Mathematics College

A sporting goods manufacturer designs a golf ball having a volume of 2.48 cubic inches.

What is the radius of the golf ball?
If the ball's volume can vary between 2.45 cubic inches and 2.51 cubic inches, how can the radius vary?
identify epsilon and limit

Answers

Answer 1
Given that the sporting goods manufacturer designs a golf ball having a volume of 2.48 cubic inches.

The golf ball is of spherical shape and the volume of a sphere is given by
[tex]V= \frac{4}{3} \pi r^3[/tex]

The radius of the golf ball is given by
[tex]\frac{4}{3} \pi r^3=2.48 \\ \\ \Rightarrow r^3= \frac{3\times2.48}{4\pi} =0.592 \\ \\ \Rightarrow r= \sqrt[3]{0.592} =0.84 cm[/tex]

For V = 2.45
[tex]\frac{4}{3} \pi r^3=2.45 \\ \\ \Rightarrow r^3= \frac{3\times2.45}{4\pi} =0.585 \\ \\ \Rightarrow r= \sqrt[3]{0.585} =0.8363 cm[/tex]

For V = 2.51
[tex]\frac{4}{3} \pi r^3=2.51 \\ \\ \Rightarrow r^3= \frac{3\times2.51}{4\pi} =0.599 \\ \\ \Rightarrow r= \sqrt[3]{0.599} =0.8431 cm[/tex]

Thus, If the ball's volume can vary between 2.45 cubic inches and 2.51 cubic inches, then the radius can vary between 0.8363 and 0.8431.

[tex] \lim_{r \to 0.84} V(r) =2.48[/tex]
because
[tex]|V(r)-2.48|\ \textless \ 0.03[/tex]
whenever
[tex]0\ \textless \ |r-0.84|\ \textless \ 0.0034[/tex]

Related Questions

What is a number greater than 1,000 whose prime factorization contains 1 prime number that does not repeat, 1 prime number that repeats three times, and 1 prime number that repeats twice

Answers

You could just fill in the spaces.

So for the prime number that doesn't repeat, you can just say a random prime number, say like 7.

For the prime number that repeats 3 times, say like 11.

And the prime number that repeats twice, you can just say something like 13.

Then it would be 7 * 11 * 11 * 11 * 13 * 13, which the solution would be 1,574,573, above 1000.
find big prime numbers
we need 3 of them
23 and 19 and 101

so we can do
does not repeat
does reapat 3 times
repeats twice
(23)(19³)(101³)=8554589203
there, that's a possible number

if ya wanted a smaller one then
2 and 5 and 11 are prime
(2)(5³)(11²)=30250
that's another possible number

What is the fourth term in the arithmetic sequence 13,10,7

Answers

Final answer:

The fourth term in the arithmetic sequence 13, 10, 7 is 4.

Explanation:

The arithmetic sequence 13, 10, 7 has a common difference of -3. To find the fourth term, we can start with the first term and keep subtracting the common difference. So, 13 - 3 = 10, 10 - 3 = 7, and 7 - 3 = 4. Therefore, the fourth term in the arithmetic sequence 13, 10, 7 is 4.

Juan's baseball card collection was worth 800$. Over the last 5 years,thw collection decreased $300 in value. What integer representa the average decrease in value each year.

Answers

Final answer:

The average yearly decrease in the value of Juan's baseball card collection, which decreased by $300 over 5 years, is $60. This integer represents the yearly reduction in value.

Explanation:

Juan's baseball card collection was worth $800. Over the last 5 years, the collection decreased by $300 in value. To find the average decrease in value each year, we can use the formula: Average decrease per year = Total decrease / Number of years.

Given that the total decrease is $300 and the time period is 5 years, the calculation would be:
Average decrease per year = $300 / 5 = $60.

Therefore, the integer that represents the average decrease in value each year for Juan's baseball card collection is $60.

Pamela is 10 years older than Jiri. The sum of their ages is 108 . What is Jiri's age?

Answers

108=x+(x-10). Pamela is 59, Jiri is 49.
Pamela is 59 and Jiri is 49 59+49=108

how can you use absolute value to represent a negative number in a real world situation

Answers

You cannot because distance cannot be negative.

Hope this helps you!

Maria wrote the equation of a line that has a slope of 4/3and passes through point (3, 5). Which statement is true?

