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densk [106]
3 years ago
13

Find the surface area of the prism. Can you show the work please?

Mathematics
1 answer:
Harrizon [31]3 years ago
8 0
I have attached the work for your first problem.

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The perimeter of a triangular field is 120m. Two of the sides are 21m and 40m.Calculate the largest angle of the field.
Mama L [17]

Answer:

the largest angle of the field is 149⁰

Step-by-step explanation:

Given;

perimeter of the triangular filed, P = 120 m

length of two known sides, a and b = 21 m and 40 m respectively

The length of the third side is calculated as follows;

a + b + c = P

21 m  + 40 m  + c = 120 m

61 m +  c = 120 m

c = 120 m - 61 m

c = 59 m

                         B

                     ↓            ↓  

                  ↓                          ↓

                ↓                                       ↓

            A →  →  → →  →  → →  → →    →    →  C

Consider ABC as the triangular field;

Angle A is calculated by applying cosine rule;

a^2 = b^2 + c^2 - 2bc \ Cos A\\\\Cos \ A = \frac{b^2 + c^2 - a^2}{2bc} \\\\Cos \ A = \frac{40^2 + 59^2 - 21^2}{2 \times 40 \times 59} \\\\Cos \ A = 0.983\\\\A = Cos ^{-1} (0.983)\\\\A = 10.6 \ ^0

Angle B is calculated as follows;

Cos \ B = \frac{a^2 + c^2 - b^2}{2ac} \\\\Cos \ B = \frac{21^2 + 59^2 - 40^2}{2 \times 21 \times 59} \\\\Cos \ B = 0.937\\\\B= Cos ^{-1} (0.937)\\\\B = 20.5 \ ^0

Angle C is calculated as follows;

Cos \ C = \frac{a^2 + b^2 - c^2}{2ab} \\\\Cos \ C = \frac{21^2 + 40^2 - 59^2}{2 \times 21 \times 40} \\\\Cos \ C = -0.857\\\\C = Cos ^{-1} (-0.857)\\\\C = 149\ ^0

Therefore, the largest angle of the field is 149⁰.

       

8 0
3 years ago
How do you find the area of a figure
Nostrana [21]

Answer:

Any figure?

Step-by-step explanation:

3 0
3 years ago
Darell buys a model railroad set online for $224.62. If shipping and handling are an additional 16% of the price, how much shipp
Serggg [28]
35.94
Sisieiekenducnfht hdendyc ok
6 0
3 years ago
A bag of marbles contains 16 blue, 8 green, 9 red, 12 yellow and 5 black marbles. What is the probability of drawing a green mar
alexgriva [62]

Answer:

8/50

Step-by-step explanation:

you would take the number of that colored marble which in this case is green so now we have our numerator which is 8 next we are going to add all of the amount of numbers including the green and we get 50 and 50 is our denominator.

8 0
3 years ago
Analyze the graph h(x).
Dominik [7]

Answer:

D h(x) = f(x)×g(x)

Step-by-step explanation:

h(x) has a wave with 2 changes in direction.

so, this needs to be an expression of the third degree (there must be a term with x³ as the highest power of x).

and that is only possible when multiplying both basic functions. all the other options would keep it at second degree (x²) or render it even to a first degree (linear).

8 0
2 years ago
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