15 POINTS!

What is the Surface area and volume of all the parts of the castle?

Ber [7]

N 1 FRONT LEFT TOWER

[surface area of a prism]=[area of the base]+perimeter*h------> only one base
[surface area of a prism]=[3*3]+[4*3]*50----> 609 units²

[surface area of a triangular pyramid]=[area of the 4 triangles]----> without base
[area of 1 triangle]=3*h/2
h²=3²+1.5²----> h²=11.25-----> h=√11.25 units
[area of 1 triangle]=3*√11.25/2-----> 5.03 units²
[surface area of a triangular pyramid]=[4*5.03]-----> 20.12 units²

surface area of the front left tower=609+20.12-----> 629.12 units²

[volume of a prism]=[3*3*50]=450 units³
volume of a triangular pyramid]=[area of the base]*h/3
volume of a triangular pyramid]=[3*3]*3/3-----> 9 units³

[volume of the front left tower]=450+9------> 459 units³

N 2 FRONT RIGHT TOWER

[surface area of a cylinder]=[area of the base]+perimeter*h--> only one base
[surface area of a cylinder]=[pi*3²]+[2*pi*50]--> 342.26 units²

[surface area of a cone]=pi*r*l------> without base
r=3 units
l²=r²+h²-----> 3²+3²-----> 18---------> l=√18 units
[surface area of a cone]=pi*3*√18------> 39.97 units²

surface area of the front right tower=342.26+39.97------> 382.23 units²

[volume of a cylinder]=pi*r²*h
[volume of a cylinder]=pi*3²*50-----> 1413 units³

[volume of a cone]=pi*r²*h/3
[volume of a cone]=pi*3²*3/3----> 28.26 units ³

[volume of the front right tower]=1413+28.26-----> 1441.26 units³

N 3 BACK LEFT TOWER
[surface area of a cylinder]=[area of the base]+perimeter*h--> only one base
[surface area of a cylinder]=[pi*3²]+[2*pi*50]--> 342.26 units²

[surface area of hemisphere]=2*pi*r²
[surface area of hemisphere]=2*pi*3²-------> 56.52 units²

surface area of the back left tower=342.26+56.52-----> 113.04 units²

[volume of a cylinder]=pi*r²*h
[volume of a cylinder]=pi*3²*50-----> 1413 units³

[volume of a hemisphere]=(4/6)*pi*r³
[volume of a hemisphere]=(4/6)*pi*3³-----> 56.52 units³

[volume of the back left tower]=1413+56.52-------> 1469.52 units³

N 4 BACK RIGHT TOWER
[surface area of a triangular prism]=[area of the base]+perimeter*h------> only one base

find the area of the base
h²=3²-1.5²-----> h=√6.75
[area of the base]=3*√6.75/2----> 3.90 units²
[surface area of a triangular prism]=[3.90]+[3*3*50]-----> 453.9 units²

[surface area of a triangular pyramid]=[area of the 3 triangles]----> without base
[area of 1 triangle]=3*h/2
h²=3²+1.5²----> h²=11.25-----> h=√11.25 units
[area of 1 triangle]=3*√11.25/2-----> 5.03 units²
[surface area of a triangular pyramid]=[3*5.03]-----> 15.09 units²

surface area of the back right tower=453.9+15.09-----> 468.99 units²

[volume of a triangular prism]=area of the base *height
find the area of the base
h²=3²-1.5²-----> h=√6.75
[area of the base]=3*√6.75/2----> 3.90 units²
[volume of a triangular prism]= 3.90*50------> 195 units³

volume of a triangular pyramid]=[area of the base]*h/3
volume of a triangular pyramid]=[3.90]*3/3------> 3.90 units³

[volume of the back right tower]=195+3.90------> 198.90 units³

N 5 CENTRAL BUILDING

[surface area]=2*[area of the base]+perimeter of the base *heigth
[surface area]=100*50*2+2*(150)*30-----> 10000+9000-----> 19000 units²

surface area of the central building=19000 units²

volume of the central building =100*50*30-----> 150000 units³

volume of the central building=150000 units³

N 6
total surface area=629.12+382.23+113.04+468.99+19000-----> 20593.38 unit²
total volume=459+1441.26+1469.52+198.90+150000------> 153568.68 units³

7 0

3 years ago

Owning a small and successful business isn't easy! There is a monthly cost of shipping supplies and

andriy [413]

Answer:

$C(x)=24,000+19,200x$

Step-by-step explanation:

<u>Mathematical Modeling</u>

To model a real-life situation, a mathematical model can be constructed in such a way it accurately represents the variables measured in the system.

This problem requires to build a model for the yearly cost of a small and successful business.

The first data is the fixed monthly cost or the money the owner must pay regardless of the number of employees he hires. This cost includes shipping supplies and products for $2,000. To operate for a full year, the fixed cost is 12*$2,000=$24,000.

The other component of the cost function is the variable cost of x employees. Given each employee costs $1,600 each month, having x employees cost 1,600x each month. For a full year, the variable cost will be

12*1,600x=19,200x.

We finally form the total cost function:

$\boxed{C(x)=24,000+19,200x}$

7 0

3 years ago

Shuffle a standard deck of playing cards and deal one card. define events j

grandymaker [24]

The question is missing some parts. To complete, J is the event of getting a jack and R is getting a red card.

The first question is to look for the P (J) and P (R) =
P (J) = 4/52 = 0.077; since there are only 4 jacks in a standard deck.

P (R) = 26/52 = 0.5; 26 because there are 13 each for diamonds and hearts.

The second question is to describe the event J and R in words. Then look for that event’s probability.

The card is a red jack or the card is red and a jack. P (J and R) = 2/52 = 0/038

The last question is explain why P (J or R) is not equal to P (J) + P (R). Then use the general addition rule to compute for P (J or R).

The event card is red and card is jack are not mutually exclusive meaning two or more events can happen simultaneously. Thus one will count two cards twice unless using the general probability addition formula.

The probability for P (J ∪ R) is:P (J ∪ R) = 2 + 2 + 24 / 52 = 28/52 = 0.0538Or the other solution would be:P (J ∪ R) = 4/52 + 26/52 + 2/52 = 28/52 = 0.0538

7 0

3 years ago

Find the slope of the line that passes through the points (4, 3) and (2, -7).

Licemer1 [7]

Answer:

slope is 5

Step-by-step explanation:

3 0

3 years ago

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Graph g(x)=−x 2 −6x−6

Nina [5.8K]