Air is escaping from a spherical balloon at the rate of 4cc/min. how fast is the surface area of the balloon shrinking when the radius is 24 cm? (a sphere of radius r has volume 4 3 πr3 and surface area 4πr2 .)

Answers

Answer 1

The volume of the ball is given by:
V = (4/3) πr ^ 3
Deriving we have:
V '= (3) (4/3) (π) (r ^ 2) (r')
Clearing r 'we have:
r '= V' / ((3) (4/3) (π) (r ^ 2))
Substituting values:
r '= 4 / ((3) (4/3) (π) ((24) ^ 2))
r '= 0.000552621 c / min
Then, the surface area is:
A = 4πr2
Deriving we have:
A '= 8πrr'
Substituting values:
A '= 8π (24) (0.000552621)
A '= 0.33 cm ^ 2 / min
Answer:
The surface area of the balloon is shrinking at:
A '= 0.33 cm ^ 2 / min

Related Questions

The weight of a mandarin orange is about 6 ounces. A basket that weighs 4 ounces will hold m mandarin oranges, the total weight is 70 ounces. Which equation represents the basket of oranges?1. 4 + 6m = 70 2. 6 + 4m = 70 3. 70 + 4m = 6 4.70 + 6m = 4

Answers

The answer to this is the first option; 4 + 6m=70.

Answer:

A is the answer on Edgen.

Step-by-step explanation:

4 + 6m = 70

6 + 4m = 70

70 + 4m = 6

70 + 6m = 4

What is the sun made of (by mass)?
a. 50 percent hydrogen, 25 percent helium, 25 percent other elements
b. 70 percent hydrogen, 28 percent helium, 2 percent other elements
c. 90 percent dark matter, 10 percent ordinary matter
d. 100 percent hydrogen and helium?

Answers

B. 70 percent hydrogen, 28 percent helium, 2 percent other elements

Whst is the remainder when f(x)=x^3+3x^2-10x-4 is diveded by x-3

Answers

The polynomial remainder theorem allows us to calculate the remainder when a polynomial is divided by a linear polynomial:
The remainder of f(x) divided by (x-k) equals f(k).

Thus
f(x)=x^3+3x^2-10x-4 divided by x-3
gives a remainder of
f(3)=27+3(9)-10(3)-4=27+27-30-4=20
Therefore the remainder required is 20.

The remainder when the polynomial [tex]f(x)=x^3+3x^2-10x-4[/tex] is divided by x-3 is found using the Remainder Theorem and is 20.

The remainder when a polynomial f(x) is divided by a linear divisor such as x - 3 can be found using the Remainder Theorem, which states that the remainder is simply f(3). To find the remainder for [tex]f(x)=x^3+3x^2-10x-4[/tex], we substitute x = 3 into the polynomial.

Calculate f(3):

[tex]f(3) = (3)^3 + 3*(3)^2 - 10*(3) - 4[/tex]

f(3) = 27 + 27 - 30 - 4

f(3) = 54 - 34

f(3) = 20

Therefore, the remainder when f(x) is divided by x - 3 is 20.

A right triangle has legs that measure 7cm and 3cm. What is the length of the Hypotenuse?

Answers

7² + 3² = c²
49 + 9 = c²
58 = c²
c = √58

Answer:

square root of 58

Step-by-step explanation:

If its wrong e2020 says its right

How to solve x in a trapezoid

Answers

For Volume is V=(base1 + base2)h and then divide by two

A 12' by 20' rectangular garden is to have a walkway of uniform width added around its entire perimeter. if the area of the walkway is 68 square feet, find the width of the walkway.

Answers

I believe you will have to times 12’ by 20’ then divide 68 by it I hope this helps

The diameter of a circle has endpoints (-3, 2) and (3, -2) which is closest to the length of the diameter of the circle?

Answers

D=√((x2-x1)²+(y2-y1)²)

D=√((x2-x1)²+(y2-y1)²) = √(3-(-3))²+(-2-2)²) = √(6² + 4²)=√(36+16)=√52
D=2√13≈7.21

[tex]\text{Diameter = } \sqrt{(2+ 2)^2+ (-3-3)^2 } = \sqrt{16 + 36} = \sqrt{52} = 7.21 \text{ units}[/tex]

Answer: Diameter = 7.21 units

The function g(x)=(x-2^2. The function f(x)=g(x) +3

The function f(x) is shifted horizontally how many places to where ?

The function f(x) is shifted vertically how many places where ?

