Answer:
11/32
Step-by-step explanation:
I took the test Please make brainlyest if can
They are traveling at right angles to each other so we can say one is traveling north to south and the other west to east. Then we can say that there positions, y and x are:
y=150-600t x=200-800t
By using the Pythagorean Theorem we can find the distance between these two planes as a function of time:
d^2=y^2+x^2, using y and x from above
d^2=(150-600t)^2+(200-800t)^2
d^2=22500-180000t+360000t^2+40000-320000t+640000t^2
d^2=1000000t^2-500000t+62500
d=√(1000000t^2-500000t+6250)
So the rate of change is the derivative of d
dd/dt=(1/2)(2000000t-500000)/√(1000000t^2-500000t+6250)
dd/dt=(1000000t-250000)/√(1000000t^2-500000t+6250)
So the rate depends upon t and is not a constant, so for the instantaneous rate you would plug in a specific value of t...
...
To find how much time the controller has to change the airplanes flight path, we only need to solve for when d=0, or even d^2=0...
1000000t^2-500000t+62500=0
6250(16t^2-8t+1)=0
6250(16^2-4t-4t+1)=0
6250(4t(4t-1)-1(4t-1))=0
6250(4t-1)(4t-1)=0
6250(4t-1)^2=0
4t-1=0
4t=1
t=1/4 hr
Well technically, the controller has t<1/4 because at t=1/4 impact will occur :)
Answer:
x = 5/2
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
12x - 30 = 2x - 5
<u>Step 2: Solve for </u><em><u>x</u></em>
- Subtract 2x on both sides: 10x - 30 = -5
- Add 30 to both sides: 10x = 25
- Divide 10 on both sides: x = 5/2
Answer:
x = 4 and y = - 5
Step-by-step explanation:
note that the product of a complex number and it's conjugate is real
That is
(a + bi)(a - bi) where a, b are real
= a² - abi + abi - b²i²
= a² + b² ← a real number
For (4 + 5i)(x + yi) to be real
we require (x + yi) to be the conjugate of 4 + 5i , that is 4 - 5i
(4 + 5i)(4 - 5i) ⇒ x = 4 and y = - 5
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