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Thepotemich [5.8K]
3 years ago
8

Explain the Proof for Lemis Theorm

Mathematics
1 answer:
11111nata11111 [884]3 years ago
3 0

You mean Lami’s Theorem?


Consider the figure. Three concurrent forces net to static equilibrium at the origin. Let's assume for simplicity force <em>a</em> is along the positive x axis.


We have equilibrium when the components of force balance in both dimensions. In particular in the y dimension,


b \sin C = c \sin B


\dfrac{b}{\sin B} = \dfrac{c}{\sin C}


We're free to move our coordinate system around to make any of the force vectors the x axis and then we'd get the same sine balance as in the Law of Sines for the remaining pair of sides.


\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}



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The moon has a surface area of approximately 14,650,000 m^2. Estimate its radius to the nearest mile
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7 0
3 years ago
A bar of soap is shaped like a right rectangular prism. The base is a rectangle that is 12 centimeters by 2 centimeters. The hei
evablogger [386]

Answer:

6 cm

Step-by-step explanation:

Volume of a Prism = base area x height =

Base area = length x width =  12 x 2 = 24 cm^2

Volume = 24 x 3 = 72 cm^3

Volume of a pyramid = 1/3( l x w x h)

72 = 1/3( 6x6 x h)

Multiply both sides of the equation by 3

216 = 36 x h

divide both sides by 36

h = 6

8 0
3 years ago
On a recent trip to the convenience store, you picked up 4 gallons of milk, 6 bottles of water and 5 snack size bags of chips. Y
cricket20 [7]

Answer:

Cost of a snack size bag of chips = $0.8

Cost of a water bottle = $1.6

Cost of a gallon of milk = $3.4

Step-by-step explanation:

Let the cost of water bottle = $a

Cost of 1 gallon milk = $b

and cost of 1 bag of chips = $c

So, cost of 4 gallons of milk, 6 bottles of water and 5 bags of chips = $(4b + 6a + 5c)

4b + 6a + 5c = 27.2 -----(1)

Cost of one water bottle = 2 × cost of one bag of chips

a = 2c -----(2)

A gallon of milk = cost of water bottle + $1.80

b = a + 1.8

From equation (2)

b = 2c + 1.8 -----(3)

Now we substitute these values from equations (2) and (3) in equation (1)

4(2c + 1.8) + 6(2c) + 5c = 27.2

8c + 7.2 + 12c + 5c = 27.2

25c = 27.2 - 7.2

c = \frac{20}{25}

c = $0.8

From equation (2)

a = 2×0.8

a = $1.6

From equation (3)

b = 2(0.8) + 1.8

b = 1.6 + 1.8

b = $3.4

Therefore, cost of a snack size bag of chips = $0.8

Cost of a water bottle = $1.6

Cost of a gallon of milk = $3.4

5 0
3 years ago
15-a=20 what value would make this true
sergejj [24]

Answer:

a = -5

Step-by-step explanation:

15 - a = 20

Move the constant of 15 to the other side by subtracting it.

-a = 5

Divide by -1 to make a positive.

a = -5

Check.

15 - (-5) = 20

15 + 5 = 20

20 = 20

5 0
3 years ago
Read 2 more answers
Solve for c: c divided by 3 equals 8
ohaa [14]

Answer:

c=24

Step-by-step explanation:

c/3 = 8

Multiply each side by 3

c/3 *3 = 8*3

c=24

5 0
2 years ago
Read 2 more answers
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