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
10. What is the length of s?
I
450
Answers
If x + 3 = 13, then the value of 5x – 74 is
Answers
Answer:
-24
Step-by-step explanation:
We are given two equations and are asked to solve if one equals a certain amount to the other.
Let's focus on x + 3 = 13, we need to first figure out what is x. Which is very simple, what plus 3 equals 13?
10 of course, therefore x = 10, and we can implement into the other equation.
5x - 74
Since x = 10, we can substitute x with 10 and then multiply.
5(10) - 74
50 - 74
What is 50 - 74?
-24
An urn contains 3 red and 5 orange marbles. 2 marbles are selected without replacement. Find the probability that the second marble selected is orange given that the first marble selected is orange.
Answers
Answer: [tex]\dfrac{5}{14}[/tex]
Step-by-step explanation:
Given: An urn contains 3 red and 5 orange marbles.
Total marbles = 3+5=8
Probability of getting orange marble = [tex]\dfrac{\text{Number of orange marble}}{\text{Total}}[/tex]
[tex]=\dfrac{5}{8}[/tex]
Now marbles left = 7
Orange marbles left = 4
and Probability of getting orange marble = [tex]\dfrac47[/tex]
The probability that the second marble selected is orange given that the first marble selected is orange[tex]=\dfrac58\times\dfrac47=\dfrac{5}{2}\times\dfrac17=\dfrac{5}{14}[/tex]
Required probability= [tex]\dfrac{5}{14}[/tex]
Let f(x) = x2 + 3
Find f(2)
f(2)=
Answers
Answer:
7
Step-by-step explanation:
f(2) = 2^2 +3
=4+3
=7
You substitute 2 for the x and then just solve the equation by multiplying first and then adding.
In QRS q=9.6 inches r=9.9 inches and S=92 Find the length of a to the nearest 10th of an inch
Answers
Answer:
14
Step-by-step explanation:
delta math gave me the answer
The length of a to the nearest 10th of an inch is 13.6 inches.
What is Trigonometry?One area of mathematics known as trigonometry examines the relationship between the sides and angles of a right triangle. The relationship between sides and angles is defined for 6 trigonometric functions.
We have,
In ΔQRS q=9.6 inches r=9.9 inches and S=92.
So, s² = q² + r² - 2qr cos s
s² = 9.6² + 9.9² + 2(9.6)(9.9) cos 92.
s² = 190.71 + 190.08 x (-0.035)
s² = 183.52
s = 13.55
s = 13.6 inches
Learn more about Trigonometry here:
https://brainly.com/question/29002217
#SPJ5
Select the answer choice that correctly describes the graph (on a number line) of the inequality: h > 7
Group of answer choices
closed circle at 7 with an arrow pointing left
open circle at 7 with an arrow pointing left
open circle at 7 with an arrow pointing right
closed circle at 7 with an arrow pointing right
Answers
Close circle at 7 with an arrow pointing
right.
hope it helps
You make a profit of $2 for each baked good (b) you sell in your fundraiser. Which
equation could help you determine how many you need to sell to earn your goal
of $950? *
How many baked goods do you need to sell to meet your goal
Answers
Answer:
an equation to find it could look like:
950=2x
you need 425 sold baked goods to reach your goal
Step-by-step explanation:
how do I explain?
Answer:
1. 2x = 950
2. you will need 475 baked goods to meet your goal.
Step-by-step explanation:
Enter the ordered pair for the vertices for 180°,0)(QRST).
Q
o
S
IR
O Q' = (-1,-3) R' = (-3,3 ) S'= (0,2)T' =(2, -1)
OQ' = (-1,3) R' = (-3,-3) S'=(0, -2)T' =(2, 1)
Q' = (1, -3) R' =(3,3) S' = (0,2)T' = (-2,-1)
Answers
Answer:
The ordered pair for the vertices for r₍₁₈₀ ₀₎(QRST), is given as follows;
Q' = (-1, -3) R' = (-3, 3) S' = (0, 2) T' = (2, -1)
Step-by-step explanation:
The coordinates of he vertices of the triangle QRST are;
Q(1, 3), R(3, -3), S(0, -2), T(-2, 1)
A rotation of a point with coordinates (x, y) 180° about the origin gives;
The coordinate of the point of the preimage before the rotation = (x, y)
The coordinate of the point of the image after the rotation = (-x, -y)
Therefore we have;
The image of point Q(1, 3) after 180° rotation = Q'(-1, -3)
The image of point R(3, -3) after 180° rotation = R'(-3, 3)
The image of point S(0, -2) after 180° rotation = S'(0, 2)
The image of point T(-2, 1) after 180° rotation = T'(2, -1)
The ordered pair for the vertices for r₍₁₈₀ ₀₎(QRST), is therefore, Q'(-1, -3), R'(-3, 3), S'(0, 2), and T'(2, -1);
Q' = (-1, -3) R' = (-3, 3) S' = (0, 2) T' = (2, -1).
