The angle of depression is 29.0521°. So it is a safe landing.
Step-by-step explanation:
Step 1:
The plane is flying at a height of 25,000 feet and 45,000 feet away from the landing strip. Assume it lands with an angle of depression of x°.
So a right-angled triangle can be formed using these measurements. The triangle's opposite side measures 25,000 feet while the adjacent side measures 45,000 feet. The angle of the triangle is x°.
To determine the value of x, we calculate the tan of the given triangle.
![tanx = \frac{opposite side}{adjacent side}.](https://tex.z-dn.net/?f=tanx%20%3D%20%5Cfrac%7Bopposite%20side%7D%7Badjacent%20side%7D.)
Step 2:
The length of the opposite side = 25,000 feet.
The length of the adjacent side = 45,000 feet.
![tan x = \frac{25,000}{45,000} = 0.5555.](https://tex.z-dn.net/?f=tan%20x%20%3D%20%5Cfrac%7B25%2C000%7D%7B45%2C000%7D%20%3D%200.5555.)
So x = 29.0521°. Since x < 30°, it is a safe landing.
Answer:
The value of y = 7.5 and the scale factor is 2/3.
Step-by-step explanation:
To get the scale factor, let's get the ratio of 17 to 25
![\frac{17}{25.5} = \frac{2}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B17%7D%7B25.5%7D%20%20%3D%20%20%5Cfrac%7B2%7D%7B3%7D%20)
To check if 17 really is the 2/3 of 25.5
![17 = \frac{2}{3} \times 25.5 \\ 17 = \frac{51}{3} \\ 17 = 17](https://tex.z-dn.net/?f=17%20%3D%20%20%5Cfrac%7B2%7D%7B3%7D%20%20%5Ctimes%2025.5%20%5C%5C%2017%20%3D%20%20%5Cfrac%7B51%7D%7B3%7D%20%20%5C%5C%2017%20%3D%2017)
Therefore, if 17 is the 2/3 of 25.5, then the line (3y-3.5) is also the 2/3 of (3y+6).
![3y - 3.5 = \frac{2}{3} (3y + 6) \\ 3(3y - 3.5) = 2(3y + 6) \\ 9y - 10.5 = 6y + 12 \\ 9y - 6y = 12 + 10.5 \\ 3y = 22.5 \\ y = 7.5](https://tex.z-dn.net/?f=3y%20-%203.5%20%3D%20%20%5Cfrac%7B2%7D%7B3%7D%20%283y%20%2B%206%29%20%5C%5C%203%283y%20-%203.5%29%20%3D%202%283y%20%2B%206%29%20%5C%5C%209y%20-%2010.5%20%3D%206y%20%2B%2012%20%5C%5C%209y%20-%206y%20%3D%2012%20%2B%2010.5%20%5C%5C%203y%20%3D%2022.5%20%5C%5C%20y%20%3D%207.5)
9514 1404 393
Answer:
250,000
Step-by-step explanation:
The thousands digit is more than 4, so the ten-thousands digit is increased by 1 before digits to its right are replaced by zeros. The rounded number is ...
250,000
Answer:
0.51cm/s
Step-by-step explanation:
Area of a circle A = πr²
r is the radius
Rate of change of area is expressed as;
dA/dt = dA/dr • dr/dt
dA/dr = 2πr
radius r = 77cm
dA/dt = 79cm²
Get dr/dt
Substitute the given values into the formula
79 = 2π(77)•dr/dt
79 = 154dr/dt
dr/dt = 79/154
dr/dt = 0.51cm/s
Hence the rate of change of the radius is 0.51cm/s
Let's say we had to multiply the two binomials (x + 1)(x + 2). We could use the grid method or FOIL, but we will use the grid method for now. Here is how you do it:
1. Identify all the terms in the expression:
x, 1, x, 2
2. Align the terms in a grid-like fashion according to their binomials:
x 1
x
2
3. Now, multiply all the terms together (ex. x × x is x²)
x 1
x x² 1x
2 2x 2
4. Put all products in decreasing order:
x²+1x+2x+2
5. Combine Like Terms (CLT):
x² + 3x + 2
Therefore, the answer is x² + 3x + 2. As you can see, the grid method is figuratively long, and the FOIL method is definitely recommended. Hope this helped!