What are the steps in solving the system?

A plane has an airspeed of 111 km/h. It is flying on a bearing of 79 degrees while there is a 25 km/h wind out of the northeast

qwelly [4]

Answer: Ground Speed = 91 km/hr, Bearing = 189°

Step-by-step explanation:

Step 1: Draw a picture (see attached) to determine the angle between the given vectors. Notice that I moved the wind vector 180° so the head of the wind vector would line up with the tail of the plane vector. This created an angle of 34° between the plane and wind vectors. Why?

the dashed line is 45°
79° (plane) - 45° (wind) = 34°

Step 2: Solve for the length of the resultant vector using Law of Cosines

c² = a² + b² - ab cos C

c² = (111)² + (25)² - (111)(25) cos 34°

c² = 12,946 - 4601

c² = 8345

c = 91

Ground speed is 91 km/hr

Step 3: Solve for the bearing of the resultant vector using Law of Sines

$\dfrac{sin\ A}{a}=\dfrac{sin\ C}{c}$

$\dfrac{sin\ A}{25}=\dfrac{sin\ 34}{91}$

$sin\ A=\dfrac{25\ sin\ 34}{91}$

$A=sin^{-1}\bigg(\dfrac{25\ sin\ 34}{91}\bigg)$

A = 9°

Reminder that we moved the wind vector 180° to create the resultant vector so we need to add 180° to our answer.

Bearing = A + 180°

= 9° + 180°

= 189°

7 0

3 years ago

Taylor is 15 years younger than Marty. Twice Marty’s age added to three times Taylors age totals 205. What are the ages of Taylo

IceJOKER [234]

Answer:

Marty = 50 Taylor = 35

Step-by-step explanation:

50 x 2 = 100

35 x 3 = 105

100 + 105 = 205

5 0

3 years ago

What is the 6th term in the geometric sequence described by this explicit formula?

Mamont248 [21]

I think it’s 243 if it’s

5 0

3 years ago

Find the radius for the circle please show how you got ur anwser so show ur work plz and thanks

ycow [4]

Answer:

Step-by-step explanation:

So first you would have to divide 113.04 by 3.14 and you would get 36. Next you would have to square 36 to get 6 which is your radius.

5 0

3 years ago

A rectangle has a perimeter of 30 feet and an area of 50 square feet. What are the dimensions of the rectangle?

REY [17]

Perimeter (p) = 2×length (l) + 2×width (w)
p = 2l+2w
area (a) = l×w, so solve for one (I'll use l):
$a = l \times w \\ l = a \div w \\ p = 2l + 2w = 2(l + w)$
since p = 30, and a = 50, substitute the "a÷w" in for l in the perimeter equation:
$p = 2(l + w) = 2((a \div w) + w) \\ = 2((a \div w) + ( {w}^{2} \div w)) \\ p= 2((a + {w}^{2}) \div w$
Now plug in p and a values:
$p= 2((a + {w}^{2}) \div w) \\ 30 = 2((50 + {w}^{2}) \div w) \\ 30 \div 2 = (50 + {w}^{2}) \div w \\ 15w = 50 + {w}^{2}$
$15w = 50 + {w}^{2} \\ {w}^{2} - 15w + 50 = 0 \\ (w - 5)(w - 10) = 0$
therefore width can be either 5 or 10 (but not both), so let's plug in:
l = a÷w = 50÷5 = 10
So if w = 5, then l = 10

D) 5 feet, and 10 feet

3 0

3 years ago