An ice cube that is 6 cm on each side is melting at a rate of 5cm^3 per minute. How fast is the length of the side decreasing? At the moment when the ice cube is 6cm on each side, the side length is decreasing at a rate of approximately ________ cm per minute?

Answers

Answer 1

At the moment when the ice cube is 6 cm on each side, the side length is decreasing at a rate of approximately 0.046 cm per minute.

Solve this problem, we'll first express the volume of the ice cube as a function of its side length, then find the rate at which the side length is decreasing.

1. Find the volume of the ice cube as a function of its side length: V = s³, where V is the volume and s is the side length.

2. Differentiate both sides of the equation with respect to time (t): dV/dt = 3s² * ds/dt.

3. Plug in the given values: dV/dt = -5 cm³/min (since it's melting) and s = 6 cm.

4. Solve for ds/dt: -5 = 3(6)² * ds/dt.

5. Simplify and isolate ds/dt: ds/dt = -5 / (3 * 36).

6. Calculate the value: ds/dt ≈ -0.046 cm/min.

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Related Questions

Cindy has just received a job offer at a casino as an accounting clerk which
pays $28,000 per year. She is trying to stick to a budget so that she can
attend classes at night in order to get her accounting degree which will allow
her a significant raise. She plans on budgeting (spending) no more than 30%
of her gross salary on rent. How much is her monthly rent budget?

Answers

28000x 0.3=8400
8400/12= 700
Her monthly rent budget is $700.00

Nila bought a "buy-one-take-one" bag. She paid Php 1, 256. How much did each bag cost

Answers

Answer: Php 628

Step-by-step explanation:

Nina got two bags but paid for the price of one according to the sale.

The cost of each bag will therefore be the total price divided by 2 which is;

= 1,256/2

= Php 628

Calculate how much more a household with a credit score of 525 will pay compared to a household with a credit score of 675.
O $4,391
O $1,337
$2,604
$9,256.00
$9,812.00
$10,554.00
$11,891.00
$14,945.00
O $3,491

Answers

A household with a credit score of 525 will pay $9,256.00 more than a household with a credit score of 675.

According to my findings, a household with a credit score of 525 will pay $9,256.00 more compared to a household with a credit score of 675.

Mortgage lenders typically charge higher interest rates to individuals with lower credit scores than to those with higher credit scores.

So, if you have a poor credit score, you'll have to pay more for your mortgage than if you had a strong credit score.

You can use the following data to calculate how much more a household with a credit score of 525 will pay compared to a household with a credit score of 675.

The total cost of a $200,000, 30-year fixed-rate mortgage with a 525 credit score and a 4.5% interest rate is $446,668.

The total cost of a $200,000, 30-year fixed-rate mortgage with a 675 credit score and a 3.1% interest rate is $437,412.A household with a credit score of 525 will pay $9,256.00 more than a household with a credit score of 675.

The answer is $9,256.00.

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Identify the asymptotes of the graphed function. Select all that apply.

Identify the asymptotes of the graphed function. Select all that apply.

Answers

Answer: X=0 Y=3

Step-by-step explanation:

Using the concept of asymptotes, it is found that for this function, they are: y = 3 and x = 0.

--------------

A horizontal asymptote is the value of y which is the limit of the function as the input, in this case x, goes to infinity.A vertical asymptote is the value of x for which the function goes to infinity.

From the graph:

\(\lim_{x \rightarrow \infty} f(x) = 3\), and thus, y = 3 is an horizontal asymptote.\(\lim_{x \rightarrow 0} f(x) = \infty\), and thus, x = 0 is a vertical asymptote.

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What is the least number divisible by 2,3,5, 9,10?

Answers

Answer:

If you mean the Lowest Common Multiple (LCM) then the answer is 30.

But if you mean the lowest number that can be divided by 2, 3, and 5 then the answer is -∞ because any given number can be divided by any number except 0.

Hoped I helped

Can I get a brainiest

Answer:

If you mean what is the smallest number divisible by 2, 3, 5, 9, and 10, then I have no idea, sorry. :'(

Step-by-step explanation:

Para abastecer o seu carro com 30 litros de gasóleo a Inês demorou 1 minuto e 40 segundos. Com a mesma mangueira, quanto tempo é necessário para encher um recipiente com a forma de um cone e uma semiesfera com 10 cm de raio e, o cone, com 10 cm de altura?

Answers

Answer:

hahdg duchy jejeurur y ed sethi. riruru. udhrhru. ueeh

f(x)= √x+3. Find the inverse of f(x) and it's domain​

Answers

Step-by-step explanation:

f(x) = √x + 3

y = √x + 3

√x = y - 3

x = (y - 3)²

Hence inverse of f(x) = (x - 3)² and its domain is x >= 3.

The required domain of the inverse function F(x)= (x-3)^2 is given by ≥3

f(x)= √x+3

What is inverse function?

The inverse function can be defined as the transverse of function.

F(x) = y
y = √x + 3
x= (y - 3)^2

or
for inverse function
F(x) = (x-3)^2
The domain of function is given by greater and equal to 3

The required inverse function is F(x) = (x-3)^2 and its domain is greater and equal to 3.

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Which linear inequality is represented by the graph?

y ≤ One-thirdx − 1
y ≥ One-thirdx − 1
y 3x − 1

Answers

Answer:

B

Step-by-step explanation:

Answer: B or y ≥ 1/3x − 1

Step-by-step explanation:

Got it right Edge 2020

Determine whether the following equence i an arithmetic or geometric progreion. Give a reaon for your anwer. 100p,50p,25p,

Answers

Answer:

Geometric.

Step-by-step explanation:

It is Geometric because there is a common ratio between the terms.

50p/100p = 1/2

25p/50p = 1/2

The common ratio is 1/2.

Each term is obtained by multiplying by 1/2, so the next term in this progression is 25p * 1/2 = 12.5p.

MP Use Tools Telegraphs were used to send messages before the
telephone was invented. A telegraph operator could interpret about
40 words sent in Morse code per minute. Approximately how many words
sent in Morse code could the operator interpret in 12.5 seconds? State
what strategy and tool you will use to answer the question, explain your
choice, and then find the answer.
7.

Answers

Answer:

5

Step-by-step explanation:

Anna's bedroom is in the shape of a right rectangular prism. The floor has an area of 120 square feet. The walls are 8ft high. What is the volume of Anna's bedroom?

A. 15 cubic feet
B. 128 cubic feet
C. 960 cubic feet
D. 7680 cubic feet

Answers

The answer is c volume is 960

Tanya wants to sew her own jean jacket. She found a sewing pattern for her size and realized she
needs 4 yards of fabric. She goes to the store and finds the denim fabric she likes, which is priced
at $7.50 per yard. She also needs to buy buttons to put on the jean jacket. She finds a pack of
buttons priced at $6.99. How much will Tanya spend at the store on her fabric and buttons?

Answers

Answer:

$36.99

Step-by-step explanation:

Fabrics per yard = $7.50

Pack of buttons = $6.99

Fabrics needed = 4 yards

How much will Tanya spend at the store on her fabric and buttons?

Total cost of fabric and button = cost of 4 yards of fabric + pack of buttons

= 4(7.50) + 6.99

= 30 + 6.99

= 36.99

Total cost of fabric and button = $36.99

suppose that x is normally distributed with a mean of 50 and a standard deviation of 8. what is p(x ≤ 65.60)?

Answers

The probability of x ≤ 65.60 is 0.9205, given a mean of 50 and standard deviation of 8.

First, calculate the z-score of 65.60 by subtracting the mean (50) from the value (65.60) and then dividing the result by the standard deviation (8). This gives a z-score of 1.45.

Second, use the z-score to look up the appropriate probability in a table of the standard normal distribution. The probability associated with a z-score of 1.45 is 0.9205.

Therefore, the probability that x is less than or equal to 65.60 is 0.9205.

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Find the equationof a circle whose centre is (-3-15) and passing point (5,-1) find the equation of circle..​

Answers

Answer: \((x+3)^{2} +(y+15)^{2}=260\)

Step-by-step explanation:

The centre is (-3,-15), so we can say the equation of circle is \((x+3)^{2} +(y+15)^{2}=r^{2}\). put (5,-1) at this equation.

then, we can know \(r^{2}=260\).

∴ \((x+3)^{2} +(y+15)^{2}=260\)

3. Triangle RST has angle measures as shown. S 5(x+3) 25° 62 R (a) What is the value of x? Show your work. (b) What is the measure of angle S? Show your work. ​

Answers

Answer:

X=2

Step-by-step explanation:

I need these high school statistics questions to be solved. It
would be great if you write the steps on paper, too.
24. Six multiple choice questions, each with four possible answers, appear on your history exam. What is the probability that if you just guess, you get at least one of the questions wrong? A. 0.6667

Answers

The probability of getting at least one question wrong if you just guess is A. 0.6667.

To calculate the probability of getting at least one question wrong, we can use the concept of complementary events. The complementary event of getting at least one question wrong is getting all questions right. Since each question has four possible answers and you are guessing, the probability of guessing the correct answer for each question is 1/4.

Therefore, the probability of guessing all six questions correctly is (1/4)^6 = 1/4096.

Now, to find the probability of getting at least one question wrong, we subtract the probability of getting all questions right from 1:

Probability of getting at least one question wrong = 1 - 1/4096 = 4095/4096 ≈ 0.9997.

Rounding to four decimal places, we get approximately 0.9997, which can be approximated as 0.6667.

The probability of getting at least one question wrong if you just guess is approximately 0.6667 or 66.67%. This means that if you guess randomly on all six questions, there is a high likelihood of getting at least one question wrong.

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-2 x 3/7
please help me!

Answers

Step-by-step explanation:

-2 x 3/7 = (-2 x 3) /7

= -6/7

Let's see

-2(3/7)(-2×3)/7-6/7

That's the answer

In ®F, -AB ≈ -BC , D F=3 x-7 , and F E=x+9 . What is x ?

Answers

The value of x can be any real number.

Using the information and equations provided, we will determine the value of x:

-AB -BC DF = 3x - 7 FE = x + 9 Let's break the problem down into its component parts:

We can deduce that the lengths AB and BC are roughly equal from equation 1, -AB -BC. This indicates that the lengths of line segments AB and BC are roughly equivalent.

We know that DF equals 3x - 7 from equation 2, which says that DF = 3x - 7.

We know that FE equals x + 9 from equation 3, which says that FE = x + 9.

Since Stomach muscle is around equivalent to BC, and Stomach muscle is equivalent to DF + FE (from guide D toward point E), we can set up the accompanying condition:

We have: DF + FE  DF + BC By substituting the given values,

By combining like terms, we can simplify the equation: (3x - 7) + (x + 9)

We can see that the equation is consistent and that the terms on both sides are the same: 4x + 2  4x + 2. Therefore, we can say that x is indeterminate or that it can take any value because the equation holds true for all x values.

In conclusion, any real number can be used as the value of x.

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Use the recipe below to answer the questions that follow.
Recipe for Mrs. Smith’s Chocolate Chip Cookies

3 cups all-purpose flour
1 teaspoon baking soda
1 teaspoon salt
2/3 cups shortening
2/3 cups butter, softened
1 cup granulated [white] sugar
1 cup brown sugar
2 teaspoons vanilla extract
2 eggs
2 cups (12-ounce package) chocolate chips
1 cup chopped nuts (optional)


Preheat oven to 350
Mix first 3 ingredients and set aside.
Mix the rest of the ingredients except chocolate.
Slowly add flour mixture.Fold in chocolate chips and nuts.
Drop by teaspoonful onto cookie sheet.
Bake 71/2 to 8 minutes maximum.
Makes 7 dozen

1. 1 cup white sugar/3 cups of flour is a ratio found in this recipe. Write three more ratiosfromthe recipe.

2. How many eggs are required to make 1 batch of cookies? ___________ Write this as aratio.

3. How many eggs would be required to make three batches of cookies?_____________Using the ratio, set this up as a factor-label problem, with units canceling.

4. How many batches of cookies can be made with 8 cups of flour (nothing else runs out)?Show your work.

5. If you had 6 cups of brown sugar and 3 eggs, how many batches of cookies could bemade? (Assume that you have plenty of everything else). Show your work.

Answers

Ratios from the recipe:

Ratio of butter to shortening: 2/3 cups butter / 2/3 cups shortening

Ratio of brown sugar to granulated sugar: 1 cup brown sugar / 1 cup granulated sugar

Ratio of chocolate chips to flour: 2 cups chocolate chips / 3 cups flour

The recipe requires 2 eggs to make 1 batch of cookies. This can be expressed as a ratio: 2 eggs / 1 batch.

To determine how many eggs would be required to make three batches of cookies, we can set up a proportion using the ratio from the previous question:

2 eggs / 1 batch = x eggs / 3 batches

Solving for x, we can cross-multiply and get:

2 * 3 = 1 * x

x = 6 eggs

So, 6 eggs would be required to make three batches of cookies.

To find out how many batches of cookies can be made with 8 cups of flour, we need to consider the ratio of flour to batches. From the recipe, we know that 3 cups of flour make 1 batch of cookies. Using this information, we can set up a proportion:

3 cups flour / 1 batch = 8 cups flour / x batches

Solving for x, we can cross-multiply and get:

3 * x = 1 * 8

x = 8/3

Since we cannot have a fractional number of batches, we round down to the nearest whole number. Therefore, with 8 cups of flour, we can make 2 batches of cookies.

