Answers
Answer:
[tex]\displaystyle \frac{dS}{dt}=\frac{3}{50r}[/tex]
Step-by-step explanation:
Water is being pumped into an inflated rubber sphere at a constant rate of 0.03 cubic meters per second.
So, dV/dt = 0.03.
We want to show that dS/dt is directly proportional to 1/r.
In other words, we want to establish the relationship that dS/dt = k(1/r), where k is some constant.
First, the volume of a sphere V is given by:
[tex]\displaystyle V=\frac{4}{3}\pi r^3[/tex]
Therefore:
[tex]\displaystyle \frac{dV}{dt}=4\pi r^2\frac{dr}{dt}[/tex]
Next, the surface area of a sphere S is given by:
[tex]\displaystyle S=4\pi r^2[/tex]
Therefore:
[tex]\displaystyle \frac{dS}{dt}=8\pi r\frac{dr}{dt}[/tex]
We can divide both sides by 2:
[tex]\displaystyle \frac{1}{2}\frac{dS}{dt}=4\pi r\frac{dr}{dt}[/tex]
We can substitute this into dV/dt. Rewriting:
[tex]\displaystyle \frac{dV}{dt}=r\Big(4\pi r\frac{dr}{dt}\Big)[/tex]
So:
[tex]\displaystyle \frac{dV}{dt}=\frac{1}{2}r\frac{dS}{dt}[/tex]
Since dV/dt = 0.03 or 3/100:
[tex]\displaystyle \frac{3}{100}=\frac{1}{2}r\frac{dS}{dt}[/tex]
Therefore:
[tex]\displaystyle \frac{dS}{dt}=\frac{3}{50r}=\frac{3}{50}\Big(\frac{1}{r}\Big)[/tex]
Where k = 3/50.
And we have shown that dS/dt is directly proportional to 1/r.
Related Questions
What is the measurement of ABC?
Answers
Answer:
118°
Step-by-step explanation:
because 28 + 90 = 118
A TV has a length of 68 inches and a height of 51
inches. When TV's are advertised the size listed is the
diagonal length. What would be the advertised size of
this TV?
Answers
Answer:
85 inches
Step-by-step explanation:
Using pythag. A^2 + B^2 = C^2
(68*68) + (51*51) = 7225^2
Thus if you square root 7225, you get your answer - 85 inches.
Pls help I rlly appreciate
Answers
Answer:
38.9%
Step-by-step explanation:
a=28
b=77
c=33
d=56
e=72
a/e=.388888888
10. A bag contains 4 red, 7 blue, 8 green, and 5 white marbles. What is the theoretical
probability that a randomly selected marble is green?
O
a 1
3
Ob.
2
c. 1
6
Answers
Answer:
C. 1
Step-by-step explanation:
C. 1
Solve for x in the equation x2 +11x+121/4=125/4
Answers
Answer:
x= −11 2 + 5 2 √5 or x= −11 2 + −5 2 5
Step-by-step explanation:
Answer:
D on edg
Step-by-step explanation:
in the following diagram find x
Answers
Answer:
⚠︎ 65 IS YOUR ANSWER!Step-by-step explanation:
180-50 = 130
130 / 2= 65
Answer:
x=65
Step-by-step explanation:
you can set up a equation
50 + x+x =180 = 50 + 2x =180
then minus the 50
2x= 130 and the divide by 2
x=65
Sam needs 7 1/2 cups of orange juice to make punch for a group of her friends. She only has 5 1/3 cups. Write and solve an equation to represent how many more cups of orange juice Sam needs
Answers
Answer:
Equation is [tex]x+\frac{16}{3}=\frac{15}{2}[/tex] where [tex]x[/tex] denotes number of cups of orange juice needed by Sam.
[tex]x=\frac{13}{6}[/tex]
Step-by-step explanation:
Let [tex]x[/tex] denotes number of cups of orange juice needed by Sam.
Number of cups needed to make punch [tex]=7\frac{1}{2} =\frac{15}{2}[/tex]
Number of cups with Sam [tex]=5\frac{1}{3}=\frac{16}{3}[/tex]
Therefore,
[tex]x+\frac{16}{3}=\frac{15}{2}\\\\x= \frac{15}{2}-\frac{16}{3}\\\\x=\frac{45-32}{6}\\\\x=\frac{13}{6}[/tex]
Four circles of radius 3 are arranged as shown. Their centers are the vertices of a square. The area of the shaded region is closest to:
A. 7.7
B. 12.1
C. 17.2
D. 18
E. 27
Answers
Answer:
Its A, 7.7
Step-by-step explanation:
if are is 24cm² find the x
Answers
Answer:
[tex]x = 6[/tex]
Explanation:
Given:
[tex]Area = 24cm^2[/tex]
See attachment for shape
Required
Find x
The attached shape is a rectangle.
