A spherical balloon is inflating with helium at a rate of 64π ft/min. How fast is the balloon's radius increasing at the instant the radius is 2 ft? How fast is the surface area increasing?
The balloon's radius is increasing at a rate of...
Answers
Answer:
let r ,v be the radius and volume of sphere.
dv/dt=64πft³/min
r=2ft
Dr/dt=?
Step-by-step explanation:
we have
volume of sphere=4/3πr²
v=4/3πr²
differentiating both side with respect to t we get
dv/dt=4πdr²/dr×dr/dt=4π×2r×dr/dt=8/3×πr×dr/dt
substituting the given value we get
dv/dt=8/3×πr×dr/DT
64π×3/(8π×2)=dr/dt
Dr/dt=12ft/min
The balloon's radius is increasing at a rate of12 ft/min
The balloon's radius increasing at the instant the radius is 2 ft will be 10106.47 ft³ per minute.
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
A spherical balloon is inflating with helium at a rate of 64π ft/min.
dr/dt = 64π ft/min
Then the balloon's radius increasing at the instant the radius is 2 ft will be
V = (4/3)πr³
Differentiate with respect to time. Then we have
[tex]\rm V' = \dfrac{dV}{dt} \\\\ V' = \dfrac{4}{3}\cdot \pi 3r^2 \cdot \dfrac{dr}{dt}[/tex]
Simplify the equation, then we have
V' = 4πr² × 64π
V' = 4π × (2)² × 64π
V' = 10106.47 ft³ per minute
The balloon's radius increasing at the instant the radius is 2 ft will be 10106.47 ft³ per minute.
More about the differentiation link is given below.
https://brainly.com/question/24062595
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Related Questions
7g + 4g + 3g − 13g + g = 10 please help!!
Answers
7g + 4g + 3g + g = 15g
15g - 13g = 2g
2g = 10
Divide by 2 on both sides.
g = 5
Answer: g=5
Step-by-step explanation:
Given
7g+4g+3g-13g+g=10
Combine like terms
2g=10
Divide 2 on both sides
2g/2=10/2
g=5
Hope this helps!! :)
Please let me know if you have any questions
2.25(p − 10) − 11 = 2.5
solve for p
Answers
Answer:
p=16
Step-by-step explanation:
A workbook is 56 pages long.If each chapter is 8 pages long, how many chapters are there?
Answers
Answer:
7
Step-by-step explanation:
Work book pages: 56
Each Chapter : 8
56/8=7
The figure below shows two triangles on the coordinate grid:
What set of transformations is performed on triangle ABC to form triangle A′B′C′? (5 points)
Group of answer choices
A translation 5 units down, followed by a 180-degree counterclockwise rotation about the origin
A translation 5 units down, followed by a 270-degree counterclockwise rotation about the origin
A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units down
A 270-degree counterclockwise rotation about the origin, followed by a translation 5 units down
Answers
Answer:
Option AStep-by-step explanation:
A translation 5 units down, followed by a 180-degree counterclockwise rotation about the origin
CorrectA translation 5 units down, followed by a 270-degree counterclockwise rotation about the origin
Incorrect. It would work with 180-degree rotation.A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units down
Incorrect. It would work with the translation 5 units up.A 270-degree counterclockwise rotation about the origin, followed by a translation 5 units down
Incorrect.The segments in each figure are tangent to the circle at the points shown.
Find each length.
Answers
Answer:
please post the figure then it will be easier to solve the problem
You have purchased a 30-pound case of lemons that has a count size of 96. About how many ounces would each lemon weigh?
Answers
Answer:
I think it would be 3.2 ounces because 96 divided by 30 is 3.2
Step-by-step explanation:
What is the area of the shaded region?
26 km
35 km
Answers
Answer:35/2=17.5*26= ?
Step-by-step explanation:
Need both equations solved with explanation.
Answers
x
x
by cross multiplying.
Exact Form:
x
=
1
2
x
=
1
2
Decimal Form:
x
=
0.5
Subtract and simplify.