Answers

the parent function is:
y = x ^ 2
Applying the following function transformation we have:
Horizontal translations:
Suppose that h> 0
To graph y = f (x-h), move the graph of h units to the right.
We have then:
g (x) = (x-2) ^ 2
Then, we have the following function transformation:
Vertical translations
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units up.
We have then that the original function is:
g (x) = (x-2) ^ 2
Applying the transformation we have
f (x) = g (x) +3
f (x) = (x-2) ^ 2 + 3
Answer:
the function f(x) moves horizontally 2 units rigth.
The function f (x) is shifted vertically 3 units up.

Answer:

The function f(x) moves horizontally 2 units right.

The function f (x) is shifted vertically 3 units up.

Step-by-step explanation:

You are considering two investment opportunities. For investment A there is a 25% chance that you lose $20,000, a 50% chance that you break even, and a 25% chance that you make $80,000. For investment B there is a 30% chance that you lose $50,000, a 50% chance that you break even, and a 20% chance that you make $180,000. Based on the expected value of each, which investment should you make?

Answers

The answer is investment B.

Solution:
For investment A - the expected value of the investment is
($20,000) * 25% = ($5,000)
$80,000 * 25% = $20,000
$15,000

For investment B - the expected value of the investment is
($50,000) * 30% = ($15,000)
$180,000 * 20% = $36,000
$21,000

So you can gain more by $6,000 if you choose investment B.

Answer:

For investment A - $15,000

For investment B - $21,000

So you can gain more by $6,000 if you choose investment B.

Step-by-step explanation:

At the zoo on Monday, 65 percent of the people in attendance were children. If 520 children were in attendance, how many people in total were visiting the zoo on Monday?

Answers

800 people because when you try to find the number of people, x, you do cross multiply. So it will be 520/x = 65/100, next you multiply 520 by 100, then divide that by 65 to get 800 people

Answer:

800+

Step-by-step explanation:

A right rectangular prism has base dimensions of 3 inches by 12 inches and a height of 5 inches. An oblique rectangular prism has base dimensions of 4 inches by 9 inches and a height of 5 inches. Are the volumes the same?

Answers

Volume of right rectangular prism = Length x Width x Height
Using the given dimensions, we can write:

Volume of right rectangular prism = 3 x 12 x 5 = 180 cubic inches

Volume of oblique rectangular prism = Base Area x Height
Base Area = 4 x 9 = 36 square inches

So, Volume of oblique rectangular prism = 36 x 5 = 180 cubic inches

Thus, we can conclude that the two volumes are the same.

A skier leaves an 8-foot-tall ramp with an initial vertical velocity of 28 feet per second. the function h = −16t^2 28t 8 represents the height h (in feet) of the skier after t seconds. the skier has a perfect landing. how many points does the skier earn? 1 point per foot in the air, 5 points per second in the air, and a perfect landing is 25 points.

Answers

The skier earns 35.875 points.

We can find the height in the air by using -b/2a:
-28/2(-16) = -28/-32 = 0.875

This will give the skier 0.875 points.

To find the amount of time in the air, we solve the related equation:
0=-16t²+28t+8

We will first factor out the GCF, -4:
0=-4(4t²-7t-2)

Now we will factor the trinomial in parentheses using grouping. We want factors of 4(-2)=-8 that sum to -7; -8(1) = -8 and -8+1=-7. This is how we will "split up" bx:
0=-4(4t²-8t+1t-2)

Now we will group the first two and last two terms:
0=-4[(4t²-8t)+(1t-2)]

We will factor out the GCF of each group:
0=-4[4t(t-2)+1(t-2)]

This gives us the factored form:
0=-4(4t+1)(t-2)

Using the zero product property, we know that either t-2=0 or 4t+1=0:
t-2=0
t-2+2=0+2
t=2

4t+1=0
4t+1-1=0-1
4t=-1
4t/4 = -1/4
t=-1/4

Negative time makes no sense, so t=2. This gives the skier 5(2) = 10 points.

Counting the perfect landing, we have 25+10+0.875 = 35.875 points.

Final answer:

The skier earns approximately 27 points.

Explanation:

To find the total points earned by the skier, we need to calculate the time it takes for the skier to reach the ground. In this case, the height function h = -16t^2 + 28t + 8 represents the height of the skier after t seconds. To find the time it takes for the skier to reach the ground, we need to find the value of t when h = 0.

