Which rule describes rotating 90° counterclockwise?

The wind is blowing N 35.0 degrees W at 1.60 * 10^2 mph. A plane has an engine speed of 3.20 * 10^2 mph. Where should the pilot

andreyandreev [35.5K]

Answer: 24.2° SouthWest

Step-by-step explanation:

First step: DRAW A PICTURE of the vectors from head to tail (see image)

I created a perpendicular from the resultant vector to the vertex of the given vectors so I could use Pythagorean Theorem to find the length of the perpendicular. Then I used that value to find the angle of the plane.

Perpendicular (x):

cos 35° = adjacent/hypotenuse

cos 35° = x/160

→ x = 160 cos 35°

Angle (θ):

sin θ = opposite/hypotenuse

sin θ = x/320

sin θ = 160 cos 35°/320

θ = arcsin (160 cos 35°/320)

θ = 24.2°

Direction is down (south) and left (west)

7 0

3 years ago

What is the true solution to 3 in 2 + in 8 = 2 in (4x)

11Alexandr11 [23.1K]

The first step for solving this equation is to determine the defined range.
3㏑(2) + ㏑(8) = 2㏑(4x), x > 0
Write the number 8 in exponential form.
3㏑(2) + ㏑(2³) = 2㏑(4x)
Using ㏑( $a^{x}$ ) = x × ㏑(a),, transform the expression.
3㏑(2) + 3㏑(2) = 2㏑(4x)
Now collect the like terms on the left side of the equation.
6㏑(2) = 2㏑(4x)
Switch the sides of the equation.
2㏑(4x) = 6㏑(2)
Using x × ㏑(a) = ㏑( $a^{x}$ ),, transform the expression on the left side of the equation.
㏑((4x)²) = 6㏑(2)
Using x × ㏑(a) = ㏑( $a^{x}$ ),, transform the expression on the right side of the equation.
㏑((4x)²) = ㏑( $2^{6}$ )
Since the bases of the logarithms are the same,, you need to set the arguments equal.
(4x)² = $2^{6}$
Take the square root of both sides of the equation and remember to use both the positive and negative roots.
4x = +/- 8
Now separate the equation into 2 possible cases.
4x = 8
4x = -8
Solve the top equation for x.
x = 2
Solve the bottom equation for x.
x = 2
, x > 0
x = -2
Lastly,, check if the solution is in the defined range to find your final answer.
x = 2
This means that the correct answer to your question is x = 2.
Let me know if you have any further questions
:)

5 0

3 years ago

Read 2 more answers

In ΔABC, what is the value of cos B?

gayaneshka [121]

The value of cos B is 12/13

4 0

3 years ago

Read 2 more answers

Which fraction below represents a terminating decimal? A. B. C. D.

Vsevolod [243]

Answer:

3/10

Step-by-step explanation:

The fraction, 1/12, can be written as 1/4 * 1/3. Since we know that 1/3 = 0.333333... and it doesn't terminate, we know that 1/12 doesn't terminate. Similarly 2/9 = 2/3*1/3 and 2/3 = 2*1/3, and neither of these fractions terminate. But, when dividing 3/10, you get 0.3, which terminates.

3 0

3 years ago

Which graph shows the solution to the inequality −2(2x+3)≤26?

krok68 [10]

Answer:

x≥−8

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

−4x−6≤26

Step 2: Add 6 to both sides.

−4x−6+6≤26+6

−4x≤32

Step 3: Divide both sides by -4.

−4x/−4 ≤ 32/−4

x≥−8

5 0

3 years ago