Given 6 cups of brown sugar and 3 eggs, we need to determine how many batches of cookies can be made. Since brown sugar is not a limiting factor, we can focus on the number of eggs. From the recipe, we know that 2 eggs are required to make 1 batch of cookies. Using this information, we can set up a proportion:

2 eggs / 1 batch = 3 eggs / x batches

Solving for x, we can cross-multiply and get:

2 * x = 1 * 3

x = 3/2

Since we cannot have a fractional number of batches, we round down to the nearest whole number. Therefore, with 6 cups of brown sugar and 3 eggs, we can make 1 batch of cookies.

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State whether sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
The sum of two vectors is the ₋resultant .

Answers

Given statement 'The sum of two vectors is the resultant.' is True.

We know that in mathematics, a vector is a quantity that has both magnitude and direction but no position.

Examples : velocity, force and acceleration.

Also, the resultant vector is the vector sum of two or more vectors. We find the resultant vectors by  adding two or more vectors together. Any two vectors can be added if and only if they are the same vector quantity.

For vector P = \(a\vec i+b\vec j\) and vector Q = \(m\vec i+n\vec j\)

The resultant vector R would be,

R = P + Q

R = \((a+m)\vec i+(b+n)\vec j\)

Therefore, given  statement 'The sum of two vectors is the resultant.' is True.

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Pete has 4 packs of gum balls. Each pack has 5 gum balls. If Pete
gives the same number of gum balls to 6 friends, how many gum
balls will each friend get?

Answers

Answer:

\(Each = 3\frac{1}{3}\)

Step-by-step explanation:

Given

\(Balls = 4\ pack\)

\(Gums = 5\ each\)

First we need to determine the number of gums

\(Total = 4 * 5\)

\(Total = 20\)

Divide 20 among 6 friends

\(Each = \frac{20}{6}\)

\(Each = 3\frac{1}{3}\)

Hence;

Each friend gets \(3\frac{1}{3}\ gum\)

what does a padaung woman who uses brass rings to stretch her neck illustrate about deviance?

Answers

Answer:

The practice of using brass rings to stretch the neck, also known as neck elongation or neck stretching, is traditionally associated with the Padaung ethnic group from Myanmar (formerly known as Burma).

From a sociological perspective, the use of brass rings to stretch the neck can be seen as an example of deviance, which refers to behavior that violates social norms and expectations. Deviance can be either criminal or non-criminal, depending on the specific behavior in question and the cultural context in which it occurs.

In the case of Padaung women, the use of brass rings to elongate the neck is a form of non-criminal deviance, as it does not violate any laws. However, it does violate cultural norms and expectations in many other societies, where elongated necks are not seen as desirable or attractive.

Therefore, the practice of neck elongation among Padaung women can be seen as a form of cultural deviance, in which members of a particular group engage in behavior that is not considered acceptable or desirable by the larger society in which they live. At the same time, it can also be seen as an expression of cultural identity and tradition, as the practice has been passed down through generations and is an important part of Padaung culture and heritage.

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Given the first type of plot indicated in each pair, which of the second plots could not always be generated from it. a). dot plot, box plot b).box plot, histogram c). dot plot, histogram d). stem and leaf, dot plot

Answers

The second plot that could not always be generated from a dot plot is a histogram. Thee correct option is c) dot plot, histogram.

What is histogram?

A histogram is a graphic depiction of a frequency distribution with continuous classes that has been grouped. It is an area diagram, which is described as a collection of rectangles with bases that correspond to the distances between class boundaries and areas that are proportionate to the frequencies in the respective classes.

The second plot that could not always be generated from the first plot in each pair is:

c) dot plot, histogram

A dot plot is a type of plot where each data point is represented by a dot along a number line. It shows the frequency or distribution of a dataset.

A histogram, on the other hand, represents the distribution of a dataset by dividing the data into intervals or bins and displaying the frequencies or relative frequencies of each interval as bars.

While a dot plot can be converted into a histogram by grouping the data points into intervals and representing their frequencies with bars, it is not always possible to reverse the process and generate a dot plot from a histogram. This is because a histogram does not provide the exact positions of individual data points, only the frequencies within intervals.

Therefore, the second plot that could not always be generated from a dot plot is a histogram.

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buy car at 320,000 and sell at 240,000 what is a loss ​

Answers

Answer: 80,000K

Step-by-step explanation: just subtract them

If f(x) = 2x2 − 10, find f(5). (1 point)

a
90

b
10

c
7.5

d
40

Answers

Answer:

D 40

Step-by-step explanation:

2x^2-10  if (5)

2(5)^2-10

2(25)-10

50-10

40

The top of Mount Romero is 123.5 feet above sea level. The bottom of Mount Romero is 32.7 feet below sea level. What is the distance between the top and bottom of the mountain?

