Explain why the rate of change of the radius of the sphere is not constant even though dV/dt is constant. dr dt depends on r2, not simply r. The volume only appears constant; it is actually a rational relationship. The rate of change of the radius is a linear relationship whose slope is dV dt . The rate of change of the radius is a cubic relationship. dr dt as a function runs parallel to the volume function, which is not linear.

Answers

Answer 1

Answer:

Hello your question has some missing parts below is the missing part

A spherical balloon is inflated with gas at a rate of 600 cubic centimeters per minute  

answer :

dr/dt  depends on r^2  not simply r

Step-by-step explanation:

The rate of change of the radius of the sphere is not constant even though dv/dt is constant is because ;

dr/dt  depends on r^2  not simply r

and this is because  dr/dt is proportional to  1/r^2 therefore the rate of change of the radius cannot be constant even though dv/dt is constant


Related Questions

what I the range of f(x)=4^x?
A. all positive real numbers
B. all real numbers
C. all real numbers grater that or equal to 4
D. all real numbers grater than 4

Answers

Answer:

We conclude that the range of the function is 'all positive real numbers'.

Thus, option (A) is true.

Step-by-step explanation:

Given the expression

[tex]f\left(x\right)=4^x[/tex]

Determining the domain:

The domain of a function is the set of input values for which the function is real and defined.

It is clear that the given function has no undefined points nor domain constraints.

Therefore, the domain is: -∞ < x < ∞

Thus,

[tex]\mathrm{Domain\:of\:}\:4^x\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]

Determining the range:

The range is the set of values of the dependent variable for which a function is defined.

We know that the range of an exponential function of the form

[tex]c\cdot \:n^{ax+b}+k\:\mathrm{is}\:\:f\left(x\right)>k[/tex]

[tex]k=0[/tex]

In other words, the range is all positive real numbers.

Thus,

[tex]\mathrm{Range\:of\:}4^x:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)>0\:\\ \:\mathrm{Interval\:Notation:}&\:\left(0,\:\infty \:\right)\end{bmatrix}[/tex]

Therefore, we conclude that the range of the function is 'all positive real numbers'.

Thus, option (A) is true.

Which statement is true about points located in quadrant Ill in the coordinate
plane?
O A. The x-coordinate is negative, and the y-coordinate is positive.
B. The x-coordinate is positive, and the y-coordinate is negative.
C. The x-coordinate is negative, and the y-coordinate is negative,
D. The x-coordinate is positive, and the y-coordinate is positive.
Please answer TODAY DEC 15
I WILL GIVE 100 POINTS TO THE FIRST PERSON THAT ANSWERS

Answers

I think the answer is the option B:))))

Answer: C

Step-by-step explanation

I Think Its C

3/5 c = 9 what is the answer

Answers

C=15, look at picture for work

g(x)=3x-5 find g(-2)

Answers

Answer:

g(2) = -11

Step-by-step explanation:

So, g(-2), basically meaning that x = -2.

Since we know that, we need to plug -2 into all of the x's.

g(2) = 3(-2) - 5

g(2) = -6 - 5

g(2) = -11

The required value of g(2) would be -11.

What are the functions?

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The function is given in the question following as:

g(x) = 3x-5

We have to determine the value of g(2) to the given function.

As per the given question, we have

⇒ g(x) = 3x-5

So, g(-2), this meaning that x = -2.

Now, substitute the value of x = -2 in the given function,

⇒ g(2) = 3(-2) - 5

⇒ g(2) = -6 - 5

Apply the addition operation, and we get

⇒ g(2) = -11

Therefore, the required value of g(2) would be -11.

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Which expressions are equivalent to 6a(5+d) ?

Select each correct answer.


30a+6ad

30ad

30a+(6a⋅d)

(6a⋅5)+(6a⋅d)

11a + d

Answers

Answer: A is correct i think

Step-by-step explanation:  6a x 5 = 30a

                                              6a x d = 6ad

Answer:

A

Step-by-step explanation:

Question in picture below will give brainly

Answers

Answer:

only student ll (2)

Step-by-step explanation:

Applesauce recipe for 8 uses 3 quarters of water. How much water for 12 people

Answers

Answer:

4.5 quarts

Step-by-step explanation:

We use a proportion to solve this.

8/3 = 12/x

Cross-multiply to get:

8x = 36

x = 4.5

The answer to the question is 4.5

0.5= x djdododododododdodod

Answers

Answer:

25

Step-by-step explanation:

cuz

Need help geometric sequences see pic for details

Answers

Given:

The recursive formula of a geometric sequence is

[tex]a_n=a_{n-1}\cdot (\dfrac{1}{8})[/tex]

[tex]a_1=-3[/tex]

To find:

The explicit formula of the given geometric sequence.

Solution:

We know that, first term of geometric sequence is [tex]a_1=-3[/tex].

Recursive formula of a geometric sequence is

[tex]a_n=a_{n-1}\times r[/tex]      ...(i)

where, r is common ratio.