So:
[tex]x * 4 = 24[/tex]
[tex]4x = 24[/tex]
Divide both sides by 4
[tex]\frac{4x}{4} = \frac{24}{4}[/tex]
[tex]x = \frac{24}{4}[/tex]
[tex]x = 6[/tex]
The perimeter Of a rectangle is 30 inches if it’s Lance is three times it’s width find the dimensions.
Answers
Answer:
Width: 3.75
Length: 11.25
Answer:
the width is 3.75 inches. The length will be 3*3.75=11.25 inches.
Step-by-step explanation:
30 inches=2(L+W) Divide each side by 2. 15 inches=L+W Substitute for L.
what is the simplest from of this expression? (-3x^2 + 4x) + (2x^2 - x -11)
A. -x^2 + 3x + 11
B. -x^2 + 5x - 11
C. -x^2 + 5x + 11
D. -x^2 + 3x - 11
Answers
Answer:
D
Step-by-step explanation:
Plz help me plz
Also phone reval XD
Answers
Answer:
5.50
Step-by-step explanation:
5 = whole number
.
5 = Tenths
0 = Hundreths
5.50
Hope this Helps!I really need help on this problem its on khan academy 27÷(−9)=?
Answers
Answer: -3
Step-by-step explanation:
[tex]\frac{27}{-9} = -3 \\[/tex]
We can check our work my multiplying -3 by -9 and see that it equals 27
[tex]-9*[\frac{27}{-9} = -3 ]* -9\\27 = 27[/tex]
A car is parked 80 feet from the base of a 120-foot building. What is the angle of depression from the top of the building to the car? Round your answer to the nearest degree.
A 48° degrees
B 34° degrees
C 42° degrees
D 56° degrees
Answers
please help due tomorrow
Answers
Answer:
We need to solve this system of equations by substitution:
-6x-2y =20
3y=x
Yu can do it with the letter you decide
You can get the x from the second equation and replace in the first:
3y = x
-6x - 2y = 20 -> -6(3y) - 2y = 20 --> -18y - 2y = 20 --> y=-1
Then we can replace in the second one:
3*(-1) = x ---> -3 = x
So the answer is x = -3, y = -1
Solved by substitution method:
I need help with this question
Answers
Answer:
12
Step-by-step explanation:
12 x 10 = 120
12
b. The highest factor that they have in common is 15.
how can you represent all of the solutions to systems of inequalities?
Answers
Answer:A closed, or shaded, circle is used to represent the inequalities greater than or equal to (≥) or less than or equal to (≤) . The point is part of the solution. An open circle is used for greater than (>) or less than (<). The point is not part of the solution. Solving" systems of linear inequalities means "graphing each individual inequality, and then finding the overlaps of the various solutions". So I graph each inequality, and then find the overlapping portions of the solution regions.Step 1: Line up the equations so that the variables are lined up vertically. Step 2: Choose the easiest variable to eliminate and multiply both equations by different numbers so that the coefficients of that variable are the same. Step 3: Subtract the two equations. Step 4: Solve the one variable system.
Step-by-step explanation:
hope this helps have a great night ❤️❤️❤️
Find the length of side AB.
Give your answer to 1 decimal place.
CB = 12 cm
AB = 62°
PLEASE HELP!!
Answers
Answer:
AB ≈ 5.6 cm
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos62° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{AB}{12}[/tex] ( multiply both sides by 12 )
12 × cos62° = AB , then
AB ≈ 5.6 cm ( to 1 dec. place )
Brett has a 30 year fixed rate mortgage for $112500 with monthly payments of $603.92. The annual interest rate is 5% what is the total cost of the principal and interest for this not rounded to the nearest dollar
Answers
Answer:
a. Total cost of the principal = $217,411.20
b. Interest for the mortgage loan = $104,911.20
Step-by-step explanation:
Total cost of the principal = Monthly payment * Number of years * Number of months in a year = $603.92 * 30 * 12 = $217,411.20
Total cost of the principal of the loan includes the mortgage loan amount and the interest for the mortgage loan. Therefore, the interest for the mortgage loan can be calculated as follows:
Interest for the mortgage loan = Total cost of the principal - Mortgage loan amount = $217,411.20 - $112,500 = $104,911.20
A family of 10 that all leave the house at the same time each morning has two bathrooms. They must share for everyone to be ready. Time is allotted to each family based on age. Is this apportionment or not apportionment?
