The Darnells are having a swimming pool installed. The pool has a radius of 14 feet and a height of 4 feet. What is the volume of the pool? Use 3.14 for pi .

The surface area of a regular pentagonal prism can be found by calculating the area of the pentagonal bases and the area of the rectangular sides and then summing those areas together.

Calculating the Surface Area of a Regular Pentagonal Prism

To find the surface area of a regular pentagonal prism with given dimensions, we need to calculate the area of two components: the area of the pentagonal bases and the area of the rectangular sides (also called the lateral faces). We are given that the side length (s) of the pentagon is 8 units, the prism's altitude (h), or height, is 20 units, and the apothem (a) is approximately 5.5 units.

Firstly, the area of a pentagon (Apentagon) is calculated using the formula Apentagon = ½ * perimeter * apothem, where the perimeter (P) of a regular pentagon is the side length multiplied by 5. Thus, the area of one pentagonal base is ½ * 5 * 8 * 5.5. Next, to find the entire area of the two pentagonal bases, we multiply this result by 2.

The area of each of the rectangular sides can be found by multiplying the side length by the prism's altitude. Since there are 5 identical rectangular sides in a regular pentagonal prism, their total area is 5 * 8 * 20.

Adding these two results together gives us the total surface area of the prism. So, the formula for the surface area is Total Surface Area = (2 * ½ * 5 * 8 * 5.5) + (5 * 8 * 20).

The spherical coordinates for the given rectangular coordinates (4,1,4) can be calculated using formulas for the transformation. They approximately yield (sqrt(33), 0.505, 1.540).

In mathematics, we can convert rectangular coordinates to spherical coordinates using given formulas. Here, we have the rectangular coordinates (4,1,4). The transformation from rectangular to spherical involves three-step calculations:

Applying the formulas, we get: r = sqrt(4^2 + 1^2 + 4^2) = sqrt(33), theta = cos^-1(4/sqrt(33)) which is approximately 0.505, and phi = cos^-1(4/sqrt(33)*sin(0.505)) which is approximately 1.540.

So, the spherical coordinates of the point whose rectangular coordinates are (4,1,4) are approximately (sqrt(33), 0.505, 1.540).

https://brainly.com/question/37212834

#SPJ11

In a glide reflection, the reflection comes first and the glide comes second.

In a glide reflection, first the reflection is applied, and second a glide is performed. The reflection is a transformation that flips the shape across a line of reflection, while the glide is a transformation that slides the shape along a vector. The combination of the reflection and glide creates a glide reflection.

https://brainly.com/question/2254222

#SPJ12

In a case whereby a star is 3.4 light years from earth. if 1 light years is 5.87×10^12 mi, the number of miles from earth the star is can be expressed as [tex]3.4 * 5.87 * 10^12 miles[/tex]

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given that  star=3.4 light years from earth

1 light years= [tex]5.87*10x^{12} miles[/tex]

The number of miles from earth is

[tex]3.4 * 5.87 *10^{12} miles\\\\=3.4 * 5.87 * 10^12 miles[/tex]

Learn more about number at

https://brainly.com/question/24644930

#SPJ2

Answer:

A on Edge 2021

[tex] \frac{x(x - 4)(x - 1)}{2(x + 4)} [/tex]

Answer:

V = 9025.8 cm3

Step-by-step explanation:

The total distance Preston covered on his camel safari is 9 km, and his displacement is 6.71 km toward the northeast.

Determining Distance and Displacement

To answer the student's question about Preston's journey during his camel safari, we need to consider the definitions of distance and displacement.

Distance is the total length of the path traveled regardless of direction. In Preston's case, he traveled 5 km north, then 3 km east, and then 1 km north again. Therefore, the total distance covered is the sum of these individual distances

Displacement, on the other hand, measures the change in position from the starting point to the final point and is direction-dependent. It is a vector quantity with both magnitude and direction. To find the displacement, we can represent Preston's movement on a coordinate system with north being the positive y-direction and east being the positive x-direction.

From the starting point, moving 5 km north and then 1 km north results in a total of 6 km in the positive y-direction.

The magnitude of the displacement can be calculated using the Pythagorean theorem:

√((6 km)² + (3 km)²) = √(36 km² + 9 km²) = √(45 km²) = 6.71 km (rounded to two decimal places)The direction of the displacement would be to the northeast. Therefore, Preston's displacement is 6.71 km toward the northeast.

Answer:

The correct answer is

C 40/41

Step-by-step explanation:

Answer:

the expression is [tex]8+2w[/tex]

Step-by-step explanation:

WE need to write the expression for the given statement

“the sum of eight and twice w”

Expression represents the terms that contains variables and operations. the variable we use for the expression is 'w'

Difference represents the subtraction operation.

Sum represents the addition operation.

twice 'w' means 2 times w that is 2w

the sum of 8 and 2w

For sum we use '+'

so ,the expression becomes [tex]8+2w[/tex]

Answer:

48  cubic meters.

Step-by-step explanation:

48x1

unit meter is cubic meters

The solution is: Jiri is 20 years old.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

Pamela is 13 years older than Jiri so:

p=j+13

Then you are told that the sum of their ages is 53 so:

p+j=53

We already know from the first statement that p=j+13, this makes p+j=53 become:

(j+13)+j=53  so we combine the two j's on the left side

2j+13=53  subtract 13 from both sides

2j=40  divide both sides by 2

j=20

So Jiri is 20 years old.

Hence, The solution is: Jiri is 20 years old.

To earn more on addition click:

brainly.com/question/29560851

#SPJ2

divide the base by the sin of the opposite angle

 base = 2

opposite angle = 30 degrees

2/sin(30) = 4

 x = 4

The maximum height would be 42.25 feet that the ball will reach.

Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.

A vertical upward throwing of a ball Its height h after t seconds (in feet) is given by the function h(t) = 52t - 16t²

Here h(t) = 52t - 16t²

Differentiate with respect to t to get maximum height

h'(t) = 52 - 2 × 16t

h'(t) = 52 - 32t

In this position, the acceleration would be zero,

So 0 = 52 - 32t

32t = 52

t = 52/ 32

t = 1.625

Substitute the value of t = 1.625 in the given function,

⇒ h = 52(1.625) - 16(1.625)²

⇒ h = 84.5 - 42.25

⇒ h = 42.25

Therefore, the maximum height would be 42.25 feet that the ball will reach.

Learn more about Velocity here:

https://brainly.com/question/12904979

#SPJ2

Segments with lengths of 36,48 and 60 can form a triangle. By employing the Pythagorean Theorem, we find that this is a right triangle as the lengths adhere to the theorem.

The question asks if segments with lengths of 36, 48, and 60 can form a triangle, and if so, the type of the triangle. Yes, these segments can form a triangle. To classify the triangle as obtuse, right or acute, we use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as c^2 = a^2 + b^2. Substituting our values: 60^2 equals to 36^2+48^2 (3600 = 1296+2304). Since both sides of the equation are equal, we get the conclusion that this is a right triangle.

https://brainly.com/question/4028542

#SPJ2

Answer with Step-by-step explanation:

We are given a pattern  

2 7 8 3 12 9

and we are asked to find the next term of this pattern

2+1=3

7+5=12

and 8+1=9

We can view this pattern in the set of three numbers and then, the next three are formed by  adding one, five & one, respectively.

See these COLUMNS of groups of three:

2  3   4

7 12 17

8  9  10

Hence, next number in the pattern is:

4