Answers

Answer:

B

Step-by-step explanation:

The slope intercept equation is [tex]y=\frac{4}{3}x+1[/tex] is true statement. Option C is correct.

From the given information the slope of the line is 4/3 and it is passing through point (3, 5).

Now, determine the equation of line in slope intercept form.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

To find the equation, first find the y intercept by considering the point values (3, 5).

[tex]5 = \frac{4}{3}+b[/tex]

[tex]5=4+b[/tex]

[tex]b=1[/tex]

Now plug in the values of slope and y intercept in slope intercept form:

[tex]y=\frac{4}{3}x+1[/tex]

Hence, Option C is correct, he equation of the line is [tex]y=\frac{4}{3}x+1.[/tex]

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The complete question is given in the attachment.

The sum of three consecutive integers is −261−261. Find the three integers.

Answers

Consecutive meanings next to

So x+x+1+x+2=-261
Meaning that 3x+3=-261
3x=-264
X=-88

So the three number are -88,-89-90

Andrew is planning a tailgate party before the big football game. He has budgeted a maximum of $60 for hamburgers and hot dogs. Hamburgers cost $3 per pound, and hot dogs cost $2 per pound. Write an inequality to describe the possible number of pounds of hamburgers and of hot dogs he can purchase.

Answers

Since 60 dollars is the maximum, the cost (c) has to be equal to or less than 60. Writing that out, we get c≤60. We want to figure out the cost. Since hamburgers are 3$ per pound, if we buy x pounds of hamburgers we pay 3x dollars due to that we add 3 for every hamburger. Similarly, if the amount of hot dogs is y, we have 2y as the cost for the hot dogs. The cost is (cost of hamburgers)+(cost of hot dogs), so c=3x+2y and since c≤60, we plug 3x+2y in for c to get 3x+2y≤60

The inequality that describes the the possible number of pounds of hamburgers and of hot dogs he can purchase is 3x + 2y ≤ 60.

We have,

Let x be the number of pounds of hamburgers that Andrew purchases, and let y be the number of pounds of hot dogs that he purchases.

The cost of x pounds of hamburgers is 3x dollars, and the cost of y pounds of hot dogs is 2y dollars.

According to the problem, Andrew has budgeted a maximum of $60 for hamburgers and hot dogs.

Therefore, we can write the following inequality:

3x + 2y ≤ 60

This inequality describes the possible combinations of x and y that Andrew can purchase, such that the total cost of hamburgers and hot dogs does not exceed his budget of $60.

Thus,

The inequality that describes the the possible number of pounds of hamburgers and of hot dogs he can purchase is 3x + 2y ≤ 60.

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Solve your formula from problem 12 for m. Then find the taxi driver’s hourly rate of his pickup rate is $2 and he charges $19.50 for a 7 - mile trip

Answers

m must equal (19.5÷7) plus 2 dollars

Answer: Cost per mile m = $4.78.

Step-by-step explanation:

Since we have given that

Pick up rate = $2

Charges for a 7 mile trip = $19.50

Charges for a mile trip would be

[tex]\dfrac{19.50}{7}\\\\=2.78[/tex]

So, amount of taxi's drivers is given by

[tex]\$2.78+\$2\\\\=\$4.78[/tex]

Hence, cost per mile m = $4.78.

What is the range of f(x) = 4x?

Answers

Range is all positive real numbers

answer is D. last one

Answer:

D. All positive real numbers

Step-by-step explanation:

The range of a function f(x) are all the possibles values that f(x) can take. So in  the function of the question it doesn't matter what value takes x, f(x) is always going to be a positive number. For example:

f(0)=[tex]4^{0}[/tex]=1

f(-1)=[tex]4^{-1}[/tex]=1/4

f(2)=[tex]4^{2}[/tex]=16

Then, the range of f(x) is all positive real numbers.

1 penny has a mass of 4 grams and is 1.55 millimeters thick. How much mass will a stack of 20 pennies tall have?

Answers

Since each penny has a mass of 4 grams, and we want to find out how much mass 20 pennies has, we do 4 (for 1 penny)*20=80 grams

To find the mass of a stack of 20 pennies, multiply the mass of a single penny by 20.

Mass of a single penny: A single penny weighs around 3 grams on average.

