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3 years ago

A block of wood has the shape of a triangular prism. The base as right triangles. Find it’s surface area

Mathematics

1 answer:

postnew [5]3 years ago

7 0

Answer:

Step-by-step explanation:

I think the attached phôt below is your full question.

<u>And here is my answer: </u>

Surface area of a triangular prism = hight * area of the base

Here we have:

h= 12
Area of the base = 1/2 *2* 1.5 = 1.5

=> Surface area = 12*1.5 = 18

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A piece of wire of length L will be cut into two pieces, one piece to form a square and the other piece to form an equilateral t

inn [45]

Answer:

(a) square: L; triangle: 0.

(b) square: L·(-16+12√3)/11; triangle: L·(27-12√3)/11

Step-by-step explanation:

<u>Strategy</u>: First we will write each area in terms of its perimeter. Then we will find the total area in terms of the amount devoted to the square. Differentiating will give a way to find the minimum total area.

In terms of its perimeter p, the area of a square is ...

A_square = p^2/16

In terms of its perimeter p, the area of an equilateral triangle is ...

A_triangle = p^2/(12√3)

Then the total area of the two figures whose total perimeter is L with "x" devoted to the square is ...

A_total = x^2/16 + (L-x)^2/(12√3)

(a) We know when polygons are regular, the one with the most area for the least perimeter is the one with the most sides. Hence, the total area is maximized when all of the wire is devoted to the square.

(b) The derivative of A_total with respect to x is ...

dA/dx = x/8 -(L-x)/(6√3)

This will be zero when ...

x/8 = (L-x)/(6√3)

x(6√3) = 8L -8x

x(8 +6√3) = 8L

x = L·8/(6√3 +8) = 8L(6√3 -8)/(64-108)

x = L·(12√3 -16)/11

The total area is minimized when L·(12√3 -16)/11 is devoted to the square, and the balance is devoted to the triangle.

5 0

3 years ago

If the three angles of a triangle<br> are equal, what is the<br> measurement of each angle?

erik [133]

Answer:

60 degrees

Step-by-step explanation:

A triangle adds up to 180 degrees. 180 divided by 3 is 60. The answer is 60 degrees.

7 0

3 years ago

Read 2 more answers

A soccer team lost 30% of its games. Suppose the team won 14 games. How many games did the team play?

-BARSIC- [3]

They would have played 20 games altogether

8 0

3 years ago

Just do number 12 please

FinnZ [79.3K]

Please make it clear:)

8 0

3 years ago

The function f(x) = 2x2 3 represents the rate of a boat traveling with the current in miles per hour. The function g(x) = x 2 re

Fofino [41]

The distance in miles the boat traveled for the modeled function of speed and time is,

$(f .g)(2) = 44$

<h3>What is the rate of speed?</h3>

The rate of speed is the rate at which the total distance is travelled in the time taken.

The function which represents the rate of a boat traveling with the current in miles per hour is,

$f(x) = 2x^2+ 3$

The function which represents the time the boat traveled in hours is,

$g(x) = x+ 2$

The distance traveled by boat is the product of rate of speed of the boat and time taken by the boat. Thus, the multiplication function for the above two function can be given as,

$(f.g)(x)=(2x^2+3)(x+2)$

Solve the above function for (f • g)(2) as,

$(f.g)(2)=(2(2)^2+3)(2+2)\\(f.g)(2)=(8+3)(4)\\(f.g)(2)=44$

Interpret the above answer with the given option we get, (f • g)(2) = 44, the distance in miles the boat traveled

Hence, the distance in miles the boat traveled for the modeled function of speed and time is,

$(f .g)(2) = 44$

Learn more about the rate of speed here:

brainly.com/question/359790

4 0

2 years ago