Setting h = 0, we get:

-16t^2 + 28t + 8 = 0

Using the quadratic formula, t = (-b ± sqrt(b^2 - 4ac)) / (2a), where a = -16, b = 28, and c = 8:

t = (-28 ± sqrt(28^2 - 4(-16)(8))) / (2(-16))

Simplifying the equation, we get:

t = (-28 ± sqrt(672)) / -32

t = (-28 ± 26) / -32

Since the skier has a perfect landing, we can disregard the negative value and take the positive value of t:

t = (-28 + 26) / -32

t = -2 / -32

t = 1/16

This means the skier takes 1/16 seconds to reach the ground. To calculate the total points earned, we need to find the total time the skier is in the air. Since the skier starts with an initial vertical velocity of 28 ft/s, we can use this velocity to find the time it takes to reach the ground:

t = h / v

t = 8 / 28

t = 2/7 seconds

Therefore, the skier is in the air for 2/7 seconds. To find the total points earned:

Points = (h * 1) + (t * 5) + 25

Points = (8 * 1) + ((2/7) * 5) + 25

Points = 8 + (10/7) + 25

Points = 189/7

So, the skier earns approximately 27 points.

Find the solution of this system of equations. Separate the x- and y- values with a comma. x+4y=1 and x-y=1

Answers

Equation 1: x+4y=1
Equation 2: x-y=1

solve equation 2 for x: x=1-y
substitute 1-y into equation 1: (1-y) +4y=1
solve for y: 1-y+4y=1
1+3y=1
3y=0
y=0
Substitute y=0 into equation 2: x-(0)=1
x=1
Solution: (1,0)

In a right triangle, the measure of one acute angle is 13°. What is the measure of the other acute angle?
32°
77°
90°
167°

Answers

77° is your answer.

-JJ

The sum of the angles in a triangle is always 180 degrees. In a right triangle, one angle is 90 degrees, and given that one acute angle is 13 degrees, the measure of the other acute angle is 180 - 90 - 13, which equals 77 degrees.

In the context of Euclidean geometry, we have a well-established theorem which stipulates that the sum of the angles in any triangle equals 180 degrees. Since we are dealing with a right triangle, we know that one of its angles measures 90 degrees. The question states that one acute angle measures 13 degrees. To find the measurement of the other acute angle, we subtract the known angles from 180 degrees.

180 degrees (sum of all angles in a triangle) - 90 degrees (right angle) - 13 degrees (given acute angle) = 77 degrees.

Therefore, the measure of the other acute angle is 77 degrees.

In the school election, votes were cast for sam, mary, and bill in the ratio of 4:3:2. if a total of 2178 votes were cast, how many votes did mary receive?

Answers

2178÷(4+3+2)=242
Sam's votes=242×4=968
Mary's=242×3=726
Bill's=242×2=484

Mary received 726 votes.

Find the quotient of -36x^3-6x^2+12x/-6x

Answers

Answer:
6x² + x - 2

Explanation:
To find the quotient of a polynomial expression divided by a monomial, divide each term by the monomial.

[tex]\frac{-36x^3-6x^2 + 12x}{-6x}[/tex] becomes [tex]\frac{-36x^3}{-6x} + \frac{(-6x^2)}{(-6x)} + \frac{12x}{(-6x)}[/tex]

-36x³ / (-6x) = 6x²

(-6x²) / (-6x) = 1x = x

12x / -6x = -2

Place each of these terms together into an polynomial expression once more and the quotient is: 6x² + x - 2

From a carton containing 50kg of sugar 24 half-kilogram packets were taken . How many kilograms of sugar remained?

Answers

24 half-kg packets = 24 x 1/2 = 12kg

Sugar remained = 50 - 12 = 38 kg

Answer: 38 kg

sigma notation 2+ (-8)+32+(-128)+...

Answers

here u go hope this helps

40 POINTS!

Find the exact value by using a half-angle identity.

⬇️⬇️⬇️

Answers

[tex]\cos\dfrac{5\pi}{12}=\cos\left(\dfrac{6\pi}{12}-\dfrac{\pi}{12}\right)=\cos\left(\dfrac{\pi}{2}-\dfrac{\pi}{12}\right)=(*)[/tex]

[tex]Use: \cos(\alpha-\beta)=\cos\alpha \cos\beta+\sin\alpha \cos\beta[/tex]

[tex](*)=\cos\dfrac{\pi}{2} \cos\dfrac{\pi}{12}+\sin\dfrac{\pi}{2} \sin\dfrac{\pi}{12}\\\\=0\cdot\cos\dfrac{\pi}{12}+1\cdot\sin\dfrac{\pi}{12}=\sin\dfrac{\pi}{12}[/tex]

[tex]\dfrac{\pi}{12}=\dfrac{\dfrac{\pi}{6}}{2}[/tex]

[tex]The\ half-angle\ identity\ \sin^2\dfrac{\alpha}{2}=\dfrac{1}{2}\left(1-\cos\alpha\right)[/tex]

