,1)
Answer:
The midpoint of the segment is at (-4,1)
Step-by-step explanation:
Since the midpoint of an line segment is the middle of the two x and y coordinates:
x-coords:
-6+-2 = -8
-8/2 = -4
y-coords
-4+6 = 2
2/2 = 1
The midpoint of the segment is at (-4,1)
I'VE TRIED EVERY METHOD POSSIBLE TO ANSWER THESE QUESTIONS AND KEEP HITTING DEAD ENDS SO PLS IF YOU CAN HELP PLS DO BECAUSE I'M STUCK
A cone-shaped kitchen funnel has a diameter of 6 inches and a height of 7 inches. About how many times would you need to fill the funnel to fill a cylindrical can that has a radius of 4 inches and a height of 13 inches?
A. 3
B. 4
C. 9
D. 10
The circumference of an orange is approximately 37.68 centimeters. What is the approximate volume of the orange? Use 3.14 for π.
A. 226.08 cubic meters
B. 678.24 cubic meters
C. 904.32 cubic meters
D. 7234.56 cubic meters
Which of the following statements about the volume of a sphere and the volume of a cone are true? Select two answers.
A. You can find the volume of a sphere with only the diameter.
B. You can find the volume of a sphere with only the radius.
C. You can find the volume of a cone with only the height.
D. You can find the volume of a cone with only the diameter.
Answer:
D.
C.
A,B
Step-by-step explanation:
Given:
Diameter of a cone-shaped kitchen funnel = 6 inches
Height of a cone-shaped kitchen funnel = 7 inches
Radius of a cylindrical funnel = 4 inches
Height of a cylindrical funnel = 13 inches
To find: Number of cylindrical funnels required to fill a cone-shaped kitchen funnel
Solution:
Radius of a cone-shaped kitchen funnel (R) = 6/2 = 3 inches
Height of a cone-shaped kitchen funnel (H) = 7 inches
Volume of a cone-shaped kitchen funnel = [tex]\frac{1}{3}\pi R^2H=\frac{1}{3}\pi(3)^2(7)=21\pi[/tex] cubic inches
Radius of a cylindrical funnel (r) = 4 inches
Height of a cylindrical funnel (h) = 13 inches
Volume of a cylindrical kitchen funnel = [tex]\pi r^2h=\pi(4)^2(13)=208\pi[/tex] cubic inches
Number of cylindrical funnels required to fill a cone-shaped kitchen funnel = 9.9≈ 10
Option D. is correct
Given:
Circumference of an orange = 37.68 centimeters
To find: volume of the orange
Solution:
Let r be the radius of the orange
Circumference of an orange = 37.68 centimeters
[tex]2\pi r=37.68\\r=\frac{37.68}{2\pi}[/tex]
Volume of the sphere = [tex]\frac{4}{3}\pi r^3[/tex]
[tex]=\frac{4}{3}\pi \left ( \frac{37.68}{2\pi} \right )^3[/tex]
[tex]=\frac{4}{3}\frac{\left ( 37.68 \right )^3}{8(3.14)^2}=904.32[/tex] cubic metres
Volume of sphere can be computed using only the radius or using only the diameter.
Option A and B are correct.
For volume of cone, both radius and height are required
X2 + y2 = 1 x = 1 Hina's work: substitute: (1)2 + y2 = 1 simplify: 12 + y2 = 1 isolate the variable: y2 = 0 solve for y: y = 0 Complete Hina's work to determine which statements are true for the system of equations. Check all that apply. The system of equations has no solutions. The system of equations has one solution. The system of equations has two real-number solutions. A solution to the system is (0, 0). A solution to the system is (1, 0).
Answer:
the correct answer is B.
Step-by-step explanation:
The system of equations has one solution. Option B is correct.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression,
x² + y² = 1
Now,
Put x = 1
1 + y² = 1
y² = 0
y = 0
Since for the given expression more than one solution can be possible but for the given condition a x = 1 only one solution is possible.