We have,

[tex]a_n=a_{n-1}\cdot (\dfrac{1}{8})[/tex]    ...(ii)

On comparing (i) and (ii), we get

[tex]r=\dfrac{1}{8}[/tex]

The explicit formula of a geometric sequence is

[tex]a_n=a_1r^{n-1}[/tex]

Putting [tex]a_1=-3[/tex] and [tex]r=\dfrac{1}{8}[/tex], we get

[tex]a_n=-3\left(\dfrac{1}{8}\right)^{n-1}[/tex]

Therefore, the correct option is D.

plz help! will give brainliest!

Answers

x^6

When multiplying numbers in exponential form, if the number is the same, you can simply add the exponents:

x^2 * x^4 = x^(2+4) = x^6

HELP!!! STATS!!!
A random sample of 100 felony trials showed a sample mean waiting time between arrest and trial = 173 days with a population standard deviation of waiting times = 28 days. Find a 99% confidence interval for the population mean waiting time.

Stats question, I'm really stck please help me!

Answers

Answer:

The 99% confidence interval is   [tex] 165.776  <  \mu <  180.224  [/tex]  

Step-by-step explanation:

From the question we are told that

     The sample size is  n  = 100

     The sample mean is  [tex]\= x = 173 \ days[/tex]

      The population standard deviation is  [tex]\sigma = 28 \ days[/tex]  

From the question we are told the confidence level is  99% , hence the level of significance is    

      [tex]\alpha = (100 - 99 ) \%[/tex]

=>   [tex]\alpha = 0.01[/tex]

Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is  

   [tex]Z_{\frac{\alpha }{2} } = 2.58 [/tex]

Generally the margin of error is mathematically represented as  

      [tex]E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }[/tex]

      [tex]E = 2.58  *  \frac{28 }{\sqrt{100} }[/tex]

=>    [tex]E = 7.224 [/tex]

Generally 95% confidence interval is mathematically represented as  

      [tex]\= x -E <  \mu <  \=x  +E[/tex]

=>     [tex] 173 -7.224  <  \mu < 173 + 7.224  [/tex]    

=>     [tex] 165.776  <  \mu < 180.224  [/tex]  

     

Write the data from greatest to least: 0.8, 0.79, 0.08, 0.81, 0.09, 0.9, 0.89

Answers

Answer:

0.9, 0.89, 0.81, 0.8, 0.79, 0.09, 0.08

Step-by-step explanation:

Answer: 0.09 , 0.89 , 0.81, 0.08, 0.79 , 0.9, 0.8

Step-by-step explanation:

First find the greatest

0.09, 0.89,0.81, 0.08, 0,79

Then the least

0.9 .0.8

Now put it all together  

0.09, 0.89. 0.81 , 0.08, 0.79 , 0.9, and lastly 0.8

Solve the inequality.

p + 14 ≥ 2

Answers

Answer:

p [tex]\geq[/tex] -12

Step-by-step explanation:

Subtract 14

p [tex]\geq[/tex] -12

The solution to the inequality from the information given is p ≥ -12

What is inequality?

Inequality shows the relationship between two expressions and this relationship is identified by using the inequality signs (<, >, ≤, ≥).

The solution to the inequality p + 14 ≥ 2 can be determined by having the variables on one side and the numbers on the other side. To do that:

Let us subtract 14 from both sides of the equation we have:

p + 14 - 14 ≥ 2 - 14

p ≥ -12

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PLEASE HELP ME I need the answer asap cause my grade is low and this determines my final.

Answers

Answer:

i cant see the graph zoom in

Step-by-step explanation:

Answer:

I'm sure it's 2/3

Step-by-step explanation:

the slope is positive and it rises up 2 and over 3

Given
f
(
x
)
=

x

3
f(x)=−x−3, solve for
x
x when
f
(
x
)
=

2
f(x)=−2.

Answers

Answer:

-5

Step-by-step explanation:

Substitute every part of the equation where x appears with the value of x, which is -2

f(-2)=-2-3

f(-2)=-5

So, f(x)=-5

The answer is -5 I hope this helps

You get a $60,000 loan for a new dump truck. With the truck, you can generate $500 more business each week at 80% margin. Your interest rate on the loan is 8.6%. Does the additional margin generated cover the Interest payments?​

a) Yes
b) No

Answers

Answer: Yes

Step-by-step explanation: got it wrong and told me the correct answer

In ΔDEF, if DE ≅ DF and EF is the hypotenuse, then ΔDEF is
a acute and scalene. c. right and isosceles.
b right and scalene. d. obtuse and isosceles.

Answers

Answer:

C. Right and isosceles

Explanation:

Since two sides of the triangle are equal in length ([tex]DE[/tex] and [tex]DF[/tex]), this means that the triangle is an isosceles triangle. Since [tex]EF[/tex] is the hypotenuse of this triangle, it also means that the triangle is a right-angle triangle (the hypotenuse refers to the longest side of a right triangle). Therefore, we can conclude that ΔDEF is right and isosceles.

Hope this helps :)

Answer:

It is C.

Step-by-step explanation:

Hope this helped have an amazing day!

