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Vladimir [108]
3 years ago
15

Two ships set sail in different directions from the same place. Tyler's ship sail 35 miles while Noah's ship sails for 42 miles.

At the same time they are 56 miles apart. What was the angle between their paths when they started?
Mathematics
1 answer:
earnstyle [38]3 years ago
6 0

Answer:

<em>The angle between their paths when they started is 93°.</em>

Step-by-step explanation:

<u>The Law of Cosines</u>

It relates the length of the sides of a triangle with one of its internal angles.

Let a,b, and c be the length of the sides of a given triangle, and x the included angle between sides a and b, then the following relation applies:

c^2=a^2+b^2-2ab\cos x

When the two ships travel in different directions from the same point in the plane, they form an angle we called x in the image below.

Tyler's ship sails a=35 miles and Noah's ship sails for b=42 miles. At some time they are c=56 miles apart.

Since we know the values of all three side lengths, we solve the equation for x:

\displaystyle \cos x=\frac{a^2+b^2-c^2}{2ab}

Substituting values:

\displaystyle \cos x=\frac{35^2+42^2-56^2}{2(35)(42)}

Calculating:

\displaystyle \cos x=-\frac{147}{2940}=-\frac{1}{20}

Computing the inverse cosine:

x = \arccos(-0.05)

x \approx 93^\circ

The angle between their paths when they started is 93°.

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There are 3 red pens, 4 blue pens, 2 Blac pens, and 5 green pens in drawer, suppose you choose a pen at random
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Answer:

1. 3/14

2. 2/7

3. 1/7

4. 5/14

5. 11/14

6. 9/14

Step-by-step explanation:

first get the total number of pens

3 red pens + 4 blue pens + 2 black pens + 5 green pens =

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1. What is the probability that the pen chosen red?

3 red pens out of a total of 14 pens = 3/14

2. What is the probability that the pen chosen is blue?

4 blue pens out of a total of 14 pens = 4/14 -> simplified -> 2/7

3. What is the probability that the pen chosen is black?

2 black pens out of a total of 14 pens = 2/14 -> simplified -> 1/7

4. What is the probability that the pen chosen is green?

5 green pens out of a total of 14 pens = 5/14

5. What is the probability that the pen chosen is NOT red?

of the 3 red pens, 4 blue pens, 2 black pens and 5 green pens

4 blue pens, 2 black pens and 5 green pens are NOT red

4 blue pens + 2 black pens + 5 green pens =

11 total number of pens that are NOT red

11 total number of pens that are NOT red out of a total of 14 pens = 11/14

6. What is the probability that the pen chosen is NOT green?

of the 3 red pens, 4 blue pens, 2 black pens and 5 green pens

the 3 red pens, 4 blue pens, 2 black pens are NOT green

3 red pens + 4 blue pens + 2 black pens =

9 total number of pens that are NOT green

9 total number of pens that are NOT green out of a total of 14 pens = 9/14

gathmath.com

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astraxan [27]

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5 0
3 years ago
Equation with a slope of -2 and point of (4,7)
s344n2d4d5 [400]

Answer:

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Step-by-step explanation:

So first we can write it in point slope form.

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y1 is the y coordinate

m is the lope

x1 is the x coordinate

This means that the equation is:

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We can then convert it to slope intercept form which is

y=mx+b

so

y-7=-2x+8

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3 0
3 years ago
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