Air is being lost from a spherical balloon at a constant rate of 3/2cm3s-1. Find the rate at which the radius is decreasing at the instant when the radius is 6 cm long.

Answers

Answer 1

Answer:

The rate at which the radius is decreasing when the radius is 6 cm is approximately 3.316 × 10⁻³ cm/s

Step-by-step explanation:

The rate at which air is being lost from the balloon = 3/2 cm³/s

The rate at which the radius is decreasing when the radius is 6 cm long is given as follows;

The rate at which air is being lost from the balloon = dV/dt = 3/2 cm³/s

dV/dt = dV/dr × dr/dt

Where;

dr/dt = The rate at which the radius is decreasing

dV/dr = d(4/3×π×r³)/dr = 4·π·r²

Therefore, we have;

dr/dt = (dV//dt)/(dV/dr) = (3/2 cm³/s)/(4·π·r²)

dr/dt = (3/2 cm³/s)/(4·π·r²)

When r = 6 cm, we have;

dr/dt = (3/2 cm³/s)/(4 × π × (6 cm)²) ≈ 3.316 × 10⁻³ cm/s

Therefore, the rate at which the radius is decreasing, dr/dt, when the radius is 6 cm long ≈ 3.316 × 10⁻³ cm/s.


Related Questions

Angelo grows vegetables and sells them at a farmers'
market. The price of 2 cucumbers and I pepper is
$3.15, and the price of 3 cucumbers and 2 peppers is
$5.35. Based on this pricing, what would be the price,
in dollars, of 4 cucumbers and 3 peppers?

Answers

Answer:

$7.55

Step-by-step explanation:

We can solve this by using a system of equations. The equations would be set up like this:

[tex]2c + p = 3.15\\3c + 2p = 5.35\\[/tex]

Let's isolate a variable in the first equation:

[tex]p = -2c + 3.15[/tex]

Now we can plug this in to the second equation:

[tex]3c + 2(-2c + 3.15) = 5.35\\3c - 4c + 6.3 = 5.35\\-c + 6.3 = 5.35 \\-c = -.95\\c = .95[/tex]

Now that we have found c we can find p by plugging c in to an equation

[tex]2(.95) + p = 3.15\\1.9 + p = 3.15\\p = 1.25[/tex]

We have found both variables now we can use the following equation to answer the question:

[tex]4c + 3p = ?\\4(.95) + 3(1.25) = ?\\3.8+3.75 = 7.55[/tex]

Therefore, the price in dollars of 4 cucumbers and 3 peppers is $7.55.

I hope this helps!!

- Kay :)

Please help me asap! pleaseee

Answers

It’s B 26 in a rhombus opposite sides are parallel
The answer is b = 26

Julio says, "If you subtract 11 from my number and multiply the difference by - 6, the result is
-78." What is Julio's number?
Julio's number is

Answers

Answer:

Julio's number is 24

Step-by-Step Explanation:

1. 24 - 11 = 13

2. 13 · -6 = -78

Answer:

26

Step-by-step explanation:

Answers choices are in the picture

Answers

Answer: I believe the answer is b.

Every day kianna practices softball and piano each day she practices for 2 hours if after 7 days she practiced both softball and piano for a total of 24.5 hours how many hours per day did kianna ptactice piano

Answers

Answer: 1.5 hours

Step-by-step explanation:

Softball was practiced for 2 hours each day.

After 7 days she must have practiced it for;

= 7 * 2

= 14 hours

She practiced both piano and softball for a total of 24.5 hours. She therefore practiced piano for;

= 24.5 - 14

= 10.5 hours

If in 7 days she practiced piano for 10.5 hours, everyday she must have practiced piano for;

= 10.5/7

= 1.5 hours

The ____is used to measure volume.
Liter
Gram
Meter

Answers

Liter

2 liters of coke, not 2 grams.
If it were grams that would be drugs, remember kids, to measure volume it has to be ounces, cups, liters, gallons, and spoons :)

Answer: A.  A liter is used to measure Volume

PLZ HELP IM TWO WEEKS BEHIND THE SCHOOL CALLED MY MOM

Which describes dependent events?

drawing a blue marble and a yellow marble at the same time from a bag of marbles

drawing the ace of spades from a deck of cards, putting it back into the deck, and
drawing the king of spades.

rolling a six-sided number cube and getting an even number, then rolling the same six-sided number cube and getting an even number again

flipping two coins at the same time and getting heads on one and tails on the other

Answers

Answer:  Drawing a blue marble and a yellow marble at the same time from a bag of marbles is the example of dependent events.

Step-by-step explanation: When the cards are replaced, or flipping coins or rolling dice, the outcome of the first event does nor affect the probability of the next event.

Drawing two marbles at the same time is essentially the same as drawing one and Not replacing it and then drawing the second one. The number of marbles left affects the probability.

Answer:

A

Step-by-step explanation:

Find the value of x. Give reasons to justify your solution-

Answers

Answer:

x = 34

Step-by-step explanation:

∠ PSR and ∠ TSU are vertical angles and congruent, then

∠ PSR = 4x, thus ∠ PSQ = x

The exterior angle of a triangle is equal to the 2 opposite interior angles.

∠ SQR is an exterior angle of Δ PQS , thus

x + x = 68

2x = 68 ( divide both sides by 2 )

x = 34

Answer:

X = 34°

Step-by-step explanation:

In order to solve this question we will need to know the following, when two lines intersect the opposite angles at that point are equal to each other, that the sum of all angles of a triangle is 180 degrees, and that the angle of a straight line is equal to 180 degrees.

Frist we will have to notice that ∠TSU is equal to ∠PSR, because they are opposite to each other (If you would like to understand this more you can research on a topic call "vertical angels"). Now it is important to understand the following.

∠PSR  = ∠PSQ + QSR

Since ∠PSR = ∠TSU = 4x, ∠QSR = 3x ⇒

⇒ ∠PSR  = ∠PSQ + QSR

   4x = ∠PSQ + 3x

   4x - 3x = ∠PSQ

   x = ∠PSQ

Now, since the sum of all angles in a triangle is equal to 180 we can now say the following:

∠QPS + ∠PSQ + ∠PQS = 180°

In order to find out what PQS is equal to we need to use our knowledge about the angel of a strait line (the angel of a strait line is equal to 180°).

So now we can say the following:

180° = ∠PQS + SQR

∠PQS = 180° - ∠SQR

Since we know that ∠SQR = 68° ⇒

⇒∠PQS = 180° - ∠SQR

  ∠PQS = 180° - 68°

  ∠PQS = 112°

Since ∠QPS = x, PSQ = x, and ∠PQS = 112° ⇒

⇒ ∠QPS + ∠PSQ + ∠PQS = 180°

   x + x + 112° = 180°

  2x = 180° - 112°

  2x = 68°

  x = 34°

PLEASE HELP

Write an equation of the line in slope-interecpt form that is perpendicular to the line below and goes through
the point below:
perpendicular to 2 – 3y = 3 and goes through (5, -9)

Answers

Answer:

Sure!

Step-by-step explanation:

Divide both sides by 3 and get
y = -2/3x + 2

m is the slope so we know that the slope of this line is -2/3.

Also two lines are perpendicular, their slopes have a special relationship as shown below:
m1 = -1/m2 (this means negative reciprocal)

Now, since the slope of the line perpendicular to y = -2/3x + 2 is equal to
m = -1/(-2/3) = 3/2
also there’s a point this line passes through, (-4, 1) so you can easily find its equation
y = mx + b
1 = 3/2*(-4) + b (plugged in the values for x and y to solve for b, the y-intercept)
1 = -6 + b
b = 7
y = 3/2x + 7

On what intervals is the graph increasing and or decreasing

Answers

Answer:

Using interval notation, it is described as increasing on the interval (1,3). Decreasing: A function is decreasing, if as x increases (reading from left to right), y decreases.

Step-by-step explanation:

I WILL MARK BR HELP PLZ

Answers

Answer:

C)8

Step-by-step explanation:

So you are supposed to fill in that bottom equation with the top to get

-4x=x2+2x+8

+4x

x2 +6x+8

(x+4)(x+2) (remember x=-2,-4)

y=-4x

y=-4(-4)

y=16

y=-4x

y=-4(-2)

y=8

Can someone please explain this

Answers

Answer: orange, correct me if i am wrong

Step-by-step explanation:

I really need help......

Answers

It is a negative correlation.

Please solve the new value of x !!!!!!! Please HELP !!!!!!! Will mark BRIANLIEST !!!!!!!!!

Answers

because it’s on a straight line, you would subtract 180-85-44 to get 51 which would be the value of x since a straight line = 180 and 85 and 44 are on the straight line.

Answer:

51

Step-by-step explanation:

How much simple interest would $1 ,400 earn in 12 months at an interest rate of 3.25%?

Answers

Answer:

$45.50

Step-by-step explanation:

Interest = Principal x rate x time (in years)

I = 1400 x .0325 x 1

Answer:

$45.50

Step-by-step explanation:

The radius of a sphere is decreasing at a rate of 2 centimeters per second. At the instant when the radius of the sphere is 3 centimeters, what is the rate of change, in square centimeters per second, of the surface area of the sphere? (The surface area S of a sphere with radius r is S​ = 4πr2.)

Answers

Answer:

The rate of change of the surface area of the sphere is;

-48π cm^2/s

Step-by-step explanation:

Here, we want to calculate dA/dt

Mathematically that will be;

dA/dt = dA/dr * dr/dt

From the question;

dr/dt = -2 cm/s

dA/dr = 8πr

So dA/dt will be;

-2cm/s * 8πr = -16 πr cm/s where r is 3 cm

So;

dA/dt = -48π cm^2/s

Using implicit differentiation, it is found that the rate of change of the surface area of the sphere is of -151 square centimetres per second.

The surface area of an sphere of radius r is given by:

[tex]S = 4\pi r^2[/tex]

Applying implicit differentiation, the rate of change is given by:

[tex]S = 8\pi r\frac{dr}{dt}[/tex]

For this problem:

The radius of a sphere is decreasing at a rate of 2 centimetres per second, hence [tex]\frac{dr}{dt} = -2[/tex]It also is of 3 centimetres, hence [tex]r = 3[/tex]

The rate of change is of:

[tex]S = 8\pi(3)(-2) = -48\pi = -151[/tex]

The rate of change of the surface area of the sphere is of -151 square centimetres per second.

A similar problem is given at https://brainly.com/question/11496075

What is the area of the triangle?
A. 8.64 ft2
B. 10.8 ft2
C. 14.4 ft2
D. 17.28 ft2

Answers

Answer: 8.64

Step-by-step explanation:

3.6 * 4.8 = 17.28

17.82/2 = 8.64

Answer:

A. 8.64 ft²

Step-by-step explanation:

The equation for the area of a triangle is A = 1/2bh

b is base and in this case 4.8

h is height and in this case 3.6

A = 1/2 (3.6)(4.8)

A = 8.64

Hope this helped :)

do anybody know the answer I need it​

Answers

Answer:

It is C

Step-by-step explanation:

Please help me! 8 pts and brainliest!! please

One angle is a complementary pair is twice as large as the other. What is the measure of the larger angle?

a. 30°
b. 60°
c. 90°
d. 120°

Answers

Answer:

60 degrees

Step-by-step explanation:LARGE ANGLE...60-degrees

So, we have x + 2x = 90. Solving for x, we get x = 30. Since the first angle was called x, that means it's measurement is 30°. The second angle, 2x, is just twice the first angle, so its measurement is 60°

help me please much appreciated❤️​

Answers

Answer:

X = -16

Step-by-step explanation:

2/3x  plus 1 equals 1/6x minus 7

2 divided by 3 equals 0.666666666667

0.666666666667 plus 1 equals 1.666666666667

1.666666666667 as a simplified fraction: 1 35/55x

1 33 /55  – 7 =  – 27 /5  =  –5 2 /5

-5 2/5 x 3 = -16

(This is just how I do it but you probably did it differently)

<3 Enjoy,

    Dea


Simplify. - (3x2)0
Please and thank you:)

Answers

-1 it’s the only answer that’s right

Answer:

the answer is A

Step-by-step explanation:

I need the answer to this question I don’t understand it

Answers

Answer:

This would be y=3/1x-3

Explanation:

They give you three points so just do rise over run. As u can see in order to get to the next point you would have to go up 3 and 1 to the right. For the y intercept you can see that the line passes -3 .

Hope this helps lmk if I’m right!!

What is the value of r in the equation?
-1.5(4-r)--12
-6
O4
O
4
O6

Answers

Answer:

I am going to say 6 , please let me know if I am wrong :)

CAN SOMEONE PLEASE HELP AND EXPLAIN THIS

Answers

Answer:

what are the options? I'll say it in the comments

7b+76=90
7b=14
b=2
2(2)+42=46
so cbt=46
hope this helps :)

the product of the roots of a quadratic equation 2x²-5x+3=0 is 5/2 if it is correct give reason

Answers

9514 1404 393

Answer:

  It is incorrect. The product is 3/2.

Step-by-step explanation:

The factored form of a quadratic with roots p and q can be ...

  a(x -p)(x -q) = ax² -a(p+q) +apq

Then the product of the roots is the ratio of the constant to the leading coefficient:

  pq = (apq)/a

In the given quadratic, that product is ...

  pq = 3/2 . . . . . . not 5/2

The statement that the product of roots is 5/2 is incorrect. That value does not have the required relationship to the coefficients of the quadratic.

HEEEEEEEELP PLEASE asap

Answers

D) 4 is the answer for 9

Where would a car traveling up a hill have the most potential energy?

A. At the bottom
B. Halfway to the top
C. At the top
D.Halfway to the bottom
E. it is always the same

Answers

Answer:

At the top

Step-by-step explanation:

When your car stops at the top of the hill, it has the most potential energy.

4 / 1.21 what’s the answer?

Answers

Answer:

3.30

Step-by-step explanation:

A man in a tower spots three hot air balloons flying at the same altitude. Balloon
A is 5 miles east and 8 miles south of the
tower. Balloon B is 7 miles west and 10 miles
north of the tower. If Balloon C is located
four-ninths the distance from Balloon A to
Balloon B, find the location of Balloon C
relative to the tower.

Answers

Answer:

90/4= 12.9

1*3/4= 0.75

Step-by-step explanation:

The location of Balloon C is 0.13 miles relative to the tower.

What is Ratio?

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

What are Arithmetic operations?

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operations is called the arithmetic operator.

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

Balloon A is 5 miles east and 8 miles south of the

tower.

Balloon B is 7 miles west and 10 miles north of the tower.

If Balloon C is located four-ninths the distance from Balloon A to Balloon B,

According to the question, AB distance is 21.64 miles

⇒ 21.64×4/9 = 9.61

⇒ 9.61 - 9.43 = 0.18

⇒ 0.18×7/10 = 0.13

Hence, the location of Balloon C is 0.13 miles relative to the tower.

Learn more about the Ratio here:

brainly.com/question/1504221

#SPJ2

WILL GIVE BRAINLIEST Bryan owes the bank $7. He gets paid $35 for
babysitting and deposits it into his account. What will
his bank balance show?

Answers

Answer:

$28

Step-by-step explanation:

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