3/4 - 11/20=
Answers
Answer:
1/5
Step-by-step explanation:
3/4 = 15/20
15/20 - 11/20 = 4/20
Can be simplified to 1/5
Answer: 3/4 - 11/20 = 1/5 or in decimal form 0.2
PLEASE HELP DUE AT 11:59
Answers
[tex] \frac{2a + b}{3} [/tex]
a=
[tex] \frac{1}{2} [/tex]
b = -4
Answers
Answer:
the value of the equation is -1
write the following number in standard notation (decimal) 3.5 x 10^4
PLS HELP ASAP THIS IS FOR A TEST
Answers
Answer:
35000
Step-by-step explanation:
[tex]3.5 \times {10}^{4} \\ \\ = 3.5 \times 10000 \\ \\ = 35000[/tex]
How do I find the side of a right triangle if I'm given the measures of 2 angles and 1 side?
Answers
Answer:
brain
Step-by-step explanation:
brain to the fullest
Use the drop-down menus to complete each statement.
Table A represents a _______
function.
Table B represents a _______
function.
Table C represents a _______
function.
Answers
Answer:
a:cubic
b:quadratic
c:linear
Step-by-step explanation:
Tables A, B, and C represent cubic, quadratic, and linear functions respectively.
What are functions?Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
In the question, 3 functions in tabulated form is given, we draw the function on the graph then we observe that,
Table A, shows the cubic function because the graph with an increase of x increase and decrease multiple times.
Table B, shows the quadratic function, is shows the curve as of the parabola.
Table C, shows the linear relationship, as it forms a line on the graph.
Thus, tables A, B, and C represent cubic, quadratic, and linear functions respectively.
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2 1/3:4 1/2 write the ratio as a fraction in simplest form
Answers
Answer:
14/27
Step-by-step explanation:
7/3 ÷ 9/2
7/3 x 2/9 = 14/27
The solution set of the equation 3x2+x = 9 is
Answers
Answer:
x=3
Step-by-step explanation:
hope this helps
Convert each to a standard number:
i) 25%
ii) 43.2%
iii) 0.02214%
iv) 2%
Answers
Answer:
a
Step-by-step explanation:
Answer:
i. 1/4
ii. 54/125
iii. 1107/5000000
iv. 1/50
Step-by-step explanation:
i.
25% = 0.25
0.25 = 25/100
25/100 (GCF 25) = 1/4
ii.
43.2% = 0.432
0.432 = 432/1000
432/1000 (GCF 8) = 54/125
iii.
0.02214% = 0.0002214
0.0002214 = 2214/10000000
2214/10000000 (GCF 2) = 1157/5000000
iv.
2% = 0.02
0.02 = 2/100
2/100 (GCF 2) = 1/50
9.
Write a function rule for the table.
A. f(x) = –4x
B. f(x) = 4 – x
C. f(x) = x + 4
D. f(x) = x – 4
Answers
Answer:
B. f(x) = 4 – x
Step-by-step explanation:
Answer:
b. f(x) = 4 -- X Amadodcnfnfkdi
Which relationship describes angles 1 and 2?
Answers
Answer:
Option B is your answer
Step-by-step explanation:
..
find the length of the arc intercepted by a central angle of 1.5 radians in a circle of radius 9 cm.
Answers
Answer:
13.5 cm
Step-by-step explanation:
The length of an arc depends on the radius of a circle and the central angle θ. We know that for the angle equal to 360 degrees (2π), and the arc length is equal to circumference. Hence, as the proportion between angle and arc length is constant, we can say that:
L/θ = C/2π (C = Circumference = 2πr)
L/θ = 2πr/2π,
L/θ = r,
L = r*θ = 9 cm * 1.5 = 13.5 cm
Sloan works 7 1/2 hours each day. How many hours h does Sloane work in d days?
