24% in simplest form

There are 3 islands A,B,C. Island B is east of island A, 8 miles away. Island C is northeast of A, 5 miles away and northwest of

Nostrana [21]

Answer:

The bearing needed to navigate from island B to island C is approximately 38.213º.

Step-by-step explanation:

The geometrical diagram representing the statement is introduced below as attachment, and from Trigonometry we determine that bearing needed to navigate from island B to C by the Cosine Law:

$AC^{2} = AB^{2}+BC^{2}-2\cdot AB\cdot BC\cdot \cos \theta$ (1)

Where:

$AC$ - The distance from A to C, measured in miles.

$AB$ - The distance from A to B, measured in miles.

$BC$ - The distance from B to C, measured in miles.

$\theta$ - Bearing from island B to island C, measured in sexagesimal degrees.

Then, we clear the bearing angle within the equation:

$AC^{2}-AB^{2}-BC^{2}=-2\cdot AB\cdot BC\cdot \cos \theta$

$\cos \theta = \frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC}$

$\theta = \cos^{-1}\left(\frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC} \right)$ (2)

If we know that $BC = 7\,mi$ , $AB = 8\,mi$ , $AC = 5\,mi$ , then the bearing from island B to island C:

$\theta = \cos^{-1}\left[\frac{(7\mi)^{2}+(8\,mi)^{2}-(5\,mi)^{2}}{2\cdot (8\,mi)\cdot (7\,mi)} \right]$

$\theta \approx 38.213^{\circ}$

The bearing needed to navigate from island B to island C is approximately 38.213º.

8 0

3 years ago

What is the solution to 15 = d - 1 ?

Fofino [41]

Answer:

d = 16

Step-by-step explanation:

15 = d-1

Add 1 to each side

15 +1 =d-1+1

16 =d

8 0

3 years ago

I will mark branlest if you are right

schepotkina [342]

Answer:

1) y=(-1/4)x+(11/4)

2) y=(4)x-33

3) y=(2/3)x-11/3

4) y=(5)x-2

5) y=(3)x-7

6) y=(-1/4)x+(6)

Step-by-step explanation:

1) y=mx+b 3=(-1/4)(-1)+b b= 11/4

2) y=mx+b -5=(4)(7)+b b= -33

3) y=mx+b -5=(2/3)(-2)+b b= -11/3

4) y=mx+b 3=(5)(1)+b b= -2

5) y=mx+b -1=(-3)(-2)+b b= -7

6) y=mx+b 7=(1/4)(4)+b b= 6

6 0

3 years ago

Please Help Me!

alexdok [17]

Answer:

The answer to your question is below

Step-by-step explanation:

(2x⁴ + 7x³ - 3x + 9) - (6x⁴ - 3x³ - 6x² - 17)

Step 1. take out the parenthesis, in the second term, change the signs

2x⁴ + 7x³ - 3x + 9 - 6x⁴ + 3x³ + 6x² + 17

Step 2. Group like terms

(2x⁴ - 6x⁴) + (7x³ + 3x³) + (6x²) + (-3x) + (9 + 17)

Step 3. Simplify like terms

-2x⁴ + 10x³ + 6x² - 3x + 26

3 0

3 years ago

José collects stamps. He has 7 used stamps for every 4 new stamps. If he has 28 new stamps, how many used stamps does he have?

jenyasd209 [6]

Answer:

José has 49 used stamps

Step-by-step explanation:

7 used stamps for every 4 new stamps

To solve this type of problem, we can use a ratio

7 : 4 ratio

He has 28 new stamps

7 : 4 = x : 28

Ratios can be written as fractions

$\frac{7}{4} = \frac{x}{28}$

Cross multiply

4x = 7(28) = 196

Divide by 4 on both sides

x = 49

Hope this helps :)

3 0

3 years ago