The wire is anchored 190 -13 = 177 ft from the ground. That distance is opposite the given angle (31°). The measure you want is the hypotenuse of the triangle with that side and angle measures.

The mnemonic SOH CAH TOA reminds you that the relation between the opposite side, hypotenuse, and angle is ...

Sin(angle) = Opposite/Hypotenuse

Filling in the given information, you have ...

sin(31°) = (177 ft)/hypotenuse

Solving for hypotenuse gives

hypotenuse = (177 ft)/sin(31°) ≈ 343.7 ft

The length of the guy wire should be 343.7 ft.

5 0

3 years ago

You manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quart of Creamy Vanilla

Mars2501 [29]

Answer:

You should make 250 quarts of Creamy Vanilla and 200 of Continental Mocha to use up all the eggs and cream.

Step-by-step explanation:

This problem can be solved by a first order equation

I am going to call x the number of quarts of Creamy Vanilla and y the number of quarts of Continental Mocha.

The problem states that each quart of Creamy Vanilla uses 2 eggs and each quart of Continental Mocha uses 1 egg. There are 700 eggs in stock, so:

2x + y = 700.

The problem also states that each quart of Creamy Vanilla uses 3 cups of cream and that each quart of Continental Mocha uses 3 cups of cream. There are 1350 cups of cream in stock, so:

3x + 3y = 1350

Now we have to solve the following system of equations

1) 2x + y = 700

2) 3x + 3y = 1350

I am going to write y as function of x in 1) and replace it in 2)

y = 700 - 2x

3x + 3(700 - 2x) = 1350

3x + 2100 - 6x = 1350

-3x = -750 *(-1)

3x = 750

x = 250

You should make 250 quarts of Creamy Vanilla

Now, replace it in 1)

y = 700 - 2x

y = 700 - 2(250)

y = 700 - 500

y = 200.

You should make 200 quarts of Continental Mocha

7 0

3 years ago