Answer:
18
Step-by-step explanation:
Suppose the temperature inside a three dimensional ball is proportional to the square root of the distance from the center. Find a formula for the average temperature in the ball. What is the limit of the average temperature as the ball gets larger?
Answer:
The formula for the average temperature in the ball is [tex]\bar T = \frac{2\cdot k\cdot R^{1/2}}{3}[/tex]. The limit of the average temperature for the ball does not exist.
Step-by-step explanation:
According to the statement, we have the following direct relationship:
[tex]T \propto \sqrt{r}[/tex]
[tex]T = k\cdot \sqrt{r}[/tex] (1)
Where:
[tex]T[/tex] - Temperature, measured in degrees Celsius.
[tex]r[/tex] - Distance from the center, measured in meters.
[tex]k[/tex] - Proportionality constant, measured in degrees Celsius per meter.
Under the assumption that ball is a continuous entity, we find that average temperature in the ball ([tex]\bar T[/tex]), measured in degrees Celsius, is represented by the following integral equation:
[tex]\bar T = \frac{1}{R}\cdot \int\limits^{R}_{0} {T(r)} \, dr[/tex] (2)
By applying (1) in (2), we find that:
[tex]\bar T = \frac{k}{R}\cdot \int\limits^{R}_{0} {\sqrt{r}} \, dr[/tex]
[tex]\bar T = \frac{2\cdot k}{3\cdot R}\cdot (R^{3/2})[/tex]
[tex]\bar T = \frac{2\cdot k\cdot R^{1/2}}{3}[/tex]
If the ball gets larger, then the limits associated to the average temperature diverges to the infinity as maximum exponent of the numerator of the rational function ([tex]n = \frac{1}{2}[/tex]) is greater than the maximum exponent of the denominator ([tex]n = 0[/tex]). Therefore, the limit of the average temperature for the ball does not exist.
When 10 gallons are removed from a tank, which is 5/8 full, the tank is completely emptied. How many gallons are now needed to fill this tank?
Help me out here pleaseeeeeeee
Answer:
1 5/8
Step-by-step explanation:
15/8 = 1 7/8
In the expression " 5.3t - (20÷4) + 11" what part is a quotient? Describe its parts.
Answer:
(20 divided by 4) is the quotient
Step-by-step explanation:
In the expression the quotient part is 20÷4 and the quotient is 5.
The given expression is 5.3t - (20÷4) + 11.
What is a quotient?In arithmetic, a quotient is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division, or as a fraction or a ratio.
In the given expression 5.3t - (20÷4) + 11,
20÷4=5
So, 5.3t - 5 + 11
5.3t + 6
Hence, in the expression the quotient part is 20÷4 and the quotient is 5.
Learn more about the quotient here:
https://brainly.com/question/16134410.
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PLEASE HELP ASAP!!!!!
Answer: for number six its y=2x-2
Noise levels at 3 airports were measured in decibels yielding the following data:
108,146,160
Required:
a. Construct the 90% confidence interval for the mean noise level at such locations. Assume the population is approximately normal.
b. Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
a) The 90% confidence interval for the mean noise level at such locations
(112.46 , 163.54)
b) The critical value that should be used in constructing the confidence interval
Z₀.₁₀ = 1.645
Step-by-step explanation:
Step(i) :-
Noise levels at 3 airports were measured in decibels yielding the following data
108 146 160
Mean of given data
[tex]x^{-} = \frac{108+146+160}{3} = 138[/tex]
x : 108 146 160
x-x⁻ : -30 8 22
(x-x⁻ )² : 900 64 484
Variance σ ² = ∑(x-x⁻ )²/ n-1
= [tex]\frac{900+64+484}{3-1}= 724[/tex]
Standard deviation
σ = √724 = 26.90
Step(ii):-
The 90% confidence interval for the mean noise level at such locations
[tex](x^{-} - Z_{0.90} \frac{S.D}{\sqrt{n} } , (x^{-} + Z_{0.90} \frac{S.D}{\sqrt{n} } )[/tex]
The critical value that should be used in constructing the confidence interval
Z₀.₁₀ = 1.645
[tex](138 - 1.645 \frac{26.90}{\sqrt{3} } , (138 + 1.645 \frac{26.90}{\sqrt{3} } )[/tex]
( 138 - 25.54 , 138 + 25.54 )
(112.46 , 163.54)
What is the value of the expression below?
6 + 5 (9 ÷ 3)²
Answer:
51
Step-by-step explanation:
follow pemdas
Will give brainliest to whoever replies with the correct answer. (Question is in the image)
Answer:x = 7
Step-by-step explanation:
Similar figures have sides that are proportional. Setting up a proportion for the sides of the figures will help solve for 'x':
Cross-multiply: 3(x + 1) = 6(x - 3)
Distribute: 3x + 3 = 6x - 18
Combine like terms: 21 = 3x
Solve for 'x': x = 7
How many 3/5 inch snicker bar are in 3 inches of snickers bars.
Answer:
there is 5 inches
Step-by-step explanation:
3/5= 5
How much would a 110 commercial coast
Answer:
Real Estate listings for Sale on the #1 commercial real estate ... $7,500,000; 1 Commercial Lot; 110 AC Lot ... If you are a Palm Coast commercial real estate broker or building owner with a ... If you continue to see this message, your account may be locked due to too many failed attempts.
Step-by-step explanation:
Jessica has a four-sided die, a six-sided die, and a 12-sided die. She rolls the three dice once. Let Z be the number of fours showing. Find E[Z] using the indicator method.
Answer:
The value of E [Z] is 0.50.
Step-by-step explanation:
The expected value is computed using the formula:
[tex]E(X)=\sum x\cdot P(X= x)[/tex]
Denote the three dices as follows:
X₁ = a four-sided die
X₂ = a six-sided die
X₃ = a 12-sided die
Define the indicator variables as follows:
[tex]I_{1}=\left \{ {{1;\ X_{1}=4} \atop {0;\ X_{1}\neq 4}} \right. \\\\I_{2}=\left \{ {{1;\ X_{2}=4} \atop {0;\ X_{2}\neq 4}} \right. \\\\I_{3}=\left \{ {{1;\ X_{3}=4} \atop {0;\ X_{3}\neq 4}} \right.[/tex]
The probability of rolling a 4 in the three dices are as follows:
[tex]P(X_{1}=4)=\frac{1}{4}\\\\P(X_{2}=4)=\frac{1}{6}\\\\P(X_{3}=4)=\frac{1}{12}[/tex]
Compute the value of E [Z] as follows:
[tex]E(Z)=E(I_{1})+E(I_{2})+E(I_{3})[/tex]
[tex]=(1\times\frac{1}{4})+(1\times\frac{1}{6})+(1\times\frac{1}{12})\\\\=\frac{3+2+1}{12}\\\\=\frac{6}{12}\\\\=\frac{1}{2}\\\\=0.50[/tex]
Thus, the value of E [Z] is 0.50.
.4.f(6)-6.g(5)= ????
Answer:
24f - 30g
Step-by-step explanation:
I'm not sure if that's how you're supposed to answer it...
Sonia uses a gift card to purchase a $5.87 gourmet coffee each week. Find the total change in the gift card balance after 3 weeks.
Answer:
$17.61
Step-by-step explanation:
5.87 x 3= $17.61 because it is each week
Answer: 17.61 dollars
Step-by-step explanation:
What is the diameter of a circle if the area is 326.9
Answer:
20.4
Step-by-step explanation:
Answer:
20.4 would be the diameter :)
Step-by-step explanation:
mark brainliest?
Melissa’s paycheck last week was $125.52. She would like to put 20% of her earnings in her savings account. How much money should she put in her savings account?