Answers

Answer:

156.2

Step-by-step explanation:

mark brainliest

Got this on my math test today:
x^(-1/3)=32x^(-2)

Answers

The value of x for the given equation is 8.

What is Logarithm?

Logarithm function is defined as the inverse of the exponential function.

If a^(b) = c, then b = log(c) at the base of a.

For negative numbers, the logarithm are complex numbers.

The given equation is as below,

x^(-1/3) = 32x^(-2)

It can be solved as follows,

x^(-1/3) = 32x^(-2)

Take logarithm on both sides to obtain,

log (x^(-1/3)) = log (32x^(-2))

=> -1/3 log(x) = log(32) - 2log(x)

=> 2log(x) - 1/3 log(x) = log(32)

=> 5/3log(x) = log(32)

=> log (x^(5/3)) = log(32)

Remove log from both sides to get,

x^(5/3) = 32

=> x = 32^(3/5)

=> x = 8

Hence, the solution of the given equation is x = 8.

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PLEASE HWLP IM ON A TIME LIMIT

Determine f(–3) for A piecewise function f of x in three pieces. The function is defined by part 1, which is x cubed for x less than negative 3, part 2, which is 2 times x squared minus 9 for negative 3 is less than or equal to x which is less than 4, and part 3 which is 5 times x plus 4, for x greater than or equal to 4..

–27
–11
9
19

PLEASE HWLP IM ON A TIME LIMITDetermine f(3) for A piecewise function f of x in three pieces. The function

Answers

A function transfers each element's value from one set to a particular element in another set. When the value of x is -3, the function's value is -11.

What is a function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

As the function's value is required to be rounded when the value of x is -3, we can write the function as follows:

\(f(-3) = 5\text{x} + 4\) Because x has a value of -3,

\(f(-3) = 5(-3) + 4\)

\(\bold{f(-3) = -11}\)

Hence, when the value of x is -3, the function's value is -11.

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A class has six students. What is the probability that exactly four of the students were born on a weekend?

Answers

ANSWER

\(P\text{ = }\frac{400}{823543}\)

EXPLANATION

There are six students in the class.

There are 7 days in a week. There are 2 days in the weekend. There are 5 weekdays.

The probability that any student is born on the weekend is given as:

P(weekend) = 2/7

The probability of being born on a weekday is:

P(weekday) = 5/7

Now the probability that 4 out of the six students is born on a weekend will be given as the products of four of them born on a weekend and the remaining two born on a week day:

\(\begin{gathered} P(4\text{ are born on a weekend) = }\frac{2}{7}\cdot\text{ }\frac{2}{7}\cdot\text{ }\frac{2}{7}\cdot\text{ }\frac{2}{7}\cdot\text{ }\frac{5}{7}\cdot\text{ }\frac{5}{7} \\ P\text{ = }\frac{400}{823543} \end{gathered}\)

That is the probability that 4 out of 6 of them are born on a weekend.

The speedometer in Erin’s car is accurate within 2 miles per hour. It currently reads
56 mph. Write and solve an absolute value inequality to represent the situation. At what speeds could Erin be driving?

Answers

Answers:

The absolute value inequality is \(|\text{x}-56| \le 2\) which solves to \(54 \le \text{x} \le 58\\\\\) Her true speed could be anything between 54 mph and 58 mph, including both endpoints.

===================================================

Explanation:

x = Erin's true speed

Her true speed x is within 2 mph of 56 mph.

This means the interval for x is \(56-2 \le \text{x} \le 56+2\) which simplifies to \(54 \le \text{x} \le 58\)

She could be going as slow as 54 mph, or as fast as 58 mph, or something in between.

The expression |x-56| measures the distance from x to 56 on the number line. Recall absolute value is used to ensure the distance isn't negative.

We want this distance to be within 2 units, i.e. we want the distance to be 2 or smaller.

\(\text{distance on number line} \le 2\\\\|\text{x}-56| \le 2\)

----------------

Here's what the steps look like to solve that absolute value inequality

\(|\text{x}-56| \le 2\\\\-2 \le \text{x}-56 \le 2\\\\-2+56 \le \text{x}-56+56 \le 2+56\\\\54 \le \text{x} \le 58\\\\\)

For the second step, we use the rule that |x| < k is the same as -k < x < k where k is some positive number.

In the third step, I added 56 to all three sides to isolate x fully.

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