A car is traveling at a rate of 48 miles per hour. If the car continues to travel at this same rate, how many hours will it take the car to travel 612 miles?

Answers

Answer:

12.75

Step-by-step explanation:

If you make a proportion: 48/1=612/x

1(612)= 612

612/48

12.75 hours

At a speed of 48 miles per hour, the car will take approximately 12.75 hours to go 612 miles.

What is the distance?

A mathematical number known as distance measures "how much ground an object has traveled" while moving. Distance is defined as the product of speed and time.

A car is traveling at a rate of 48 miles per hour.

To determine the number of hours it will take the car to travel 612 miles at a rate of 48 miles per hour, you can divide the distance traveled by the rate at which the car is traveling:

⇒ distance ÷ rate

⇒ 612 miles / 48 miles/hour

Apply the division operation, and we get

⇒ 12.75 hours

Therefore, it will take the car about 12.75 hours to travel 612 miles at a rate of 48 miles per hour.

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whats 7, −6, 4, −10, 3 least to greatest

Answers

Answer:

-10, -6, 3, 4, 7

Step-by-step explanation:

Hope it helps ^^

Explain how to graph 8 is greater than it equal to y

Answers

Answer:

t w e n t y c h a r e c t e r s l o n g

Which statement best describes a unit rate?

1. John drove 350 miles in 5 hours

2. John drove 10 miles

3. John drove a car and a motorcycle

4. John drove 25 miles in 1 hour

Answers

Answer:

4. John drove 25 miles in 1 hour

Step-by-step explanation:

The unit rate is the number of something per unit. There should be a first number and the second number should always be 1.

The statement which best describes a unit rate is John drove 25 miles in 1 hour .

What is unit rate?

Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.

According to the question

Best describes a unit rate is that which have second term as 1 unit

So,

Only John drove 25 miles in 1 hour satisfy the condition ,

Hence, The statement which best describes a unit rate is John drove 25 miles in 1 hour .

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A survey showed that 72% of
teens bought new athletic shoes for the
new school year. Based on that survey,
how many teens in a group of 225 bought
new athletic shoes for the new school
year?

Answers

Answer:

162

Step-by-step explanation:

225 x 0.72 = 162

will give brainliest!

Answers

Correct answer: A, 2

Answer:

2/1=2

Step-by-step explanation:

Which of the following hace a value equal to |37|? Select all that apply

A. -37
B. |-37|
C.0
D. -(-37)
E. 37

Answers

B, D, and E
The absolute value of -37 is 37.
The absolute value of 37 is also 37.
When you distribute the negative in the parenthesis the -37 becomes positive.

Maggie is participating in her school reading challenge. She reads 80 books in 6 months. If 40 of the books are fiction, then what percent of the books that she read are fiction?

Answers

Answer:

50%

Step-by-step explanation:

*In this question, the 6 does not matter*

If 40/80 books are fiction, and if you simplify that fraction, you get 1/2.

Percentages are just fancy fractions and decimals. 50% means 1/2.

Thus, the answer is 50%

Delete this already.

Find the solution to the system of equations.
You can use the interactive graph below to find the solution.
\begin{cases} y=-7x+3 \\\\ y=-x-3 \end{cases}









y=−7x+3
y=−x−3

Answers

Answer:

(1,-4)

Step-by-step explanation:

Given:

y = −7x+3

y = −x−3

Computation:

y = −7x+3......eq1

y = −x−3.......eq2

Eq 1 - 2

-6x + 6 = 0

x = 1

So,

y = −7x+3

y = −7(1)+3

y = -4

So,

(1,-4)

Pls answer this is very easy

Answers

Answer:

A and B

Step-by-step explanation:

The original equation simplifies down to -4m - 2

Answer A and B also simplify down to -4m -2, and therefor are equivalent

A: -2(4m + 1) + 4m

-8m - 2 + 4m

-4m - 2

B: 2(2m - 1) - 8m

4m - 2 - 8m

-4m - 2

it’s a and b
person on top is right

The area of rectangle is 35 square feet.the length of rectangle is 5feet what is the width of the rectangle ​

Answers

What class is this ? Tell me if you can

Answer:

the answer should be 7

Step-by-step explanation:

Help a birb. Get a crown.

Answers

Answer:

6.

in 24/4=6,

24 is the dividend

4 is the divisor

6 is the quotient

in 4*6 = 24,

4 and 6 are the factors

24 is the product

7. division is an operation on two numbers to find the quotient

8. fact family is a group of related facts using the same numbers

9. multiplication is an operation on two numbers to find the product

Answer:

6. 24/4 = 6

7.24

8.4

9.6

4 * 6 = 24,

4 și 6 sunt factorii

24 este produsul

7. împărțirea este o operație pe două numere pentru a găsi coeficientul

8. familia de fapte este un grup de fapte conexe care utilizează aceleași numere

9. multiplicarea este o operație pe două numere pentru a găsi produsul

Step-by-step explanation:

Help me with this plz!?!? I will mark brainliest!!!

Answers

If the temp is 12f and changes by -26f
Is 38f
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