If

A pilot flies on a bearing of 160° for 30 miles. The pilot then executes a quick turn and flies another 15 miles at a bearing of

vivado [14]

Answer: 34.65 miles at an angle of 325.39°

Step-by-step explanation:

Ok, the initial position is (0,0)

Then she flies 30 miles at an angle of 160°, if we count the angle counterclokwise from the x-axis, the new position will be:

p = (30*cos(120°), 30*sin(120°))

Then she travels another 15 miles at an angle of 205°, the new position is:

p = (30*cos(120°) + 15*cos(205°), 30*sin(120°) + 15*sin(205°))

p = (-28.59 , 19.64)

If she now travles X miles at an angle Y, we must have that the final position is the point (0,0)

this means that:

X*cos(Y) = -(-28.59) = 28.59

X*sin(Y) = -19.64

Now, we can find the quotient between those two equations and use that tan(x) = sin(x)/cos(x)

X*(sin(Y))/(X*cos(Y)) = -19.64/28.59

Tg(Y) = -0.69

Y = ATg(-0.69) = -34.61°

If we use only positive angles, this angle is equivalent to:

360° - 34.61° = 325.39°

now lets find the distance:

Xcos(325.39°) = 28.59

X = 28.59/cos(325.39°) = 34.65 miles.

4 0

4 years ago

Which list shows these lengths in order from greatest to least?

finlep [7]

9514 1404 393

Answer:

√3/11, π/24, 3/25, 9/100

Step-by-step explanation:

The 2-decimal value of each of the numbers is ...

9/100 = 0.09

π/24 = 0.13

3/25 = 0.12

√3/11 = 0.16

Then the order from greatest to least is 0.16, 0.13, 0.12, 0.09. In the original form, that is ...

√3/11, π/24, 3/25, 9/100 . . . . . matches choice B

8 0

3 years ago

Asphere which has a diameter of 6 inches has a volume of:

earnstyle [38]

Answer:

9.42 cubic inches

Step-by-step explanation:

In order to find the volume for a sphere, we use the formula V = πr. For the sake of simplicity, we will be using 3.14 for π. Before we plug anything in, let's get our radius. Remember, the radius is half of the diameter.

Equation: d = 2r

Replace: 6 = 2r

Divide: 3 = r

Now that we have our radius, let's plug in what we have and solve.

Equation: V = 3.14r

Replace: V = 3.14(3)

Multiply: V = 9.42

Remember, volume is measured in cubic units, so use cubic inches for the unit here.

4 0

3 years ago

The points (–2, 4) and (–2, –2) are vertices of a heptagon. Explain how to find the length of the segment formed by these endpoi

Scrat [10]

Answer:

The segment is 6 units long.

Step-by-step explanation:

The points (–2, 4) and (–2, –2) are vertices of a heptagon. We have to explain how to find the length of the segment formed by these endpoints.

If two points at the ends of a straight line PQ are P( $x_{1},y_{1}$ ) and Q( $x_{2},y_{2}$ ), then the length of the segment PQ will be given by the formula