Thus, the system of equations has one solution. Option B is correct.
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A random sample of monarch butterflies and a random sample of swallowtail butterflies were selected, and the difference in the average flying speed for each sample was calculated. A two-sample t-test for the difference in means was conducted to investigate whether the speed at which monarchs fly, on average, is faster than the speed at which swallowtails fly. All conditions for inference were met, and the p-value was given as 0.072.
Which of the following is a correct interpretation of the p-value?a. The probability that monarchs fly faster than swallowtails is 0.072.b. The probability that monarchs and swallowtails fly at the same speed is 0.072.c. Assuming that monarchs and swallowtails fly at the same speed on average, the probability of observing a difference equal to or greater than the sample difference is 0.072.d. Assuming that monarchs fly faster than swallowtails on average, the probability of observing a difference equal to or greater than the sample difference is 0.072.e. Assuming that monarchs fly faster than swallowtails on average, the probability of the monarchs and swallowtails flying at the same speed is 0.072.
Answer:
Option C is the correct answer
Step-by-step explanation:
Let μ1 be the average flying speed of monarch butterflies and let μ2 be the average flying speed of swallowtail butterflies.
Also, let n1 be the sample size of monarch butterflies and let n2 be the sample size of swallowtail butterflies.
Thus, defining the hypothesis, we have;
Null hypothesis;H0: μ1 = μ2
Alternative hypothesis; H1: μ1 > μ2
In this case, the p-value = P_H0[t_(n1 + n2 - 2) ≥ t] where t is the test statistic based on tbe differences of sample mean,that follows t distribution with degrees of freedom (n1 + n2 - 2)
With respect to the question, the probability of the monarchs and swallowtails flying at the same speed is 0.072.
Thus,
P_H0[t_(n1 + n2 - 2) ≥ t] = 0.072
We can therefore conclude that in this case, the p-value is the probability of observing a difference equal to or greater than the sample difference under the null hypothesis which states that μ1 = μ2, which is 0.072
Thus, option C is the correct answer
Answer:
The correct option is;
b. The probability that monarchs and swallowtails fly at the same speed is 0.072
Step-by-step explanation:
The p- value indicates the probability of which the hypothesis tested, the null hypothesis is true and it is compared against a given confidence level. Whereby the p-value is more than the given confidence level then it indicates that the null hypothesis assumption is correct.
Therefore, whereby the null hypothesis tests proposes the equality of the two means, then at a 5% confidence level or α = 0.05, whereby p-value = 0.072 > α = 0.05 we accept the null hypothesis and state that the probability that monarchs and swallowtails fly at the same speed is 0.072.
5x + 6 = 2(2x – 3)
( 30 pts 4 answering right)
Answer:
x =-12
Step-by-step explanation:
5x + 6 = 2(2x – 3)
Distribute
5x+6 = 4x -6
Subtract 4x from each side
5x-4x +6 = 4x-4x-6
x +6 = -6
Subtract 6 from each side
x+6-6 = -6-6
x = -12
Answer:
x = -12
Step-by-step explanation:
5x + 6 = 2(2x – 3)
5x + 6 = 4x - 6
x = -12
Usually LeRoy practices the bass for 2 4/5 hours a day. Today he practiced half his
usual time. For how long did he practice?
Answer:
[tex]1 \frac{2}{5} hours[/tex]
Step-by-step explanation:
LeRoy practiced for 1 2/5 hours today.
Explanation:To find how long LeRoy practiced today, we need to determine half of his usual practice time of 2 4/5 hours. To do this, we divide 2 4/5 by 2. If we simplify the fraction, we get 14/5. Dividing 14/5 by 2, we get 7/5 or 1 2/5 hours. Therefore, LeRoy practiced for 1 2/5 hours today.
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Liz flips a coin 70 times. The coin lands heads up 21 times and tails up 49 times. Complete each statement. The theoretical probability of the coin landing heads up is what%.
The theoretical probability of the coin landing heads up is 30%.
Explanation:The theoretical probability of the coin landing heads up is 30%.
The number of times the coin lands heads up out of the total number of coin flips is called the experimental probability. In this case, the experimental probability is 21/70 = 0.3, or 30%.
The theoretical probability of getting heads on a fair coin is always 50%, but in this specific experiment, the experimental probability varied due to chance. As the number of coin flips increases, the experimental probability should approach the theoretical probability of 50%.
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Which functions have a horizontal asymptote? Y = f(x) y = h(x) y = g(x) y = k(x) On a coordinate plane, 4 exponential functions are shown. Y = f (x) approaches the x-axis in quadrant 1 and increases exponentially in quadrant 2. It goes through (0, 1) and (negative 4, 5). Y = g (x) approaches the x-axis in quadrant 1 and increases exponentially in quadrant 2. It goes through (0, 1) and (negative 1, 3). Y = h (x) approaches the x-axis in quadrant 2 and increases exponentially in quadrant 1. It goes through (0, 1) and (1, 3). Y = k (x) approaches the x-axis in quadrant 2 and increases exponentially in quadrant 1. It goes through (0, 1) and (4, 5).
Answer:
Is all of them !!
Step-by-step explanation:
Because they all have asymptote
Answer:
all of them
Step-by-step explanation:
all have asymptote
Which equation is written in slope-intercept form?
y = 3 x minus 2
x = one-half y + 8
2 x + 5 y = 12
3 y = 8 x minus 5
Answer:
A) y = 3x - 2
Step-by-step explanation:
slope-intercept form is represented by y=mx+b
your answer choices look like this
A) y = 3x -2
B) x = 1/2y + 8
C) 2x + 5y = 12
D) 3y = 8x - 5
right away, you can eliminate B & C, since they just don't represent the formula correctly.
D is your trick answer choice. at first glance, it looks right, however, the 'y' is not isolated, which is a key interpretation of the formula.
therefore, from process of elimination, A is right because is correctly represents the formula of slope-intercept form.
i hope this helps!
stay safe!
:)
The equation written in slope-intercept form is y = 3x - 2. The correct option is A.
What is an equation?The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.
The equation of a line is given as:_
y = mx + c
The slope-intercept form is represented by y=mx+b. Right away, you can eliminate B & C, since they just don't represent the formula correctly.
D is your trick answer choice. at first glance, it looks right, however, the 'y' is not isolated, which is a key interpretation of the formula.
Therefore, from the process of elimination, A is right because is correctly represents the formula of slope-intercept form.
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If 2+2=44 and 3+3= 96 and 4+4=168 and 5+5=2510 then what is 6+6=?
Answer:
3612
Step-by-step explanation:
boom
If g(4) = 16, g(5) = 18, g(6) = 20, then g(3) =
?
Answer:
14
Step-by-step explanation:
it's going up by 2 everytime so you just take away 2
An aquarium holds 3D 3.75 gallons of water it has a length of 2 feet and a height of 1.5 ft what is the volume of the aquarium what is the width of the aquarium explain
The width of the aquarium is 0.1625 ft.
Step-by-step explanation:
Given,
The length (l) of the aquarium = 2 ft
Height (h) = 1.5 ft
The capacity of water it holds = 3.75 gallons
That means the volume (V) = 3.75 gallon
To find the width(b) of the aquarium.
Formula
The volume of a cuboid with l as length, b as width and h as height = lbh1 gallon = 0.13 cube ftSo,
V = 3.75×0.13 cube ft
According to the problem,
2×1.5×b = 3.75×0.13
or, b = (3.75×0.13)÷(2×1.5)
or, b = 0.1625 ft
Hence,
The width of the aquarium is 0.1625 ft.
what is 1+1 times 1,000,000,000,000,000,000,000,000
Answer: 2e +24 which equals 130.477527766
:)
Answer:
1e+24
Step-by-step explanation:
Suppose that $2000 is loaned at a rate of 18%, compounded semiannually. Assuming that no payments are made, find the amount owed after 9 years.
Do not round any intermediate computations, and round your answer to the nearest cent.
The amount owed after 9 years on a $2000 loan compounded semiannually at an 18% interest rate is approximately $8599.63.
When we need to find the amount owed after 9 years on a $2000 loan compounded semiannually at an 18% interest rate, we use the formula for compound interest:
A = P (1 + r/n)^(nt)
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount ($2000).
r is the annual interest rate (18% or 0.18).
n is the number of times the interest is compounded per year (2 for semiannual).
t is the time the money is invested for, in years (9 years).
Substituting the values into the formula, we have:
A = 2000 (1 + 0.18/2)^(2*9)
A = 2000 (1 + 0.09)^(18)
A = 2000 (1.09)^18
Calculating this expression gives us the amount owed after 9 years. Do not round any intermediate computations, and round your answer to the nearest cent.
The calculation is as follows:
A = $2000 * (1.09)^18
A ≈ $2000 * 4.299816955
A ≈ $8599.63
Therefore, the amount owed after 9 years would be approximately $8599.63.
Please help due today
Answer:
523.3
Step-by-step explanation:
[tex]Volume = \frac{4}{3} * 3.14 * 5^{3} \\Volume = 523.3[/tex]
Please give me brainliest
What is the length of a diagonal of a rectangular picture whose sides are 15 inches by 17 inches? Round to the nearest tenth of a inch.
Answer:
First, 32 rounded to the nearest ten is:
30
Step-by-step explanation:
When rounding to the nearest ten, like we did with 32 above, we use the following rules:
A) We round the number up to the nearest ten if the last digit in the number is 5, 6, 7, 8, or 9.
B) We round the number down to the nearest ten if the last digit in the number is 1, 2, 3, or 4.
C) If the last digit is 0, then we do not have to do any rounding, because it is already to the ten.
Is 29.99 the same as 30
Answer:
No
Step-by-step explanation:
HELP ME WITH THIS FAST
Answer:
About 374 people.
Step-by-step explanation:
[tex] \frac{11}{50} \times 1700 = 374[/tex]
Which circle has a radius that measures 10 units?
A) Circle D is shown. A line segment goes from one point to another point on the circle and has a length of 10.
B) Circle F is shown. A line segment goes from one point to another point on the circle and goes through point F. It has a length of 20.
C) Circle G is shown. A line segment goes from one point to another point on the circle and goes through point G. It has a length of 10.
D) Circle H is shown. A line segment goes from one point to another point on the circle and has a length of 20.
Answer:
B) Circle F is shown. A line segment goes from one point to another point on the circle and goes through point F. It has a length of 20.
Step-by-step explanation:
A segment that goes through the center of the circle and that has its ends on the circle is a diameter. The radius is half the length of the diameter.
A chord through the center of circle F with a length of 20 units means circle F has a radius of 10 units.
Final answer:
Option B is the correct answer because it describes a line segment that passes through the center and is 20 units long, indicating it's a diameter; hence the radius is half of that, which is 10 units.
Explanation:
To determine which circle has a radius of 10 units, we need to recall that the radius is a straight line from the center of the circle to a point on its boundary. Two radii lined up end-to-end across a circle form a diameter. Therefore, a diameter is twice the length of the radius.
Option A describes a line segment of length 10, but we cannot confirm if it's a radius or a diameter without additional information.
Option B describes a line segment that goes through the center point F and is 20 units long, indicating it's a diameter. Since the diameter is twice the radius, a circle with a diameter of 20 units has a radius of 10 units.
Option C, like option A, cannot be confirmed without additional information about the line segment's relation to the center of the circle.
Option D also describes a line segment of 20 units, but again, without confirmation that it's a diameter, we cannot be sure.
Therefore, the correct answer is Option B, where the circle's diameter is explicitly mentioned to be 20 units, meaning the radius is 10 units.