[tex]Using\ the\ above\ formulas,\ we\ get:\\\\\sin^2\dfrac{\pi}{12}=\dfrac{1}{2}\left(1-\cos\dfrac{\pi}{6}\right)\\\\\sin^2\dfrac{\pi}{12}=\dfrac{1}{2}\left(1-\dfrac{\sqrt3}{2}\right)\\\\\sin^2\dfrac{\pi}{12}=\dfrac{1}{2}-\dfrac{\sqrt3}{4}[/tex]

[tex]Since\ 0 \ \textless \ \dfrac{\pi}{12} \ \textless \ \pi,\ then\ \sin\dfrac{\pi}{12}\ is\ a\ positive\ number.\\\\ Therefore,\ we\ have:\\\\\sin\dfrac{\pi}{12}=\sqrt{\dfrac{1}{2}-\dfrac{\sqrt3}{4}}=\sqrt{\dfrac{2-\sqrt3}{4}}=\dfrac{\sqrt{2-\sqrt3}}{2}[/tex]

[tex]Answer:\ \boxed{\cos\dfrac{5\pi}{12}=\dfrac{\sqrt{2-\sqrt3}}{2}}[/tex]

I agree with him because it's correct and makes sense!

A restaurant offers 88 appetizers and 99 main courses. in how many ways can a person order a two-course meal

Answers

Number of ways = 88 x 99 = 8712

Answer: 8712

Tabby Soft believes that it will need new equipment in 5 years. The equipment will cost $26,000. What lump sum should be invested today at 6%, compounded semiannually, to yield $26,000? a. $22,558.87 c. $22,390.94 b. $23,948.47 d. $19,346.44

Answers

The following compounding formula applies:
A = P (1+R/2)^2t

Where, A = Amount after 5 years = $26,000; P = Amount invested now; R = Annual rate of earning = 6% = 0.06; t = time = 5 years.

Substituting;
26000 = P(1+0.06/2)^2*5 = P(1.3439)

Therefore, P = 26000/1.3439 = $19,346.44

The correct answer is d.

Answer:

Step-by-step explanation just put D

A truck tire has a diameter of 4 feet and is revolving at a rate of 45 rpm. at t = 0, a certain point is at height 0. what is the height of the point above the ground after 15 seconds?

Answers

45 rpm=2π rad*45/60=1.5π rad/sec
radius=1.5 ft
axle at 2 ft and up and down from there:
thus
y=2-1.5cos(1.5πt)
to make y=0 at 0
at 15 sec
y=2-1.5cos(15*1.5π)
y=2-0
y=2 ft

A lady bought plates and bowls, 24 items in all. The price of each bowl was 60 cents; the price of each plate was 75 cents. The cost of the whole purchase was $15. How many plates did the lady buy?

Answers

plate bowl total
.60 .75 1.35
8.4(14) 7.5(10) 15.9
7.8(13) 8.25(11) 16.05
9.6(16) 6(8) 15.6
9(15) 6.75(9) 15.75
13.8(23) .75 14.55
13.2(22) 1.5(2) 14.7
12.6(21) 2.25(3) 14.85
12(20) 3(4) 15

answer: 4

in a certain area of Brazil, deforestation is currently the most critical Socio economic problem. The area of a certain rain forest is currently 1156.25 square miles. after every year, the area of this rain force decreases by 2% which of the following statements is correct
A- deforestation problem is an example of exponential growth
B- The growth or decay rate for the area of the rainforest is 0.2
C- The function of equals 1156.25(1 -0.02 )^t
D- in less than a century the rain forest will be completely wiped out
E- in about 35 years the area of the rain forest will be cut by more than half
F-The domain of the function that model the deforestation problem above is 0<_t<_100 (less than or equal to <_)

Answers

i need help with this answer!!!!!

A is INCORRECT because here we have degrowth and growth

B is INCORRECT because the decay factor is 2% or 0.02 , not 0.2

C is CORRECT, the function is which is used to calculated the area of rainforest at time t is given by 1156.25(1 -0.02 )^t

D is INCORRECT, if we plug in t=100 in the above equation , we get = 1156*(1-0.02)^100 = 153 square miles of forest. So it will not be wiped out

E is CORRECT, if we plug in t =35, we get = 1156*(1-0.02)^35 = 570 square miles. So more than half will be cut in 35 years

F is INCORRECT becuase domain goes beyond 100 years as shown by option D

So, correct options are C and E

What is the volume of the cone to the nearest tenth?