Answers
BRAINLIESTTTTT PLS ANSWERRRRR
Solve the system of equations using substitution. Show all your work.
y = 9x +34
y = 16x –29
Answers
Answer:
x=9 and y=115
Step-by-step explanation:
Solve y=9x+34;y=16x−29
Steps:
I will solve your system by substitution.
y=9x+34;y=16x−29
Step: Solvey=9x+34for y:
Step: Substitute9x+34foryiny=16x−29:
y=16x−29
9x+34=16x−29
9x+34+−16x=16x−29+−16x(Add -16x to both sides)
−7x+34=−29
−7x+34+−34=−29+−34(Add -34 to both sides)
−7x=−63
−7x
−7
=
−63
−7
(Divide both sides by -7)
x=9
Step: Substitute9forxiny=9x+34:
y=9x+34
y=(9)(9)+34
y=115(Simplify both sides of the equation)
Hope this helps :)
For the right triangles below, find the values of the side lengths a and h . Round your answers to the nearest tenth.
Answers
Four friends shopped at the Sale Depot for movies. Robby went on Monday and bought three movies for $15.36. Paula went on Wednesday and bought five movies for $27.40. Trey went on Thursday and bought four movies for $20.08. Madison went on Friday and bought six movies for $31.44.
Answers
Answer: See explanation
Step-by-step explanation:
You didn't say what you want to get but I'm guessing that you want to know who had the cheapest deal or the best deal.
Robby went on Monday and bought three movies for $15.36. The cost per movie will be:
= $15.36/3
= $5.12
Paula went on Wednesday and bought five movies for $27.40. The cost per movie will be:
= $27.40/5
= $5.48
Trey went on Thursday and bought four movies for $20.08. The cost per movie will be:
= $20.08/4
= $5.02
Madison went on Friday and bought six movies for $31.44. The cost per movie will be:
= $31.44/6
= $5.24
We can see that Trey had the best deal.
Solve x + 5x + 6 = 0
Answers
x+5x=6x
6x+6=0
-6 -6
6x=-6
\6. /6
x= -1
so the answer would be -1
please help me with this slope problem! :) (brainliest)
Answers
Answer:
Plot these points
(1,935)
(2,870)
(3,805)
(4,740)
(5,675)
Slope= -65
y intercept = 1000
and what it's saying is that we travel at a speed of 65 units an hour and we start 1000 miles away
Step-by-step explanation:
Just graph these points which you can get by plugging in the numbers
1000-65= 935
(1,935)
1000-65*2=870
(2,870)
1000-65*3= 805
(3,805)
1000-65*4=740
(4,740)
1000-65*5= 675
(5,675)
B:
y= mx+b where m is the slope and B is the y intercept
we can re write the equation as follows
-65x+1000
It's pretty clear that -65 is the slope and 1000 is the y intercept
Find the perimeter of this parallelogram:
8.2 cm
6.5 cm
Find the perimeter of this triangle:
7.3cm
6.1cm
9.6cm
Answers
Answer:
parallelogram 's perimeter =2(8.2+6.5)
""" =2×14.7
... = 29.4
perimeter of triangle=7.2+6.1+9.6
""""" =22.9
Can someone explain how I can solve this?
Answers
Answer: q≤36
Step-by-step explanation: 6≥ q /6
6≥ 1 /6 q
1 /6 q≤6
6(1 /6 q)≤(6)(6)
q≤36
7. 8x - 4= 4(2x + 1) have how many solutions
Answers
Answer:
0
Step-by-step explanation:
Let's solve for x
8x-4=4(2x+1)
8x-4=8x+4
0= 8
This obviously isn't true and therefore there are 0 solution
Answer:
No solution as both side not equal.
is palpatine the strongest sith
Answers
Answer:
One may think that he is the most powerful Sith Lord, and on some levels this is correct, but that title falls to another, even more powerful Sith Lord. That is Jar Jar Binks. He possesses the power to wipe out entire universes without blinking an eye. Jar Jar is an entity that was here before the universe was created. He made God. He even made Shaggy in his image so that he could have a set of eyes on Earth. He needed a right hand man to corrupt humanity at its source. Some might say that Jar Jar is the true form of evil, but I refute that claim with an argument of my own. Jar Jar Binks may have destroyed countless lives, but he did so in order to keep the balance of the universe, and for that, I thank him. All hail Jar Jar.
Step-by-step explanation: