The base of a pentagonal prism is regular with an apothem of 4 cm. The height of the prism is 16 cm. Find the volume of the prism. Round your answer to the nearest cubic cm.

Answers

Answer 1

Answer:

volume ≈ 930 cm³ (nearest cubic cm)

Step-by-step explanation:

The base of the prism which is a pentagon is regular. The apothem which is a line drawn from the center to any side of the pentagon is 4 cm. The height of the prism is 16 cm.

The volume of a prism = Bh

where

B = base area

h = height of the prism

The base of the prism can be divided into 5 congruent triangles.But the base of the triangles is unknown.

The sum of interior angle of a pentagon is 540°. That means each angle is 108° . The triangle divide the angle into 2. Making the 2 base angle as 54° each. The last angle of the triangle at the center is 72°(remember sum of angle in a triangle is 180° which is 54° + 54° + 72° = 180°) .

The angle form the center can be divided by the line of height of the triangles. The angle will then be 36°. Using tangential ratio half of the length of the base of the triangle can be known. Therefore,

tan 36° = opposite/adjacent

tan 36° = opposite/4

opposite = 4 tan 36°

The full base of the triangles = 2(4 tan 36°)

area of each triangle = 1/2 × 2(4 tan 36°) × 4 = 16 tan 36°

Base area of the prism(pentagon) = 5 × 16 tan 36° = 80 tan 36°

Volume of the prism = Bh

where

h = 16 cm

B = 80 tan 36°

volume =  80 tan 36° × 16 = 1280  tan 36° = 1280  × 0.726542528

volume = 929.974435847  cm³

volume ≈ 930 cm³ (nearest cubic cm)


Related Questions

Answer choices for both of them are
A) linear
B) exponential
C) quadratic

Answers

Answer:

#16 is linear but idk what 17 is

PLEASE HELP ME I BEG

Answers

Answer:

x = 3

Step-by-step explanation:

Applying Pythagoras' identity to the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + x² = ([tex]\sqrt{18}[/tex] )², that is

2x² = 18 ( divide both sides by 2 )

x² = 9 ( take the square root of both sides )

x = [tex]\sqrt{9}[/tex] = 3

I will give brainliest to the first person who answers.

Answers

Answer:

the answer is [tex]\sqrt{5\\}[/tex] , and - [tex]\sqrt{5\\}[/tex] which is C.

Step-by-step explanation:

well I got that answer by doing this

we have [tex]x^{2}[/tex]= 5

For [tex]x^{2}[/tex]= f (a) the solutions are x = [tex]\sqrt{f(a)\\}[/tex] , - [tex]\sqrt{f(a)\\}[/tex]

so in this case the solutions are [tex]\sqrt{5\\}[/tex], and - [tex]\sqrt{5\\}[/tex]

HOPE THIS HELPS :)

Doug believes that the function y=6 is linear, while Olga believes that it is not linear. Who is right, and why?
A
Doug is right, because the function cannot be written in the form y = mx + b.
B
Doug is right, because the function can be written in the form y = mx + b, with m = 0.
С
Olga is right, because the function cannot be written in the form y = mx + b
D
Olga is right, because the function can be written in the form y = mx + b. with m = 0

Answers

Answer:

A

Step-by-step explanation:

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be  0  or  1  for each of its variables. In this case, the degree of variable  y  is  1 .

Sara has x dollars and Dina has 15 dollars less than Sara . Together the number

of dollars they have is?

Answers

Answer:

2x-15

Step-by-step explanation:

Sara has x dollars

dina has 15 less which is

x-15

together it will be

x+x-15

=2x-15

Doing a test and timed so please help1

Answers

Answer:

20

Step-by-step explanation:

The hypotenuse is always the largest number and side length in a right triangle. We know the answer is 20 because it is the largest number.

'Ello there! 20 points and brainliest!!! FOR JOHAN!!

List 3 expressions that equal the number 12
List 2 expressions that equal the number 2

Wow this question is literally the hardest thing I have ever seen PLEASE HELP MEEE!!!

Answers

Answer:

for twelve: 4 x 3, 9 + 3, 24 / 2.

for two: 1 x 2, 1 + 1.

Step-by-step explanation:

4 x 3 = 12, 9 + 3 = 12, 24 / 2 = 12

1 x 2 = 2, 1 + 1 = 2.

plz help!!! Drag the tiles to the correct boxes to complete the pairs.
Match each point of intersection with the system of equations whose solution is at that point. (look at image)

Answers

Answer:

Step-by-step explanation:

Each point of intersection with the system of equations was matched.

what is a linear equation?