1,244.1 m^3

829.4 m^3

552.9 m^3

1,520.5 m^3

Answers

The formula for the volume of a cone is
V = (1/3)π*r^2*h
Of course, the radius is half the diameter, so is 11 m. Substituting the given values, you have
V = (1/3)π(11 m)^2*(12 m)
V = 484π m^3
V ≈ 1520.5 m^3

The volume of the cone to the nearest tenth is ...
1520.5 m³

A boat traveled upstream a distance of 90 miles at an average speed of (v-3) miles per hour and then traveled the same distance downstream at an average of (v+3) miles per hour. if the trip upstream took half an hour longer than the trip downstream, how many hours did it take the boat to travel downstream?

Answers

Trip upstream took 90v−390v−3 hours and trip downstream took 90v+390v+3 hours. Also given that the difference in times was 1212 hours --> 90v−3−90v+3=1290v−3−90v+3=12;

90v−3−90v+3=1290v−3−90v+3=12 --> 90(v+3)−90(v−3)v2−9=1290(v+3)−90(v−3)v2−9=12 --> 90∗6v2−9=1290∗6v2−9=12 --> v2=90∗6∗2+9v2=90∗6∗2+9 --> v2=9∗(10∗6∗2+1)v2=9∗(10∗6∗2+1) --> v2=9∗121v2=9∗121 --> v=3∗11=33v=3∗11=33;

Trip downstream took 90v+3=9033+3=2.590v+3=9033+3=2.5 hours.

24 MIN LEFT anyone know the answer?

Answers

Because the two shapes are congruent to one another, we can assume all angles of ABEF to be the same as CBED. Create a formula that adds up to 360 degrees using the values given and equate it to 360 degrees. Then, solve algebraically.

A+B+E+F=360
A+152+82+98=360
Angle A=28 degrees

The length of a rectangle is twice the width. the area is 256 squared. find the length and the width.

Answers

The solution is quite simple.
First, draw a rectangle. Label two opposite sides as "w", representing the width. Label the other two sides as "2w", since the length is twice the width.
Next, write an equation. In this case, the equation would be 256=2w*w.
Simplify the equation to 2w^2=256. Divide both sides by two to get w^2=128. The width would be the square root of 128. The length would be twice that, so it would be the square root of 256. That would be 16, so the length is 16.

Find the mean, median, and interquartile for the data set below. Round your answer to the nearest tenth. 27,16,8,5,19,14,22,31,13,5,23,16,8 Mean: Median: Interquartile range:

Answers

mean: 15.92
Median: 26
interquartile range: 14-16

The mean of the data set is 15.9, the median is 16, and the interquartile range is 14.5 after rounding to the nearest tenth.

To find the mean, median, and interquartile range for the data set 27, 16, 8, 5, 19, 14, 22, 31, 13, 5, 23, 16, 8, we need to follow these steps:

Organize the data in ascending order: 5, 5, 8, 8, 13, 14, 16, 16, 19, 22, 23, 27, 31.

Calculate the mean by adding all numbers and divide by the total count. Mean: (5+5+8+8+13+14+16+16+19+22+23+27+31)/13 = 207/13 ≈ 15.9.

Find the median which is the middle number. Since there are 13 values, the median is the 7th number: Median: 16.

For the first quartile (Q1) and third quartile (Q3), divide the list into two halves. The Q1 is the median of the first half, and Q3 is the median of the second half. Q1: Median of 5, 5, 8, 8, 13, 14 ≈ 8.5; Q3: Median of 19, 22, 23, 27, 31 ≈ 23.

Calculate the interquartile range (IQR) by subtracting Q1 from Q3. Interquartile range: IQR = Q3 - Q1 = 23 - 8.5 = 14.5.

The mean is approximately 15.9, the median is 16, and the interquartile range is 14.5.

One circle has a circumference half as large as that of a second circle what ratio compares the diameter of the first circle

Answers

The diameter of the first circle is 1/2 the diameter of the second circle.

These are linear measurements. This means that the ratio of the circumference, distance around, of two circles is the same as the ratio of their diameters, or distance across.

The diameter of first circle is half of the second one.

What is a circle?

A circle is a geometric shape, all of which points are equidistant from a fixed point called as the Centre. The centre of the circle does not lie on it. The tangents drawn from the same point outside a circle are equal in length.

The given problem can be solved as follows,

The circumference of a circle is given as C = πd where d is the diameter of the circle.

Suppose, the circumference and diameters for both the circles are C₁, d₁ and C₂,d₂ respectively.

Now, the expression for circumference can be written as,

C₁ = πd₁

And, C₂ = πd₂

As per the question C₁ = 1/2C₂, then the following equations can be written as,

πd₁ = 1/2πd₂

⇒ d₁ = 1/2d₂

Hence, the diameters of the two circles are also in the same ratio.

To know more about circle click on,

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