Answers
Answer:
Not apportionment
Step-by-step explanation:
Apportionment can be described as a way of sharing out or dividing out in the best fair method.
If a family of 10 leave the house at the same time and have to share just two bathrooms, the time allocation should not be based on age rather should be based on how early each person wakes up in the morning.
Pls answer quick I will give brainliest
Answers
Answer:
EBC and CBF are supplementary.
EBD=66
Step-by-step explanation:
Since vertical angles are congruent, ABE=CBF
ABE=40-x
40-x + 6x-30=90
5x+10=90
5x=80
x=16
16(6)-30=66
what is 4 and 1/2 in decimal form
Answers
Answer:
4.50
Step-by-step explanation:
4 = Whole number. 1 = Numerator. 2 = Denominator. To get 4 1/2 in decimal form, we basically convert the mixed number to a fraction and then we divide the numerator of the fraction by the denominator of the fraction.
The decimal form of 4 and 1/2 is 4.5
DecimalDecimal is a fraction written in a unique form. The dot notation is used to represent the fraction form.
Therefore, 4 and 1/2 in decimal form is represented as follows;
Mixed fraction = 4 1 / 2
Improper fraction = 9 / 2
decimal form of 1 / 2 = 0.5
Therefore, 4 1 / 2 = 4.5
learn more on decimal here: https://brainly.com/question/236928
Please help!!!! The roots of x^2-2x-2=0 are A.1+square root of 3 B.1+square root of 12 or C.No real roots
Answers
Answer:
A
Step-by-step explanation:
We have the equation:
[tex]x^2-2x-2=0[/tex]
We can use the quadratic formula. In this case, a = 1, b = -2, and c = -2. Hence:
[tex]\displaystyle x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-2)}}{2(1)}[/tex]
Evaluate:
[tex]\displaystyle x=\frac{2\pm\sqrt{12}}{2}[/tex]
Simplify:
[tex]\sqrt{12}=\sqrt{4}\cdot\sqrt{3}=2\sqrt{3}[/tex]
Hence:
[tex]\displaystyle x=\frac{2\pm2\sqrt{3}}{2}[/tex]
Divide:
[tex]x=1\pm\sqrt3[/tex]
The correct answer is A.
Who is a fan of baby Yoda/Grogu lol sorry about the spoiler alert!
Answers
Answer:
It's not really a spoiler but I like baby yoda
Answer:
I think Baby Yoda is adorable u.u
evaluate each expression if m = 13 and n = 8
1.) 2m - n
2.) 3m + 2n
3.) 12 + 3 x m - n
4.)
Answers
26-8
=18
2. 3(13)+2(8)
39+16
=55
3. 12+3x13-8
12+39-8
51-8
=43
4 is blank
Hope this helps
Answer:
1.) 18
2.) 55
3.)43
Step-by-step explanation:
10. A line with a negative slope and a negative
y-intercept is graphed on a coordinate
plane. Which quadrant will the line not pass
through? Justify your response.
Answers
Answer:
The line will not pass through the first quadrant.
Step-by-step explanation:
Since the y-intercept is negative, and the slope is negative, the line will start in the second quadrant, pass through the third quadrant to intercept the y-axis, then pass through the fourth quadrant. It will never touch the first quadrant.
Carlos has read 45% of his book. If his book has 480 pages, how many pages did he read? *
Answers
How many solutions does the equation have? -10(x - 1) = 10 - 10x *
O Zero Solutions
O 1 Solution
O Infinite Solutions
Answers
Answer:
infinite
Step-by-step explanation:
it results in 10-10x=10-10x if you simplify
can also be simplified more into x=x
but we already know x has to equal x.
14. AMKL is an isosceles triangle with MK ML.If MK = 7x - 15, KL = 4x - 6, and ML = 10X - 12, find x and the measure of each side.
Answers
Answer:
You can do it! Sorry i can't help because your on a different level. Try your best!
Step-by-step explanation:
Plz help!!
What is the value of x when f(x)=20? What does this mean in context?
Answers
Answer:
It means that x = 20
Step-by-step explanation: