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Given problem is ![\frac{(5+2i)}{(6+i)}](https://tex.z-dn.net/?f=%5Cfrac%7B%285%2B2i%29%7D%7B%286%2Bi%29%7D)
To simplify that we need to multiply and divide by conjugate of the denominator
conjugate of denominator 6+i will be 6-i as we just need to change sign of the imaginary part
Now multiply and divide by 6-i
![=\frac{(5+2i)}{(6+i)}\cdot\frac{(6-i)}{(6-i)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%285%2B2i%29%7D%7B%286%2Bi%29%7D%5Ccdot%5Cfrac%7B%286-i%29%7D%7B%286-i%29%7D)
![=\frac{30-5i+12i-2i^2}{36-6i+6i-i^2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B30-5i%2B12i-2i%5E2%7D%7B36-6i%2B6i-i%5E2%7D)
![=\frac{30+7i-2i^2}{36-i^2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B30%2B7i-2i%5E2%7D%7B36-i%5E2%7D)
![=\frac{30+7i-2\left(-1\right)}{36-\left(-1\right)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B30%2B7i-2%5Cleft%28-1%5Cright%29%7D%7B36-%5Cleft%28-1%5Cright%29%7D)
![=\frac{30+7i+2}{36+1}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B30%2B7i%2B2%7D%7B36%2B1%7D)
![=\frac{32+7i}{37}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B32%2B7i%7D%7B37%7D)
![=\frac{32}{37}+\frac{7}{37}i](https://tex.z-dn.net/?f=%3D%5Cfrac%7B32%7D%7B37%7D%2B%5Cfrac%7B7%7D%7B37%7Di)
Hence final answer is ![\frac{32}{37}+\frac{7}{37}i](https://tex.z-dn.net/?f=%5Cfrac%7B32%7D%7B37%7D%2B%5Cfrac%7B7%7D%7B37%7Di)
Answer:
Johnny will be able to reach the safe zone before the gate is closed.
Step-by-step explanation:
Given that:
Distance of Little Johnny from safe zone = 4000 feet
Time = 3 minutes
Speed = 22 mph
To find:
Will Johnny be able to reach the safe zone ?
Solution:
Johnny can only be safe if he can travel 4000 feet in 3 minutes with the given speed.
Let us try to find out, the distance that he can travel in 3 minutes at speed of 22 mph.
Let us have a look at the formula of distance traveled:
![Distance = Speed \times Time](https://tex.z-dn.net/?f=Distance%20%3D%20Speed%20%5Ctimes%20Time)
Time = 3 minutes =
hrs
Speed = 22 mph
![Distance = 22 \times \frac{3}{60}\\\Rightarrow Distance = \dfrac{22}{20}\ miles \\\Rightarrow Distance = 1.1\ miles](https://tex.z-dn.net/?f=Distance%20%3D%2022%20%5Ctimes%20%5Cfrac%7B3%7D%7B60%7D%5C%5C%5CRightarrow%20Distance%20%3D%20%5Cdfrac%7B22%7D%7B20%7D%5C%20miles%20%5C%5C%5CRightarrow%20Distance%20%3D%201.1%5C%20miles)
We know that 1 mile = 5280 feet
Therefore 1.1 miles = 5280
1.1 feet = 5808 feet
Distance traveled by Little Johnny is greater than 4000 feet.
Therefore Johnny will be able to reach the safe zone before the gate is closed.
Answer:
x + 2 = y
Step-by-step explanation:
y = x - 2
x = y - 2
x + 2 = y