Calculate the total mass: Multiply the mass of a single penny by the number of pennies in the stack (4 grams/penny * 20 pennies).Answer: A stack of 20 pennies will have a mass of 80 grams.

Find the domain of each function. (enter your answers using interval notation.) (a) f(x) = 2 4 + ex

Answers

I assume 2 4 is the number 24, so f(x) = 24 + e^x ???

Domain (-co, co)    Range (24, co)

Write forty and eight tenths as a decimal

Answers

Hello!

Forty and eight tenths as a decimal would be:
40.8

The 8 is in the "tens" spot on the right side of the decimal, and 40 is on the left side. 

I hope this helps you!
Hello there! 

Question: Write forty and eight tenths as a decimal

 Looking for our answer
 [tex]forty = 40, right? \\ eight = 8,right? \\ decimal = . , right? [/tex]

So, thus our answer would most likely be: [tex]40.8[/tex]

Remember, to highlight your key information and your answer will come to you, it can come in handy in the future :)

Good luck on your assignment and enjoy your day!

                          ~[tex]MeIsKaitlyn:)[/tex]                  

If y = 8 when x = 3, determine y when x = 45 (write an equation)

Answers

The equation should be y = mx. Let's calculate m, when x = 3 and y = 8:
8=3m and m = 8/3, then the equation is:

y = (8/3)x. Now if x = 45 then y = (8/3).(45)  and y = 120

897100 rounded to the nearest ten thousand/5756492/ec680fa8?utm_source=registration

Answers

900,000 is your answer

hope this helps

The sum of three numbers is 105 . The third number is 3 times the first. The second number is 5 more than the first. What are the numbers?

Answers

The answer is 17+9+79

A sample of n = 8 scores has ss = 50. if these same scores were a population, then the ss value for the population would be ____.

Answers

A sample of n=8 has an ss=50 if these were a population the ss value of the population would be (50/8) of the sample = 6.25 of sample. Usually, ss value of the population i s calculated by dividing ss by the sample values. This is the way to calculate ss value of the population.

Answer:

5.69999

Step-by-step explanation:

subtracting 3 from the product of 6 and a number results in the number added to 52. how would i write this out

Answers

Here you go!! It would be, 6-3+52!

URGENT
The depth of water in the port at hinchinbrook is given by: d(t)= 2.6 sin (Pi over 6 t) + 13.1, where d is in meters and t is the number of hours since high tide.

Use the model to determine how many hours are there between high tides.
If high tide was at midnight, draw a graph to determine during which hours should it be safe for the boats to be in the port and between which hours they would have to stay away from the port. Justify answers mathematically

Answers

The best way to approach this problem is to look at the graph of the given function. Replace values of x from 1 to 24 to indicate the numbers of hours in a day. As seen on the graph, there is only one point where the port is at high tide. That would be at 1:00 am. 

Looking at the graph, it would be safe for the boats to be in the port when the graph levels off at around 10 to 24. That's from 10 am to before 12 midnight. Then, they would have to stay away between 12 midnight to before 10 am.

A piece of land is to be fenced and subdivided as shown to that each rectangle has the same dimensions. Express the total amount of fencing needed as an algebraic expression in x. Find the total amount of fencing.

Answers

There are 3 rectangles.

In the plane, each rectangle has 2x + 7 horizontal side.

The fence covers 3 horizontal sides => 3 (2x + 7)

In the plane, the vertical sideis x. And the fence covers 4 vertical sides => 4x

Then the total amount of fecncin is: 3(2x+7) + 4x = 6x + 21 + 4x = 10x + 21

Answer: 10x + 21 

i need help to evaluate this p + (-q) - 2 where p = -3 and q =5

Answers

p + (-q) - 2 where p = -3 and q =5
= -3 + (-5) - 2
= -3 - 5 - 2
= -10

hope it helps
the answer would be -10-3-5-2= -10

Joe practiced his trumpet 3/4 hour on Monday and 7/12 hour on Tuesday. How long did he practice altogether

Answers

1 1/3 hours. 3/4 plus 7/12 equals 1 1/3. Hope this helps

what is length of DE

Answers

check the picture below.

evaluate the expression 4(2x + 3) + 2(x + 1)-7

Answers

4 (2x + 3) + 2 (x + 1) - 7

8x + 12 + 2x +  2 - 7

10x + 7

10x = -7
10x/10 = -7/10

x = -7/10

hope this helps


You and a friend of getting ready to study for an assessment on expressions and
equations. Knowing that your friend is still getting expressions and equations mixed
up and doesn’t always know how to tell if two expressions or two equations are
equivalent, your job is to create a set of problems (and solutions) to help your friend
study. Create a minimum of six problems that will address your friend’s misconcep-
tions and include the solutions for her/him to study. Make sure your reasoning is
clearly articulated in the solutions.

