A cylinder has a radius of 14m and a height of 6m what is the exact volume of this cylinder

The rocket takes approximately 8.6 seconds to return to earth.

To calculate the time it takes for the rocket to return to earth, we need to consider the projectile motion in the vertical direction. The initial vertical velocity of the rocket is 42 m/s. We can use the equation for vertical displacement to find the time:

Δy = v0yt + (1/2)gt²

Since the rocket returns to the same altitude, the displacement is 0. Therefore, we have:

0 = (42)t + (1/2)(-9.8)t²

Simplifying this equation and solving for t, we find that it takes approximately 8.6 seconds for the rocket to return to earth.

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The lateral area of the triangular prism is 21 square inches and the total surface area is 35 square inches.

To find the lateral area of the triangular prism, we need to calculate the area of all three sides excluding the bases. Since the bases are equilateral triangles with side lengths of 4 inches, the area of each base is ½ × base length × height = ½ × 4 × 3.5 = 7 square inches. The lateral area is the sum of the areas of the three sides, which is 3 × 7 = 21 square inches.

The total surface area of the prism includes the bases as well. So we need to calculate the area of the two triangular bases and add it to the lateral area. The total surface area is 2 (area of base) + lateral area = 2 × 7 + 21 = 35 square inches.

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The lateral area of the triangular prism is 60 square inches, and the total surface area is 74 square inches.

To find the lateral area and total surface area of a triangular prism:

Step 1: Calculate the Area of One Triangular Base

        [tex]Area = \frac{1}{2}*base*height[/tex]

       [tex]Area = \frac{1}{2} *4\ in*3.5\ in = 7\ square\ inches[/tex]

Step 2: Calculate the Perimeter of the Base

        Perimeter = 3 * side length = 3 * 4 in = 12 inches

Step 3: Calculate the Lateral Area

        Lateral Area = Perimeter * height of the prism

        Lateral Area = 12 in * 5 in = 60 square inches

Step 4: Calculate the Total Surface Area

Thus, the lateral area and total surface area are 60 square inches and 74 square inches.

Answer:

[tex]9x^{2}+42xy+49y^{2}[/tex]

Step-by-step explanation:

we know that

[tex](a+b)^{2}=a^{2}+2ab+b^{2}[/tex]

In this problem we have

[tex](3x+7y)^{2}[/tex]

so

[tex]a=3x[/tex]

[tex]b=7y[/tex]

substitute

[tex](3x+7y)^{2}=(3x)^{2}+2(3x)(7y)+(7y)^{2}[/tex]

[tex]=9x^{2}+42xy+49y^{2}[/tex]

The Earth is older than any rock layer. This fact is determined through the use of principles like the law of superposition and radioactive dating methods, such as uranium-lead dating. The oldest rocks on Earth have been dated to be almost 4.4 billion years old, whereas the Earth itself is estimated to be around 4.5 billion years.

This is based on geological principles and radioactive dating methodologies. One of the foundational principles in geology is the law of superposition, which states that in an undisturbed sequence of rock layers, each layer is younger than the one below it.

The age of Earth is estimated to be around 4.5 billion years. We can deduce this from radioactive dating methods, such as uranium-lead dating. In this method, the oldest rocks on Earth, known as the Jack Hills zircons from Australia, have been dated at almost 4.4 billion years old.

Given these findings, it is understood that no existing rock layer can be older than the Earth itself.

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B. The Earth is older than any rock layer.

The Law of Superposition states that in an undeformed sequence of sedimentary rocks, the bottom layer is the oldest and the top layer is the youngest. Applying this principle to the Earth's rock layers, we can conclude that the Earth is older than any rock layer as the layers closer to the surface are younger compared to those at the bottom.

Answer:

2(5x + 6)

Step-by-step explanation:

i think you need to rearrange 12 + 10x which that is also 2(5x + 6) ?

sorry if i didn't explain well  

Answer:

i Don’t understand

Step-by-step explanation:

pls give me brainliest for the love of god

We can use the Pythagorean theorem to find the length of the third sides.

c²=a²+b²

Where c is the longest (unkwon ) side, a and b are the remaining sides. So,

c²=7²+3²

= 49+9

= 58

So, c=√58

So, the length of the third side or the side length of square is √58.

So, the area of the shaded region (square)= c²

=(√58)²

=58

So, the area of the square is 58 units².

Answer: 58 units squared

Step-by-step explanation:

We are given

sequence is 2 , 4 , 8 ,16 , 32 , .....