Answer:
Step-by-step explanation:
125.52*20%= $25.10
8. 360 jelly beans were in a jar. 40 of
them were red. If you pick 18, how
many of those should be red?
Answer:
2 jelly beans were red
Step-by-step explanation:
40/360=20/180=10/90=(divide 5)2/18=1/9-simplifying
1/9/0.1111111111111111111
1/9 times 18 =2,
.06 is 10 times as much as
Answer:
0.006
Step-by-step explanation:
write 5 8/100 as a decimal
Answer: 5.08
Step-by-step explanation: you have to convert it to an improper fraction
-2 1/4 divide by {-3 1/3}
Write −0.35 as a fraction in simplest form.
Answer:It equals -7/20 because Here's how to convert 0.35 to a fraction...There is not much that can be done to figure out how to write 0.35 as a fraction, except to literally use what the decimal portion of your number, the .35, means. Since there are 2 digits in 35, the very last digit is the "100th" decimal place. So we can just say that .35 is the same as -35/100. The fraction -35/100 is not reduced to lowest terms. We can reduce this fraction to lowest terms by dividing both the numerator and denominator by 5. Why divide by 5? 5 is the Greatest Common Divisor (GCD) or Greatest Common Factor (GCF) of the numbers 35 and 100. So, this fraction reduced to lowest terms is -7/20. So your final answer is: 0.35 can be written as the fraction -7/20 Hope this helps... Plz mark me brainliest if the answer is correct... Stay safe and have a great weekend!!! :D
Step-by-step explanation:
The simplest fraction form id the number -35 is -7/100.
To write -0.35 as a fraction in simplest form, we need to convert the decimal number into a fraction.
Count the number of decimal places. In this case, we have two decimal places.
Write the decimal as a fraction with the denominator as a power of 10. Since we have two decimal places, the denominator will be 10^2, which is 100.
Place the decimal number over the denominator. In this case, -0.35/100.
Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF). In this case, the GCF of 35 and 100 is 5.
Dividing both the numerator and denominator by 5,
-0.35/100 = -35/500
Further simplify the fraction if possible. In this case, we can divide both the numerator and denominator by 5 again:
-35/500 = -7/100
So, -0.35 as a fraction in simplest form is -7/100.
To know more about fractions follow
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What ratios arr proportional..?
3/4: 4/8
3/4:6/8
3/4:7/8
Answer:
the 3/4:6/8. Hope that helped
what does 23884 times 3457387 make
Answer:
Your answer should be the following ; 23884*3457387 = 82576231108
So, 82576231108.
Step-by-step explanation:
Jill wrote the number 66 If her rule is add 9,what is the fourth number in jills pattern
Answer:
102
Explanation: 66+36 (9 times 4 is 36 and u add it to the 66 because u have to add 9 four times.)
self check
66+9= 75 (1st slot)
75+9=84 (2nd slot)
84+9= 93 (3rd slot)
93+9= 102 (4th and final slot, what u were looking for to begin with)
def~=jkl and de =x^3-3x, kj=28,m
Select all that apply.
Which decimals in the list are repeating decimals?
03101 | 0166
4
1.000
3
OK NOW I NEED HELP ASAP
Don't get mad at me for at least trying to help because i also have no idea
Step-by-step explanation:
which is bigger 2.35 or 2.346 decimals
Answer:
2.35
Step-by-step explanation:
bruh
Answer:
2.35 is larger.
Step-by-step explanation:
Plug in a zero at the end of 2.35 and you'll be able to see that it's is bigger than 2.346.
Caesar finished 12 problems in
20 minutes. At that rate, how many problems
can he do in 60 minutes?
A boat travels 3 miles south and then 9 miles east. How far is the boat from the starting point
A line segment AB has the coordinates A (2,3) AND B ( 8,11) . What is the slope of AB?
Answer:
4/3
Step-by-step explanation:
11 - 3 = 8
8 - 2 = 6
8/6 = 4/3
Rise 4 Run 3