Any equation in the form [tex]ax+by+c=0[/tex] is called a linear equation where a,b,c∈R.

In the given diagram, to find the intersection of two lines, solve the equations of two lines.

1)[tex]\left \{ {{y=-2x-3} \atop {y=2x-1}} \right.[/tex]

The solution of the given system of equations comes to be x=-1/2 and y=-2.

So they will intersect at (-1/2, -2) i.e. same as the graph.

2)[tex]\left \{ {{y=x+4} \atop {y=-x+2}} \right.[/tex]

The solution of the given system of equations comes to be x=-1 and y=3.

So they will intersect at (-1,3)

Similarly, the other two systems of equations will intersect at (-7/3,5/3) and (-1,1) respectively.

Hence, each point of intersection with the system of equations was matched.

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Please give me the answer

Answers

Answer:

5.3

Step-by-step explanation:

Which expressions can never result in a negative real number when evaluated for any value of x? Select all that apply.
1) x^1/2

2)x^2/3

3)x^-3/5

4)x^-1/2

5)x^1/3​

Answers

It is 5 beacause the x^1/3

The expressions that can never result in a negative real number when evaluated for any value of x are x^1/2, x^2/3 and x^1/3

1) x^1/2

find the square root

[tex]= √x^1/2

[/tex]

[tex]= x^1[/tex]

= x

2) x^2/3

[tex]= 3√x^2/3[/tex]

=

3) x^-3/5

[tex]= 5√x^-3/5[/tex]

[tex]= x^-3[/tex]

[tex]= 1/x^3[/tex]

4) x^-1/2

[tex]= √x^-1/2[/tex]

,

[tex]= x ^-1[/tex]

[tex]= 1/x[/tex]

5) x^1/3

[tex]= 3√x^1/3[/tex]

[tex]= x^1[/tex]

= x

Therefore, the expressions that can never result in a negative real number when evaluated for any value of x are x^1/2, x^2/3 and x^1/3

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Use the values log 48 congruant to 1.68 and log 3 congruant to 0.48 to find the approximate value of log3 48.

Answers

Answer:log(48) = 1.68124

Step-by-step explanation:

After checking for the values of log 48 and log 3, then the approximate value will be 1.08.

What is an arithmetic operation?

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers.

Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given information in the question,

log(48) = 1.68

log(3) = 0.48

Then, the approximate value of log 3 and log 48 will be: 1.08

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What is the average rate of change of g over the interval -8≤t≤2? Give an exact number.

Answers

Per the plot, looks like g(-8) = 1 and g(2) = -4. Then the average rate of change of g over [-8, 2] is

(g(2) - g(-8)) / (2 - (-8)) = (-3  - 1)/10 = -2/5


Consider the equation -2x+3y=6.
Write the equation in slope-intercept form.


Identify the y-intercept.

Identify the slope.

Answers

Answer:

y=2/3x+2

Step-by-step explanation:

PLS ANSWER ASAP 12 POINTS

Answers

Answer:

2/9

Step-by-step explanation:

its in the range to be 2/9

Function A is represented by the equation

y=1/3x+5. Function B is represented by the graph. Which function has a greater rate of change? explain.

Answers

Answer:

They have the same rate of change.

Step-by-step explanation:

Well the graph of Function B is y = 1 / 3x + 2

So they have the same rate of change, since they have the same slope.

Identify the points corresponding to P and Q.

Answers

Answer:

the first one( even though it has an error : P is (-2,1) ) and because the Q is correct there too.

2. Making sure your calculator is in DEGREE MODE, evaluate each of the following an
verify that they either match or are close to the ratios you found in #1.
(a) sin( 67 ) =
(b) cos(67 ) =
(c) tan (67") =

Answers

Answer:

a. 0.921

b. 0.391

c. 2.356

Enter the quotient.
6532 ÷ 23 =

Answers

The answer is 284.

If you know how to do long division, you will be able to show your work.

Answer:

284

Step-by-step explanation:

Below are the average incomes for different education levels. How does the outlier affect the mean?mm

Answers

Answer:

It affects the Mean by how many different numbers.

Step-by-step explanation:

Find the medianDetermine all of your answers. and Figure out if the mean and the outlier are similiar.

HURRY!! WILL MARK BRAINLIEST!!!
whixhxh two points on the number line are opposites? !!HURRY WILL CASHAPP 10 BUCKS. ​

Answers

Points A and D are opposites.

Answer:

points a and d because point a is -1 and 2/3 and point d is 1 and 2/3 so they are opposites

The diameter of a circle measures 8 cm. What is the circumference of the circle?
Use 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.

