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Over [174]
2 years ago
6

Finf the exact value of sin A and cos A where a = 9 and b = 10 and <c is a right angle

Mathematics
2 answers:
Katyanochek1 [597]2 years ago
8 0
To solve for the longest side, the hypotenuse, you have to use the pythagorean theorem. It will be 10^2 + 9^2 = c^2. 100 + 81 =c^2. 
c^2 = 181 so c = sqrt(181).
to find sin of A do opposite/hypotenuse which gives you 9/sqrt(181)
to find cos of A do adjacent/hypotenuse which gives you 10/sqrt(181)

Artemon [7]2 years ago
3 0

Answer:

sin A = 0.6666666667 ≈ 0.67

cos A = 0.7407407407  ≈ 0.74

Step-by-step explanation:

The triangle above is a right angle triangle . Angle C is the angle 90°. we can use the cosine law for triangle to solve for side c.

c² = a² + b² - 2ab.cos(C)

a = 9

b = 10

C = 90°

c² = 9² + 10² - 2 × 9 × 10 cos( 90)

c² = 81 + 100 - 180 × 0

c² = 181

c = √181

c = 13.45362405  ≈ 13.5

Using sine rule

a/sin A = b/sin B = c/sin C

a = 9

b = 10

c = 13.5

C = 90°

9/sin A = 13.5/sin 90°

13.5 sin A = 9 × sin 90°

13.5 sin A = 9

sin A = 9/13.5

sin A = 0.6666666667

Use SOHCAHTOA principle to find cos A

cos A = b/c

cos A =  10/13.5

cos A = 0.7407407407

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A movie theater charges $9.50 for adults and $4.50 for children. For a recent showing of a movie, the theater sold 33 tickets an
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Answer:

The  number of children's tickets sold was 31 and the number of  adult tickets sold was 2

Step-by-step explanation:

Let

x ---> the number of children's tickets sold

y ---> the number of  adult tickets sold

we know that

the theater sold 33 tickets

so

x+y=33 -----> equation A

the theater made a total of $158.50

so

4.50x+9.50y=158.50 ----> equation B

Solve the system by graphing

Remember that the solution of the system is the intersection point both graphs

using a graphing tool

The solution is the point (31,2)

see the attached figure

therefore

The  number of children's tickets sold was 31 and the number of  adult tickets sold was 2

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A dairy company gets milk from two dairies and then blends the milk to get the desired amount of butterfat. Milk from dairy I co
lisov135 [29]

Answer:

The complete solution and step by step explanation is written below.

<em>Note:</em>

Here is the complete question you were probability asking as you may have unintentionally missed to mention the parts (a) and (b). So, after a little research, I figured out that this was probably the complete question you had meant to ask. So, I am answering based on the reference of this complete question that may indeed clear your concepts.

Complete Question:

<em>A dairy company gets milk from two dairies and then blends the milk to get the desired amount of butterfat. Milk from dairy I costs ​$2.40 per​ gallon, and milk from dairy II costs ​$0.80 per gallon. At most ​$144 is available for purchasing milk. Dairy I can supply at most 50 gallons averaging 3.9​% ​butterfat, and dairy II can supply at most 80 gallons averaging 2.9​% butterfat. Answer parts a and b</em>.

<em>A. How much milk from each supplier should the company buy to get at most 100 gallons of milk with the maximum amount of butterfat? (Also, what IS the maximum amount of butterfat?)</em>

<em>B. The solution from part A leaves both dairy 1 and dairy 2 with excess capacity. Calculate the amount of additional milk each dairy could produce.</em>

Step-by-step explanation:

Let A be number of gallons of the amount of milk the company bought from Dairy 1.

(100 - X) be the number of gallons of the amount of milk the company bought from Dairy 2.

Milk from dairy I costs ​$2.40 per​ gallon and milk from dairy II costs ​$0.80 per gallon.

So, the equation of total cost available for purchasing the milk be:

                            Cost =  2.40A + ( 100 - A)0.80

As $144 is the total cost available for purchasing the milk.

Hence, Cost equation would be as follows:

                             Cost =  2.40A + ( 100 - A)0.80

                               144 =  2.40A + ( 100 - A)0.80

                               144 = 2.40A + 80 - 0.80A

                              1.6A = 64

                            So, A = 64 ÷ 1.6

                                      = 40 gallons

<em>Calculation of gallons of Dairy 1 and Dairy 2:</em>

gallons of Dairy 1 ⇒ A = 40 gallons

gallons of Dairy 1 ⇒ 100 - A = 100 - 40 = 60 gallons

<em>The equation for Fat will be:</em>

Fat for dairy 1 = 40 × 3.9​% = 1.56

Fat for dairy 2 = 60 × 2.9​% = 1.74

ADD = 1.56 + 1.74 = 3.3 %

<em>Calculation Part B:</em>

Dairy 1 will have = 50 - 40 = 10 gallons ( excess)

Dairy 2 will have = 80 - 60 = 20 gallons (excess)

   

Keywords: word problem, equation solving

Learn more about word problems and equation solving from brainly.com/question/8917703

#learnwithBrainly

5 0
2 years ago
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