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Los Angeles Airport bears 140 degrees from San Francisco Airport and is 540 km away. A pilot is planning a direct flight from Sa

Roman55 [17]

Create a triangle starting with the length of 540 coming out of SF to LA bearing 140.
This looks like it leaves SF in IV quadrant and enters LA in II quadrant. The wind will take the plane more to the east (right). Therefore the pilot must aim to the west (left) in order for the wind to push it to the intended destination of LA. The second side of the triangle should come out of LA from the II quadrant bearing 290. The length of this side is 60t (60 km/h * t = time flying). The third side of the triangle connects the first two. There for it comes out of SF at some unknown angle > 140 and connects with the 60t side. The length of this third leg is 640t. (640 km/h * t = time flying). The angle between the 540 side and the 60t side is 30. This is found because the 540 side enters LA in 2nd quadrant as 130 angle . The 60t side enters LA in 2nd quadrant as 160 angle. Using law of sin's: sin 30/640t = sin x/60t. The t's cancel and you are left with sin x = 3/64. When solving for the angle x you get x = 2.6867 degrees. Adding this to the bearing of 140, the compass bearing should be 142.6867 or 142.7 degrees. To find the value of t, you use the law of sin's to get sin 30/640t = (sin (180 - 30 - 2.6867))/540. Solving for t gives you: t = .7811. This is in hours. To convert to minutes multiply by 60 to get t = 46.87 minutes. Add this to the 2pm departure time to get 2:47 pm arrival time.

8 0

3 years ago

a coin is flipped eight times where each flip comes up either heads or tails. how many possible outcomes: 1). are there in total

Ymorist [56]

There are 256 ways in total and 56 possible outcomes contain exactly three heads. The possible outcomes contain at least three heads is 219.

Consider the provided information.

A coin is flipped eight times where each flip comes up either heads or tails.

Part (a) How many possible outcomes are there in total?

Each time we flip a coin it comes up either heads or tail.

Therefore the total number of ways are: 2⁸ = 256

Hence, there are 256 ways in total.

Part (b) contain exactly three heads?

We want exactly 3 heads, therefore,

n=8 and r=3

According to the definition of combination:

To get exactly 3 heads,

n=8 and r=3

(⁸C₃ ) = 8! / 3!(5!) = 56.

Therefore, there are 256 ways in total and 56 possible outcomes contain exactly three heads. The possible outcomes contain at least three heads is 219.

Read more about Probability here

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6 0

1 year ago

The sum of two numbers is 12 The sum of the squares of the two numbers is 80. What are the two numbers?

defon

Answer:

4 and 8

Step-by-step explanation:

The square of 4 is 16 and the square of 8 is 64.

16 + 64 = 80

4 0

3 years ago

Find the missing number of each unit rate. 18/3= ?/1 and 12/2= ?/1

gtnhenbr [62]

the answer is 6/1 and 6/1 simply divide and put the answer over one

3 0

3 years ago

A nature center offers 2 guided walks. The morning walk is two-third mile. The evening walk is three-sixths mile. Which walk is

MArishka [77]

Answer:

Evening walk is shorter.

Step-by-step explanation:

We have been given that a nature center offers 2 guided walks. The morning walk is two-third mile. The evening walk is three-sixths mile. We are asked to find the shorter walk.

Let us compare both fractions by making the same denominator.

$\text{Two-thirds}=\frac{2}{3}$

$\text{Two-thirds}=\frac{2\times2}{3\times2}$

$\text{Two-thirds}=\frac{4}{6}$

$\text{Three-sixth}=\frac{3}{6}$

Upon making common denominator, we can see that two-thirds are equal to four sixths.

Since three-sixths is less than four-sixths, therefore, evening walk is shorter.

We will draw two rectangles, one with 6 sub-parts and other with three sub-parts.

We will shade 2 parts out of 3 sub-parts to represent 2/3 and shade 3 parts out of 6 sub-parts to represent 3/6.

Then we will further divide three sub-parts into 6 sub-parts as shown in the diagram that will represent 4/6.

5 0

3 years ago