Answers

Answer:

16π or 50.266

Step-by-step explanation:

Circumference formula is just 2πr ,and the radius is 8, so just sub into the formula

Answer: 25.12 cm

Step-by-step explanation:

The formula for the circumference of a circle is [tex]2\pi r[/tex], when r = the radius.

Diameter = 2 x radius = 8 cm. Therefore, the radius = 4 cm.

Plug r = 4 cm in to the circumference formula: [tex]2\pi (4)[/tex] = 8 x 3.14 = 25.12 cm.

Given: m arc AB = 4x, m arc BC = 3x
m arc CD = 2x, m arc DA = 3x
Find: m∠APB

Answers

Answer:

a > m/bp

Step-by-step explanation:

flip the equation

abp > m

divide both sides with bp

abp/bp > m/bp

a > m/bp

Answer:

m<APB = 30 degrees

Step-by-step explanation:

The sum of angles in a circle is 360 degrees. Add up all the arcs to get the equation : 4x+3x+2x+3x=360 degrees.

x is equal to 30 degrees

m arc AB = 4x = 120 degrees

m arc DC = 2x = 60 degrees

By secants exterior angles, m<APB = 1/2(m arc AB - m arc DC) = 1/2(120-60) = 30 degrees.

The answer is m<APB = 30 degrees

pls help will mark as brainliest

Answers

Answer:

The measure of the hypotenuse is 25.

Step-by-step explanation:

To solve, we can use the Pythagorean theorem a² + b² = c² where,

a = 7

b = 24

(7)² + (24)² = 625

We have to take the square root of 625 to get our answer.

[tex]\sqrt{625} = 25[/tex]

Answer:

25

Step-by-step explanation:

This is a right triangle. This is because of the little square in the corner that indicates a right angle. Therefore, we can use the Pythagorean Theorem.

a^2+b^2=c^2

where a and b are the legs, and c is the hypotenuse.

We know that 7 and 24 are the legs, because they make up the right angle. We know c is the hypotenuse because it is opposite the right angle.

7^2+24^2=c^2

Evaluate the exponents on the left side.

49+576=c^2

Add 49 and 576

625=c^2

Since c is being squared, take the square root of both sides. This will cancel out the exponent, and leave c by itself.

√625= √c^2

√625=c

25=c

The measure of the hypotenuse is 25

DUE NOW PLZ HELP
6, 9, 3, 7, 8, 7, 5
minimum:
maximum:

Answers

Answer:

minimum is 3 and maximum is 9

Step-by-step explanation:

your min is 3 and ur max is 9

PLZ HELP I NEED IT ASAP!

Answers

Answer:

4

Step-by-step explanation:

Since it is going up four and over one you would just simplify 4/1 to just being 4.

The correct answer is 4 as it’s going up 4 —> 4/1 simplified to 4

Please help due in 20 minutes!

Answers

Answer:

x =12

Step-by-step explanation:

We use the Pythagorean theorem

a^2 + b^2 =c^2 where a and b are the legs and c is the hypotenuse

x^2 + 5^2 = 13^2

x^2 +25 =169

Subtract 25 from each side

x^2 +25-25=169-25

x^2 = 144

Take the square root of each side

sqrt(x^2) = sqrt(144)

x = 12

10 over 13 as a decimal rounded to the nearest tenth

Answers

Answer:

0.7

Step-by-step explanation:

If you divide 10 by 13 you get 0.76923 which rounded to the nearest tenth is 0.7

Hope this helped!

Answer:

0.8

Step-by-step explanation:

To find the decimal form of [tex]\frac{10}{13}[/tex] you'll need to divide 10 by 13.

10 ÷ 13 = 0.76923076923

The tenths decimal place is one to the right of the decimal: 0.1

Because the number after the tenths place is greater than or equal to 5, we will round the 0.7 up to a 0.8

convert the mixed number to an improper fraction. enter your answer below using the slash mark ( / ) as the fraction bar.
4/frac{1}{8}

Answers

33/8 is the correct answer

What is y=2(x+1)^2 in standard form

Answers

Y=4x+4
I think this is it u just have to simplify to get it to y=mx+b

Answer:

[tex]y=2x^2+4x+2[/tex]

Step-by-step explanation:

[tex]y=2(x+1)^2[/tex]

[tex]y=2(x^2+2x+1)[/tex]

[tex]y=2x^2+4x+2[/tex]

Need Help On This
simplify:
9a(-4a^3 b^5)(-2a^4 bc^6)

Answers

Answer:

72a^8b^6c^6

Step-by-step explanation:

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