Answer:
j=-7
Step-by-step explanation:
-5j-7=-4j
-5j+4j=7
-j=7
j=-7
Answer:
64°
Step-by-step explanation:
Check the attachment for the diagram. Since the triangle has one of its angle as 90°, it is a right angled triangle.
Using the SOH CAH TOA trigonometry ratios:
Since ∠P is opposite to side QR,
QR = opposite side = 8ft
RP = adjacent side = 3.9ft
According to TOA
Tan∠P = Opposite/Adjacent = QR/RP
Tan∠P = 8/3.9
Tan∠P = 2.05
∠P = arctan 2.051
∠P = 64°
Answer:
Option B.
Step-by-step explanation:
Area of the composite figure = Area of the rectangle- area of the semicircle removed
= (length × width) -
Since diameter of the semicircle is the width of the rectangle.
So, radius of the semicircle = ![\frac{3.8}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B3.8%7D%7B2%7D)
= (3.8 × 9.2) - ![\frac{1}{2}(3.14)(\frac{3.8}{2})^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%283.14%29%28%5Cfrac%7B3.8%7D%7B2%7D%29%5E%7B2%7D)
= 34.96 - 5.6677
= 29.2923
≈ 29.3 in²
Therefore, area of the given composite figure is 29.3 in².
Option B is the correct option.
Answer:
<u>B. 57.8</u>
Step-by-step explanation:
Changing 46% to a decimal it would be 0.46
125.7 * 0.46 = ?
125.7 * 0.46 = 57.822
57.822 rounds to 57.8 which is answer B.
<span>p = 780
w = 180
You didn't provide a list of equations to select from, so let's see about creating them and solving. For this I'll use the variable p for the airspeed of the jet and w for the speed of the wind in the jet stream. So when the jet is traveling in the same direction as the jet stream, the ground speed is p+w and when the jet is traveling in the opposite direction, the ground speed is p-w. With that in mind, we can create two equations and solve them. The equations are:
(1). 1920 = 2(p+w)
(2). 1920 = 3.2(p-w)
Let's take equation (1) above and distribute the 2.
1920 = 2(p+w)
(3) 1920 = 2p + 2w
And do the same for equation (2) above.
1920 = 3.2(p-w)
(4) 1920 = 3.2p - 3.2w
Let's multiply (3) above by 1.6 to make the w terms equal in magnitude and opposite in sign to that in equation (4) above.
1920 = 2p + 2w
(5) 3072 = 3.2p + 3.2w
Add (4) and (5) above together, then solve for p
(4) 1920 = 3.2p - 3.2w
(5) 3072 = 3.2p + 3.2w
4992 = 6.4p
780 = p
So the Jet's speed is 780 km/h
Now use the speed of the Jet and (1) above to get the wind speed.
1920 = 2(p+w)
1920 = 2(780+w)
960 = 780 + w
180 = w
So the wind speed is 180.</span>