Firstly , we will check whether it is geometric sequence

Checking geometric sequence:

We will find common ratio between successive terms

and then we check whether they are equal

r1=(second term)/(first term)

[tex] r_1=\frac{4}{2}=2 [/tex]

r2=(third term)/(second term)

[tex] r_2=\frac{8}{4}=2 [/tex]

r3=(fourth term)/(third term)

[tex] r_3=\frac{16}{8}=2 [/tex]

r4=(fifth term)/(fourth term)

[tex] r_4=\frac{32}{16}=2 [/tex]

we can see that all four ratios are same

[tex] r_1=r_2=r_3=r_4=2 [/tex]

so, this is geometric sequence

Calculation of general term:

We got

common ratio is

[tex] r=2 [/tex]

Let's assume

number of terms is n

first term is 2

[tex] a_1=2 [/tex]

now, we can use formula

[tex] a_n=a_1 (r)^{n-1} [/tex]

we can plug values

and we get

[tex] a_n=2(2)^{n-1} [/tex]

[tex] a_n=2^1(2)^{n-1} [/tex]

[tex] a_n=(2)^{n-1+1} [/tex]

[tex] a_n=(2)^{n} [/tex]..................Answer

Answer:

a1: 2     r1: 2

Step-by-step explanation

just did it on edge :)

the answer for the second part is the 1st and 4th formulas

Answer:

sometimes

Step-by-step explanation:

Two prisms with the same volume sometimes have the same surface area, but not always, because surface area depends on the dimensions of all prism faces. Different shapes with the same volume, such as a sphere, a cube, and a cylinder, can have significantly different surface areas, especially if their proportions change.

If two prisms have the same volume, they do sometimes have the same surface area, but not always. The volume of a prism is determined by the area of the base multiplied by the height, but the surface area includes the areas of all the faces of the prism.

Therefore, two prisms can have the same volume, but if their dimensions—base areas and heights—are different, their surface areas can be very different as well. This holds true for other geometric shapes as well.

For instance, consider a sphere, a cube, and a cylinder that all have the same volume. According to the formula for a sphere, sphere: volume = 4/3 (pi) (r)³; surface area = 4 (pi) (r)², for a cube, cube: volume = (s)³; surface area = 6 (s)², and for a cylinder, cylinder: volume = height (pi) (r)²; surface area = 2 (pi) (r) (height) + 2 (pi) (r)². Even if all these shapes have a volume set at 1 unit cubed, their surface areas can vary significantly.

Furthermore, changing the shape's proportions while keeping the volume constant (such as elongating a cylinder or a cube) generally increases the surface area.

This is showcased in data where cylinders and cubes shapes elongated in length or width have different surface areas but maintain the same volume.

x = 112  

This is because

7/4 x 4/7 = 64/1 x 7/4                        

1x= 448/4                                           

Answer:

d

Step-by-step explanation:

hope it helps

Answer: A . selection bias

Step-by-step explanation:

The required d is the dependent variable and t is the independent variable.

In mathematics, an equation is a statement that asserts the equality of two expressions. It typically contains one or more variables, which represent unknown values.

In the equation, d=60t, t is the independent variable and d is the dependent variable. The value of d depends on the value of t, which is the amount of time the car travels, and hence is the independent variable.

Thus, d is the dependent variable and t is the independent variable.

Learn more about equations here:

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Answer:

What music genre is the 26 to 36 age group’s favorite?  It's pop

How many people from the 37 to 47 age group like ‘other’ music? 20 people

Which three genres has the most fans? "Pop", "Rock" and "Dance"

Step-by-step explanation:

What music genre is the 26 to 36 age group’s favorite?

 The colors indicate the different age ranges. So first you must locate the color belonging to the range of 26 to 36 years, which is gray.

Now, you place that color in the graph and to determine which genre of music is the favorite in that age, you must place the genre with more people aged between 26 and 36. That reads on the “y” axis, which in the graph is seen as "the tallest gray rectangle". Once this is located, you read on the "x" axis the genre to which it belongs. This results in the music genre "pop"

How many people from the 37 to 47 age group like ‘other’ music?

For this case, as in the previous case, you first locate the color belonging to the age range of 37 to 47, which is the color yellow.

But now you must first place that color on the "x" axis, which is the one corresponding to the music genre. In this case you locate the genre "others". Then with the yellow color you read the number of people on the "y" axis.

Note that the numbers marked are every 100, but that between each number there are 5 divisions. This means that the scale is 20 people (obtained as 100 divided by 5)

The color belonging to the age range of 37 to 47 in the genus "others" reaches the first division. This means that the number of people who like this genre is 20.

Which three genres has the most fans?

In this case you should pay attention to which genders ("x" axis) have the greatest number of people ("y" axis), regardless of age. Observing "the longest colored rectangles", which indicate that more people like the genre, and reading the axis of music genres, you can see that the three genres that have more fans are "Pop", "Rock" and "Dance"