Answers

Final answer:

Here are six problems and their solutions to help you study expressions and equations.

Explanation:

Here are six problems to help you study expressions and equations:

Simplify the expression (3x - 4) + (2x + 5).Solution: Combine like terms: 3x + 2x - 4 + 5 = 5x + 1.Solve the equation 2x + 3 = 9.Solution: Subtract 3 from both sides: 2x = 6. Divide both sides by 2: x = 3.Determine if the expressions 2x + 5 and 5 + 2x are equivalent.Solution: Since addition is commutative, the expressions are equivalent.Determine if the equations 2x + 3 = 9 and 2x + 6 = 12 are equivalent.Solution: Subtracting 3 from both sides of the first equation gives 2x = 6, which is equivalent to the second equation.Simplify the expression 2(3x + 4) - (5x - 2).Solution: Distribute the 2: 6x + 8 - (5x - 2). Use the distributive property: 6x + 8 - 5x + 2. Combine like terms: x + 10.Solve the equation 3(x - 2) = 9.Solution: Distribute the 3: 3x - 6 = 9. Add 6 to both sides: 3x = 15. Divide both sides by 3: x = 5.

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What is the retail price of a couch at a furniture store that has a wholesale price of $115 and is marked up by 75 percent? $86.25 $190.00 $201.25 $316.25

Answers

115+75%*115=201.25 yeah the answer is this

A percentage is a way to describe a part of a whole. The retail price of a couch at a furniture store that has a wholesale price of $115 and is marked up by 75% is $201.25.

What are Percentages?

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given that the wholesale price of the couch at a furniture store is $115. Now, as the retail price is marked up by 75%, therefore, the new price of the couch can be written as,

The new price of the couch = 175% of the wholesale price

                                              = 1.75 × $115

                                              = $201.25

Hence, the retail price of a couch at a furniture store that has a wholesale price of $115 and is marked up by 75% is $201.25.

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In the parabola y = (x + 1)2 + 2, what is the vertex?

Answers

Vertex: (-1,2)
as general form is y=a(x-p)^2+q and vertex is (p,q)
so p=-1 ands q=2 so vertex is (-1,2)

The vertex form of a quadratic equation is expressed as y = a(x - h)^2 + k. The vertex of the parabola is (-1, 2)

Vertex form of an equation

The vertex form of a quadratic equation is expressed as:

y = a(x - h)^2 + k

where (h, k) is the vertex of the equation

Given the equation of the parabola as  y = (x - 1)^2 + 2, On comparing;

h = -1

k =2

Hence the vertex of the parabola is (-1, 2)

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The length of a rectangle is 18 cm less than five times it's width. It's area is 35 cm². Find the dimensions of the rectangle.

Answers

5 x 7 because if 5 is the width is 25 then 18 minus that is 7 and 7x5 = 35

Which of the various ways of orienting the definitional triangle must be used to resolve n⃗ into components in the tilted coordinate system shown? (in the figures, the hypotenuse is blue (long dashes), the side adjacent to θ is red (short dashes), and the side opposite is yellow (solid).)?

Answers

The answer picture 4. So the first step is to figure out the sines and cosines of theta (along with their signs in perspective). The next step is to find the trigonometric functions based on the results of first step. Sine and cosine are defined according to the following convention, with the key lengths shown in green: The hypotenuse has unit length, the side adjacent to has length , and the side opposite has length.

what is the answer to "What is the LCM of two numbers thay have no common factors greater than 1 ?

Answers

If they have no other common factors other than one, the LCM is equal to the product of the two numbers.

For example, the factors of 3 are 3 and 1 and the factors of 10 are 1, 2, 5, and 10. Since they share no common factors other than one, the LCM is equal to 3*10= 30.
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