answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Mkey [24]
2 years ago
7

Find the volume of the regular hexagonal prism with side lengths of 4 ft, height of 3ft and apothem of approximately 3.5 ft

Mathematics
1 answer:
nexus9112 [7]2 years ago
3 0

Answer:

A(p)  = 84 ft³

Step-by-step explanation:

Volume of regular prism is equal to V(p):

V(p)  = Area of the face * h

we know h = 3 ft

A regular hexagonal prism has 6 equal sides forming its face.

Finding the area (A₂) of a triangle formed  by center of the prism, straight lines between the center and two adjacents vertex and side between these two vertex, and then multiply that area by 6 (number of equal triangles inside hexagonal prism) we get the area of the face, but  we need further consideration, the triangle described above, has doble area of (A₁), the triangle formed by apothem, half side, and straight line between center of the face and the vertex, therefore.

Area of small triangle = base * height

A₁  = (1/2) * 4 * 3,5

A₁  =  2*3,5

A₁  = 7 ft²

A₂  = 2* 7    

A₂  = 14 ft²

Finally volume  of the hexagonal prism is:

V(p) = 6 * 14

A(p)  = 84 ft³

You might be interested in
Alan, Bill, and Calvin are playing a game with collectible cards. At the moment, Alan has 11 less than times the number of cards
Mama L [17]
<span> a=2.5b-11, c=1.5b+1, and a=c so

2.5b-11=1.5b+1

b=12 so a=19 and c=19

so a+b+c=50 </span>
8 0
2 years ago
The resultant of a certain system of forces has the X and Y components shown in Fig. 220. Determine the components of this resul
Alchen [17]
First, you need to determine the resultant force and its angle. This one is real easy, since you only have one (x) and one (y) component. X = 300 and Y = 480 

<span>1) sqrt (300^2 + 480^2) = ? (round your answer) </span>
<span>2) tanθ = y/x Solving for θ: θ = tan^-1(y/x): θ = ? (round your answer) </span>

<span>Now, you should have a resultant force value and its angle, from zero, in the first quadrant and between the Y and N axes. Draw yourself a diagram showing all of the axes, the resultant and the angles. You're going to have to do some very easy math to determine the angles between the Y and N axes and the resultant. Call these new angles α and β. α is the angle between N and the resultant and β is the angle between T and the resultant. Hint: one of them is 28 deg. </span>

<span>Once you've gotten those figured, the Y and N axes become your new axis, ignore the X and Y. Find the X and Y components of the resultant (again). ? * cos(α) = 500 and ? * sin(β) = 266 (round your answers)</span>
7 0
2 years ago
What additional information could be used to prove that △ABC ~ △NML? Check all that apply. ∠B ≅ ∠M △ABC is a right triangle. △AB
Elena L [17]

Answer:

1,3,5

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
An air conditioning technician charged Robert $77.25 to repair his air conditioning system after 3 hours of work. The technician
agasfer [191]

Answer:B

Step-by-step explanation:

He charged the man $25.75 for each hour and he worked for 3 hours so multiply $25.75 x 3 = $77.25

5 0
1 year ago
Suppose we have a group of 10 light users and 10 heavy users. what is the probability that exactly 3 of the 20 users are hiv pos
dmitriy555 [2]

Answer: The answer is 30%.


Step-by-step explanation:  Given that there is a group of 10 light users and 10 heavy users. We are to find the probability that exactly 3 of the 20 users are HIV positive.

We have the following four possible cases -

(i) All 3 are light users.

(ii) 1 is a light user and 2 are heavy users.

(iii) 2 are light users and 1 is a heavy user.

(iv) All 3 are heavy user.

Since there is a 45% chance of a light user to be HIV positive and 55% chance of a heavy user to be HIV positive, so the required probability is given by

p\\\\=\dfrac{3\times 0.45+1\times 0.45+2\times 0.55+2\times 0.45+1\times 0.55+3\times 0.55}{20}\\\\=\dfrac{6}{20}\\\\=0.3\\\\=30\%.

Thus, the probability is 30.

4 0
2 years ago
Other questions:
  • The 230 people at a party decide to order pizza for a snack. If each pizza has 8 slices, how many pizzas should they order so th
    5·2 answers
  • If f'(x)=2/x and f(sqrt(e))=5, then f(e)=
    14·1 answer
  • NEED HELP!!!! Based on this part of the soliloquy, which best describes Hamlet’s perception of life?
    6·2 answers
  • Which two equations would be most appropriately solved by using the zero product property? Select each correct answer.
    6·2 answers
  • Please answer ASAP<br><br> 5x−29&gt;−34 OR 2x+31&lt;29
    11·2 answers
  • Enrollment in a school has grown exponentially since the school opened. A graph depicting this growth is shown. Determine the pe
    14·2 answers
  • N 1928, when the high jump was first introduced as a women's sport at the Olympic Games, the winning jump for women was 70.0 inc
    11·1 answer
  • This graph shows how much Marie earns babysitting, compared with the number of hours she works. Select the correct statement abo
    7·2 answers
  • Find the value of y for a given value of x, if y varies directly with x.
    10·1 answer
  • 12 pots cost $27 . what is the cost of 8 pots?​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!