Need help ASAP Geometry
Answers
Answer:
Step-by-step explanation:
5x-1 is twice the bisector angle 4x-17 so
5x-1=2(4x-17)
5x-1=8x-34
-3x=-33
x=11, abc=5x-1
5(11)-1=54
A function is given:
f(x) = 3x + 12
a. Determine the inverse of this function and name it g(x).
b. Use composite functions to show that these functions are inverses.
c. Evaluate f(g(–2)). Explain: What is the domain?
Answers
Answer:
See explanations below
Step-by-step explanation:
Given the function
f(x) = 3x+12
Let y = f(x)
y = 3x+12
Replace y with x
x = 3y+12
Make y the subject
3y = x-12
y = (x-12)/3
Hence the required inverse is!
g(x) = (x-12)/3
b) To show that the functions are inverses, we must show that f(g(x)) = g(f(x))
f(g(x)) = f((x-12)/3)
Replace x in f(x) with x-12/3
f(g(x)) = 3(x-12)/3 +12
f(g(x)) = x-12+12
f(g(x)) = x
Similarly for g(f(x))
g(f(x)) = g(3x+12)
g(f(x)) = (3x+12-12)/3
g(f(x)) = 3x/3
g(f(x)) = x
Since f(g(x)) = g(f(x)) = x, hence they are inverses of each other
c) Given f(g(x)) = x
f(g(–2)) = -2
The domain is the input variable of the function. Hence the domain is -2
2
X. - 144
(Type your answer in factor
Answers
Answer:
(x+12) (x-12)
Step-by-step explanation:
12x12=144
A ride in a taxi costs a flat rate of $4.25 and $1.75 per mile.
If my bill was $14.75, how many miles did I ride?
Answers
Answer:
6
Step-by-step explanation:
take 14.75 and minus the flat rate of 4.25 and then divide the 1.75 per mile and you get that you rode 6 miles
Directions: Tell whether the following are characteristics of stocks or bonds. Write stock or
bond
1. A form of equity financing or raising money by allowing investors to be part owners of
the company.
2. It can be appropriate for retirees or for those who need the money soon
3. Investors can earn if the security prices increase, but they can loose money if the
security prices decrease or worse if the company goes bankrupt.
4. A form of debt financing or raising money by borrowing from investors
5. Investors are guaranteed interest payments and a return of their money at the maturity
date
Answers
Answer:
I need help with my question. can someone help me
¿Están los números 89 y 144 en relación
áurea?
a. No porque su producto es 12816.
b. No porque su cociente es 0,5.
c. Si porque su diferencia es 55.
d. Si porque su cociente es 0,618...
Answers
Answer:
b. No porque su cociente es 0,5.
Can somebody please only answer this if u know the answer im very low on points thank you!
Answers
Answer + Explanation:
Find the coordinates of each point and multiply it by 4:
J (1, 4) --> J' (4, 16)
K (6, 4) --> K' (24, 16)
L (6, 1) --> L' (24, 4)
M (1, 1) --> M' (4, 4)
The yearbook club had a meeting. The meeting had 24 people, which is three-fourths of the club. How many people are in the club?
Answers
Answer:
32
Brainiest plz? :)
help me with this answer please !
Answers
Answer:
pick number 3 I think that's the one
Which function is shown on the graph?
A. f(x)=1/2cos x
B. f(x)=1/2sin x
C. f(x)=-1/2cos x
D. f(x)=-1/2sin x
Answers
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
I took the test
Ajani's mother baked 5 peanut butter cookies for every 7 chocolate chip cookies she baked. If she made a total of 96 cookies, how many were peanut butter cookies?
Answers
Answer:
5+7=12
96/12=8
5*8=40 cookies
Step-by-step explanation:
What is the value of y?
72°
A. 1080
B. 540
C. 36°
D. 720
Answers
Answer:
B. 54
Explanation:
Take 72 from 180.
180 - 72 = 108.
Since there are two y's AND they're congruent, divide 108 by two and get 54.
B. 54
Explanation:
180 - 72 = 108
108 / 2 = 54
Please answer this and show your work!:)
Answers
4b = 28
b = 7
Answer:
Hope this helps
Step-by-step explanation:
Evaluate h(16) for the function h(x) = -|x/-4|
Answers
Answer: h(16)=-4
Step-by-step explanation:
Given
h(x)=-|x/-4|
Substitute the value into the function
h(x)=-|x/-4|
h(16)=-|(16)/-4|
h(16)=-|-4|
h(16)=-4
Hope this helps!! :)
Please let me know if you have any questions
Find the product of (x − 8)2 and explain how it demonstrates the closure property of multiplication.
A. x2 − 64; is a polynomial
B. x2 − 16x + 64; is a polynomial
C. x2 − 64; may or may not be a polynomial
D. x2 − 16x + 64; may or may not be a polynomial
Answers
Answer:
B
Step-by-step explanation:
(x-8)^2=(x-8)(x-8)=x^2-8x-8x+64=x^2-16x+64
Answer:
x2 − 16x + 64; is a polynomial
x^2+4y^2=36 the lenght of the major axis is?
Answers
Answer:
Step-by-step explanation:
x² + 4y² = 36
divide by constant
x²/36 + y²/9 = 1
x²/6² + y²/3² = 1
6>3, so length of major axis is 2×6 = 12
si un costal de azúcar contiene 61.5Kg ¿cuántos paquetes de 0.750Kg se pueden llenar?
Answers
Answer:
Cantidad total = 82 Paquetes
Step-by-step explanation:
Dados los siguientes parámetros;
Cantidad de azucar = 61.5kg
Tamaño de cada paquete = 0.75kg
Para encontrar la cantidad total de paquetes;
[tex] Cantidad \; total = \frac {Cantidad}{Tamano \; de \; cada \; paquete} [/tex]
[tex] Cantidad \; total = \frac {61.5}{0.75} [/tex]
Cantidad total = 82 Paquetes.
Por lo tanto, se pueden llenar 82 paquetes de azúcar.
Stephanie has 7/8 pounds of bird seed she used 3/8 pound to fill a a bird feeder how munch bird seed does Stephanie have left
Answers
Answer:
1/2 is your answer = 4/8 because 7/8 - 3/8 = 4/8 = 1/2.
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
7/8 - 3/8 = 4/8
4/8 = 1/2
Divide P. 80.00 people so that the second will have twice as much as the first and the third will have P. 5.00 less than the second. how much the first, second and third person gets?
Answers
Answer:
first collects 17, second 34 and third 29
Step-by-step explanation:
Total amount to be shared = 80.00
If first person received x
second received y
Third received z
If the second will have twice as much as the first, then;
y = 2x
x = y/2
If the third will have P. 5.00 less than the second, then
z = y-5
y = z+5
Substitute both equation in original equation
x+y+z = 80
y/2 + y + y-5 = 80
y + 2y + 2y -10 = 160
5y = 160+10
5y = 170
y = 170/5
y = 34
x = y/2
x = 34/2
x = 17
z = y - 5
z = 34-5
z = 29
Hence the first collects 17, second 34 and third 29
please help me ASAP this is very important explain for brainlist.
Answers
Answer:
A= 320 in^2
Step-by-step explanation:
A = 1/2 (d1)(d2)
A = 1/2(20)(32)
A= 320 in^2
When using the distributive property, the expression
3(2x - 1) would be simplified to
Answers
Answer:
[tex]6x - 3[/tex]
Step-by-step explanation:
consider downloading photomath
please help me
Which measurements could create more than one triangle?
A. A triangle with sides measuring 5 cm and 10 cm and an included angle measuring 40°
B. A triangle with sides measuring 4 inches, 8 inches, and 15 inches
C. A triangle with sides measuring 6 inches, 8 inches, and 10 inches
D. A triangle with angles measuring 75°, 60°, and 45°
Answers
Answer:
your answer is up there
Step-by-step explanation:
Sorry for not being some help i really am Red Riot out