A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 70 cm/s. Find the rate at which the area within the circle is increasing after each of the following. (a) after 1 s $$40 cm2/s (b) after 4 s cm2/s (c) after 6 s cm2/s
Answer:
(a) 9800π cm²/s
(b) 39200π cm²/s
(c) 58800π cm²/s
Step-by-step explanation:
As we know,
The area of circle is:
[tex]A= \pi r^2[/tex]
[tex]\frac{dA}{dt}=2 \pi r\frac{dr}{dt}[/tex]
The given value is:
[tex]\frac{dr}{dt} =70 \ cm/s[/tex]
Now,
(a)
After 1 second,
r = 70×1
= 70 cm
⇒ [tex]\frac{dA}{dt}=2\pi(70)\times (70)[/tex]
[tex]=9800 \pi \ cm^2/s[/tex]
(b)
After 2 second,
r = 70×4
= 280 cm
⇒ [tex]\frac{dA}{dt}=2\pi \ (280)\times (70)[/tex]
[tex]39200\pi \ cm^2/s[/tex]
(c)
After 6 seconds,
r = 70×6
= 420 cm
⇒ [tex]\frac{dA}{dt}=2\pi \ (420)\times (70)[/tex]
[tex]58800\pi \ cm^2/s[/tex]
The rate will be:
(a) 9800 π cm²/s
(b) 39200 π cm²/s
(c) 58800 π cm²/s
Circle:A circle seems to be a closed object or structure generated by tracing a point that travels together in plane at quite a constant distances from either a specific location.
According to the question,
Speed, [tex]\frac{dr}{dt}[/tex] = 70 cm/s
We know,
The area of circle:
→ A = πr²
[tex]\frac{dA}{dt}[/tex] = 2πr[tex]\frac{dr}{dt}[/tex]
(a) After 1 s, the rate be:
r = 70 × 1
= 70 cm
[tex]\frac{dA}{dt}[/tex] = 2π(70) × 70
= 9800 π cm²/s
(b) After 2 s, the rate be:
r = 70 × 4
= 280 cm
[tex]\frac{dA}{dt}[/tex] = 2π(280) × 70
= 39200 π cm²/s
(c) After 6 s, the rate be:
r = 70 × 6
= 420 cm
[tex]\frac{dA}{dt}[/tex] = 2π(420) × 70
= 58800 π cm²/s
Thus the response above is correct.
Find out more information about area of circle here:
https://brainly.com/question/12069107
l10l= -10 what is the correct answer
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Identify and select all of the segments that form a radius of the circle.
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A large boulder falls from a cliff located 1,044 meters away from a herd of elephants. The temperature of the alr is 28°C.
How long after the boulder crashes will the elephants hear the sound?
O 30 sec
3.20 sec
0.30 sec
3.00 sec
Answer:
it is b
Step-by-step explanation:
I got it right! I also took a test and I reviewed my question
Answer:
3.20
Step-by-step explanation:
What is the slope of the line on the graph?
Answer:
1/2
Step-by-step explanation:
Pick to easy to read points on the line: (-4, 0) and (0, 2)
Start at (-4, 0). To go to (0, 2), you go 2 units up. That is a rise of 2.
Then you go 4 units right. that is a run of 4.
slope = rise/run = 2/4 = 1/2
Answer: 1/2
1. At a restaurant, a customer can choose between 3 appetizers, 2 main courses, and 3 desserts. (a) A customer wants to order exactly one appetizer, one main course, and one dessert. How many different meals could this customer order
Answer:
Total probability = 7/6
Step-by-step explanation:
Given:
Number of appetizer = 3
Number of main course = 2
Number of desserts = 3
Computation:
Probability of choosing 1 appetizer = 1/3
Probability of choosing 1 main course = 1/2
Probability of choosing 1 dessert = 1/3
Total probability = 1/3+1/2+1/3
Total probability = 7/6
1. F & G industries manufacturers a motor that is marketed with a warranty that guarantees it will be replaces free of charge if it fails within the first 13,000 hours of operation. On average, F & G, motors operate for 15,000 hours with a standard deviation of 1,250 hours before failing. The number of operating hours before failure is approximately normally distributed. a. What is the probability that a motor will have to be replaced free of charge
Answer:
The value is [tex]P(X < 13000) =0.054799[/tex]
Step-by-step explanation:
From the question we are told that
The number of hours considered is [tex]x= 13000 \ hours[/tex]
The population mean is [tex]\mu = 15000\ hours[/tex]
The standard deviation is [tex]\sigma = 1250\ hours[/tex]
Generally the the probability that a motor will have to be replaced free of charge is mathematically represented as
[tex]P(X < 13000) = P(\frac{ X - \mu }{\sigma } < \frac{13000 - 15000}{1250} )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
[tex]P(X < 13000) = P(Z<-1.6 )[/tex]
From the z table the probability of (Z<-1.6 ) is
[tex]P(Z<-1.6 ) = 0.054799[/tex]
So
[tex]P(X < 13000) =0.054799[/tex]
A truck has used 39 liters of gas. It has 59 liters left in the tank. How many liters will the tank hold when it is full? =
Answer:
98 liters
Step-by-step explanation:
add 39 and 59
What is eulers identity derivation
Hello friend! Hope this helps!
Euler's formula is eⁱˣ=cos(x)+i⋅sin(x), and Euler's Identity is e^(iπ)+1=0. See how these are obtained from the Maclaurin series of cos(x), sin(x), and eˣ.
f(x) = -3X - 4 ; Domain= {-17, -14, -6, -2,4, 15}
Range :
Answer:
g(x)={47,38,14,2,-16,-49}
Step-by-step explanation:
f(-17)=-3*-17-4=51-4=47
f(-14)=-3*-14-4=42-4=38
f(-6)=-3*-6-4=18-4=14
f(-2)=-3*-2-4=6-4=2
f(4)=-3*4-4=-12-4=-16
f(15)=-3*15-4=-45-4=-49
1- 8
2- 12
3- 5
4- 13
Answer:
4- 13
Step-by-step explanation:
AC = √ AB^2 + BC^2
AC = √ 5^2 + 12^2
AC = √ 25 + 144
AC = √ 169
AC = 13
If the fabric, thread, buttons, and zipper cost $13.30, how much is the sales tax if the tax is 8%?
Answer:
it'd be $1.06 rounded to the nearest thousendth or $1.06400
Step-by-step explanation:
13.30*8/100=Your Answer
Find the largest interval for which the following initial value problems are guaranteed to have a unique solution. Explain your reasoning (5 points each). DO NOT SOLVE THE EQUATIONS.
Answer and Step-by-step explanation:
Solution:
The given equation is:
t (t -4)y” + 3ty’ + 4y = 2
Where,
Y (3) = 0, y’ (3) = -1
To find out the largest interval, which have unique solution,
Divide the given equation with t(t – 4):
Y” + 3y’ / t(t-4) + 4y / t(t-4) = 2 / t (t -4)
Solution exists on (0, 4)
Because:
P(t) = 3 / t -4, continuous on ( -∞, 4) and (4, ∞)
Q(t) = 4/t(t-4) , continuous on (-∞, 0), (0,4) and (4, ∞)
G(t) = 2 / t(t-4) continuous on (-∞, 0), (0,4) and (4,∞)
T0 = 3,
So solution exist on (0, 4)
Hence, (0, 4) is the largest interval for which the initial value problem:
t (t -4)y” + 3ty’ + 4y = 2
have a unique solution.
6. A college is trying to determine if there is a significant difference in the mean GMAT score of students from different undergraduate backgrounds who apply to the MBA program. The Excel file GMAT Scores contains data from a sample of students. What conclusion can be reached using ANOVA
Answer:
All mean of GMAT scores might not be equal.
Reject null hypothesis.
Step-by-step explanation:
ANOVA is a statistical technique which analyzes and estimates different procedures to find variance among them. For the given GMAT scores the null hypothesis is considered as all means of GMAT scores are equal and the alternative hypothesis is all mean of GMAT score is not equal. Using excel the ANOVA technique is used to reach the conclusion.
Harry coaches 25 children on Wednesday. On Saturday, he coaches 9 more children. How many children does he coach in all? How did you know to regroup to solve this problem?
Answer:
34
Step-by-step explanation:
25+9=34
We don't know if he did or how much he coached on other possible days so in total with the information given. He did 34
what is 0.36 repeating in simplest form?
Identify the domain and range of the function graphed below.
5. Factor and solve.
x2+3x=18
6^3m x 6^-m= 6^-2m expotential function
Answer:
Step-by-step explanation:
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 413 gram setting. It is believed that the machine is underfilling of overfilling the bags. A 22 bag sample had a mean of 417 grams with a standard deviation of 13. Assume the population is normally distributed. A level of significance of 0.05 will be used. Specify the type of hypothesis test.
Answer:
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is insufficient evidence to conclude that the machine is under filling the banana chips.
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 413 \ g[/tex]
The sample size is n = 22
The sample mean is [tex]\= x = 417 \ g[/tex]
The standard deviation is [tex]s = 13[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \mu = 413[/tex]
The alternative hypothesis is [tex]H_a : \mu < 413 \ g[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\= x - \mu }{ \frac{s}{\sqrt{n} } }[/tex]
=> [tex]z = \frac{417 - 413}{ \frac{13}{\sqrt{22} } }[/tex]
=> [tex]z = 1.443[/tex]
Generally from the z table the probability of [tex](Z > 1.443 )[/tex] is
[tex]p-value = P(Z > 1.443) = 0.07451[/tex]
From the value obtained we can see that [tex]p-value > \alpha[/tex] hence
The decision rule is
Fail to reject the null hypothesis
The conclusion is
There is insufficient evidence to conclude that the machine is under filling the banana chips.
The perimeter of a triangle is 51 cm. The lengths of its sides are x cm, x + 2 cm, and x + 4 cm. What is the length, in cm, of the longest side of the triangle
Answer: 24
Step-by-step explanation:
Help quickly with this math question
Answer:
The circumference of circle is 8π ft.
Step-by-step explanation:
Given that the formula of area of a circle is A = π×r² where r represents the radius of circle. So you have to find the radius first :
[tex]area = \pi \times {r}^{2} [/tex]
[tex]let \: area = 16\pi[/tex]
[tex]\pi {r}^{2} = 16\pi[/tex]
[tex] {r}^{2} = 16[/tex]
[tex]r = \sqrt{16} [/tex]
[tex]r = 4 \: feet[/tex]
Next, you have to apply circumference of circle formula, C = 2×π×r :
[tex]c = 2 \times \pi \times r[/tex]
[tex]let \: r = 4[/tex]
[tex]c = 2 \times \pi \times 4[/tex]
[tex]c = 8\pi \: feet[/tex]
A mother explains to her child that the price on the sign is not the total price for a ladder, because the price does not include tax. She points out that a $24 ladder actually costs $26.40 once the sales tax is added. What is the sales tax percentage?
Write your answer using a percent sign (%).
Answer:
2.4%
Step-by-step explanation:
Answer:
hi
Step-by-step explanation:
Explain the difference between Gross Income & Net Income
I need help right now please !!!!
a student earns $70 over the summer. he spends 1/5 of the total amount on movies. He then spends 1/2 of the remaining money on school clothes.
how much money is left?
Given:
Total earning = $70
He spends [tex]\dfrac{1}{5}[/tex] of the total amount on movies.
He then spends [tex]\dfrac{1}{2}[/tex] of the remaining money on school clothes.
To find:
The remaining money.
Solution:
We have,
Total earning = $70
He spends [tex]\dfrac{1}{5}[/tex] of the total amount on movies.
Money spent on movie is
[tex]\$70\dfrac{1}{5}=\$14[/tex]
Remining money after movie is
[tex]\$70-\$14=\$56[/tex]
He then spends [tex]\dfrac{1}{2}[/tex] of the remaining money on school clothes.
Money spent on school clothes is
[tex]\$56\times \dfrac{1}{2}=\$28[/tex]
Remining money after movie and school clothes is
[tex]\$56-\$28=\$28[/tex]
Therefore, the remaining money is $28.
If x = −5, which number line shows the value of |x|?
A. A number line is shown from negative 6 to positive 6 with increments of 1. All the numbers are labeled on the number line. A dot is shown on a point at 5 tick marks to the left of 0. Above the number line, a bracket is shown extending from a point at 5 tick marks to the left of zero to a point at 5 tick marks to the right of zero. A horizontal line is shown between the brackets, and 5 is written on the line.
B. A number line is shown from negative 6 to positive 6 with increments of 1. All the numbers are labeled on the number line. A dot is shown on a point at 5 tick marks to the left of 0. Above the number line, a bracket is shown extending from a point at 5 tick marks to the left of zero to a point at zero. A horizontal line is shown between the brackets, and 5 is written on the line.
C. A number line is shown from negative 6 to positive 6 with increments of 1. All the numbers are labeled on the number line. A dot is shown on a point at 5 tick marks to the left of 0. Above the number line, a bracket is shown extending from a point at 5 tick marks to the left of zero to a point at 5 tick marks to the right of zero. A horizontal line is shown between the brackets, and negative 5 is written on the line.
D. A number line is shown from negative 6 to positive 6 with increments of 1. All the numbers are labeled on the number line. A dot is shown on a point at 5 tick marks to the left of 0. Above the number line, a bracket is shown extending from a point at 5 tick marks to the left of zero to a point at zero. A horizontal line is shown between the brackets, and negative 5 is written on the line.
THIS ANSWER WILL BE (A.)
HOPE THIS HELPS
HAVE A GOOD DAY
STAY SAFE
Answer:
The answer is A.
Step-by-step explanation:The number of ticks between 0 and -6 is exact.
What's the opposite of -4/5
Answer:
The answer to the question provided is 4/5.
Answer:
4/5 because you just flip the negative sign
Step-by-step explanation:
Is 24, 29, 32 a right triangle?
Answer:
No.
Step-by-step explanation:
hope u got it.........
Multiply.
1/6⋅3/4
Express your answer in the simplest form.
A.310
B.18
C.16
D.410
Answer:
none of the above
Step-by-step explanation:
the answer is less than 1, maybe you got the question wrong?
