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diamong [38]
2 years ago
11

Approximately what is the length of the rope for the kite sail, in order to pull the ship at an angle of 45° and be at a vertica

l height of 150 m, as shown in the diagram opposite?
Mathematics
1 answer:
Lera25 [3.4K]2 years ago
8 0

Answer:

212m

Step-by-step explanation:

The set up will be equivalent to a right angled triangle where the height is the opposite side facing the 45° angle directly. The length of the rope will be the slant side which is the hypotenuse.

Using the SOH, CAH, TOA trigonometry identity to solve for the length of the rope;

Since we have the angle theta = 45° and opposite = 150m

According to SOH;

Sin theta = opposite/hypotenuse.

Sin45° = 150/hyp

hyp = 150/sin45°

hyp = 150/(1/√2)

hyp = 150×√2

hyp = 150√2 m

hyp = 212.13m

Hence the length of the rope for the kite sail, in order to pull the ship at an angle of 45° and be at a vertical height of 150 m is approximately 212m

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Caleb made the table below to show the number of hours he works and the amounts he earns over a four-week period. Caleb’s Earnin
Ganezh [65]
<h2>Answer:</h2>

The ratios of earnings to hours are not the same each week, so the earnings do not vary directly with the hours.

<h2>Step-by-step explanation:</h2>

We know that the data points given by (x,y) are in direct variation if:

\dfrac{y}{x}=k  for each (x,y)

We are given data as:

Caleb’s Earnings Hours(x)        12          15         18         21

Earnings (in dollars)(y)              140        170      200     230

So, we could see the ratio as:

  • \dfrac{140}{12}=\dfrac{35}{3}
  • \dfrac{170}{15}=\dfrac{34}{3}
  • \dfrac{200}{18}=\dfrac{100}{9}
  • \dfrac{230}{21}

Hence, we could see that each ratio are not equal.

Hence, the relationship between the earnings and the number of hours does not represents a direct variation.

6 0
2 years ago
Read 2 more answers
mcgregor is growing alfalfa on 180 acres,which is 30% of his farmland. mcgregor has how many acres of farmland?
emmasim [6.3K]

Answer:

600 acres

Step-by-step explanation:

Hope this helps!

5 0
1 year ago
A lock has two buttons: a "0" button and a "1" button.To open a door you need to push the buttons according to a preset 8-bit se
ratelena [41]

Answer:

Step-by-step explanation:

The problem relates to filling 8 vacant positions by either 0 or 1

each position can be filled by 2 ways so no of permutation

= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

= 256

b )

Probability of opening of lock in first arbitrary attempt

= 1 / 256

c ) If first fails , there are remaining 255 permutations , so

probability of opening the lock in second arbitrary attempt

= 1 / 255 .

7 0
2 years ago
8.5b−3.4∙(13a−3.2b)+a
Nesterboy [21]

Answer:

8.5b - 3.4(13a - 3.2b) + a = 19.4b - 43.2a

Step-by-step explanation:

It is a simple mathematical problem with multiple like terms. We can solve it by applying basic mathematical rules of multiplication and addition/subtration.

8.5b - 3.4(13a - 3.2b) + a

= 8.5b - 3.4*13a -3.4*(-3.2b) + a

= 8.5b - 3.4*13a + 3.4*3.2b + a

= 8.5b - 44.2a + 10.88 b + a

Now, only like terms can be added to each other

= (8.5b + 10.9b) + (a - 44.2a)

= 19.4b + (-43.2a)

= 19.4b - 43.2a    

8 0
2 years ago
Transform the equation to isolate x: ax = bx + 1. How is the value of x related to the difference of a and b? The equation ax =
butalik [34]

Answer:Transform the equation to isolate x: ax = bx + 1. How is the value of x related to the difference of a and b

Step-by-step explanation:

4 0
2 years ago
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