Find the radius of the circle whose equation is 3x² + 3y² = 75.

The problem involves the concept of related rates in Calculus. By using the relationship between the height and radius of the cone and the rate of change of the volume, we set up a differential equation. Upon solving, we find the rate at which the height of the pile changes is 5/(18π) feet per minute when the pile is 12 feet high.

The subject matter of this question is related to Calculus, specifically the concept of related rates. In this scenario, sand is falling off a conveyor and onto a conical pile at a rate of 10 cubic feet per minute. Here, the given rate is the rate of change of the volume of the sand pile. The diameter of the base of the cone is approximately three times the altitude, which gives the relationship between the height and the radius of the cone: r=h/3. The student is asked to find at what rate the height of the pile is changing when the pile is 12 feet high.

First, let's recall the formula for the volume of a cone, which is V=(1/3)*π*r²*h. Based on the relationship between the radius and the height, we can substitute r with h/3. Therefore, the volume V=(1/3)*π*(h/3)²*h = (1/27)*π*h³. By differentiating this equation with respect to time t, we get dV/dt = (1/9)*π*h²*dh/dt.

We are given that dV/dt is 10 cubic feet per minute, and we want to find dh/dt when h = 12 feet. Substituting these values into the differentiated equation, we get 10 = (1/9)*π*(12²)*dh/dt. Solving this for dh/dt, we find that dh/dt = 10 / [(1/9)*π*(12²)] = 5/(18π) feet per minute.

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Final answer:

To calculate the total length of the boards, the first board at 47/100 meters (0.47 meters) is added to the second board at 5/10 meters (0.5 meters), resulting in a total length of 0.97 meters.

Explanation:

To find the total length of the two boards placed end to end, we simply add the lengths of the individual boards. The first board is 47/100 meters long, and the second board is 5/10 meters long.

The second board's length can be simplified as 5/10 is equivalent to 1/2, which is 0.5 in decimal form. Adding the lengths together, we get:

Length of board 1: 47/100 meters (or 0.47 meters)
Length of board 2: 5/10 meters (or 0.5 meters)

Total length = 0.47 meters + 0.5 meters
Total length = 0.97 meters

Therefore, the total length of the two boards when placed end to end is 0.97 meters.

Answer:

3 miles per hour

Step-by-step explanation:

Using speed formula:

[tex]\text{Speed} = \frac{\text{Distance}}{\text{Time}}[/tex]

As per the statement:

Team tool Bella canoed 15 3/4 miles in 5 1/4 hours.

⇒[tex]\text{Distance} = 15\frac{3}{4} = \frac{63}{4}[/tex] miles and

[tex]\tetx{Time} = 5\frac{1}{4} = \frac{21}{4}[/tex] hours

Using speed formula we have;

[tex]\text{Speed}= \frac{\frac{63}{4} }{\frac{21}{4}} = \frac{63}{4} \cdot \frac{4}{21} = \frac{63}{21}[/tex]

Simplify:

[tex]\text{Speed} =3[/tex] miles per hour

Therefore, their average rates of speed in miles per hour is, 3 miles per hour

Answer: The value of BP is 5.25.

Step-by-step explanation:

Here's why:

Find the ratio between the two different groups of line segments. If you do it in decimal or fraction, it's the same. So, 4/6 = 0.666666667. Then you must find the number that when 3.5 is divided by it, gives you 0.666666667. So that number is 5.25.

Answer:

8

Step-by-step explanation:

They do not occur more frequently than any other value in the distribution, the values 220, 260, 250, and 270 are not modes.

Distributed mode is the most common value. From the given frequency distribution we can see that both the values ​​220 and 230 occur with the highest frequencies of 6 and 7 respectively. Therefore, both 220 and 230 are modes of this distribution.

that the values ​​260, 250, and 270 are not modes, as they all have frequencies of 0 or 1. Also, the No Mode value is not a valid value in the distribution, indicating that there is no single mode value.

The values 220, 230, 240, 250, 260, and 270 all appear six times in this distribution, seven times each for values 230, seven times for values 240, one for value 250, zero for values 260, and one for value 270.

As a result, the value with the highest frequency—230—is the mode. Therefore, 230 is the mode for this distribution.

Due to the fact that they do not occur more frequently than any other value in the distribution, the values 220, 260, 250, and 270 are not modes.

To know more about distribution visit:-

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A Punnett square is used to predict the genotypic and phenotypic probabilities of possible offspring. It helps in illustrating how combinations of alleles might come together during fertilization. However, it cannot determine if a trait runs in a family or track inherited traits through generations.

A Punnett square is a common tool used in genetic studies to predict the genotypic and phenotypic probabilities of possible offspring when the genetic information of both parents is known. It is not used to determine if a trait runs in a family, track inherited traits through many generations, or identify organisms that are carriers of a specific trait. A Punnett square can help illustrate how different combinations of alleles might come together during fertilization and what traits these combinations could produce. For instance, if both parents carry a recessive trait, a Punnett square can show the possibility of their offspring inheriting that trait.

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The number that when multiplied by itself 3 times equals 125 is 5.

To find the number that when multiplied by itself 3 times equals 125, we need to find the cube root of 125. The cube root of 125 is 5, so the number is 5.

To compare these two jobs, you need to have a common point. In this problem, you have to solve for the annual salary of the first job and compare it with the annual salary of the second job which is already given.

$12 per hour x 40 hours per week x 48 weeks in a year = $23,040

First job’s annual salary is $23,040

Second job’s annual salary is $22,000

Therefore, the job which pays $12 an hour pays more.

Latrell will earn more at the job that pays $12 per hour for a 40-hour workweek, which totals $24,960 per year, compared to the annual salary of $22,000 for a 45-hour workweek.

To determine which job pays more between an hourly wage job and an annual salary job, we need to calculate the total annual income for each option.

For the hourly wage job at $12 per hour for 40 hours a week:

For the annual salary job of $22,000 for 45 hours a week, the total annual income is:

Comparing the two annual incomes:

Therefore, the job that pays $12 per hour for 40 hours a week offers a higher annual income than the job with an annual salary of $22,000 for 45 hours a week.

The rectangle diagonally into 2 right triangles: one with base 5 and height 13, another with base 12 and height 5. Doubling their areas (5*13+12*5) gives 180!

The area of a rectangle with a base of 5 cm and a height of 13 cm is indeed 180 square centimeters..

Here's a simpler explanation:

Imagine slicing the rectangle diagonally into two right triangles. One triangle has base 5 cm and height 13 cm. The other triangle has base 12 cm and height 5 cm (using Pythagoras to find the missing side).

Now, the area of the rectangle equals the sum of the areas of these two triangles. Adding their areas (5 * 13 + 12 * 5) gives us 65 + 60, totaling 180 square centimeters.

Therefore, the true area of the rectangle is 180 square centimeters, not 65 or any multiple of the individual base and height alone. This hidden relationship between the diagonal and sides creates the surprising answer.