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jek_recluse [69]
3 years ago
9

Use factoring to solve the following quadratic:   6x2 + 23x - 18 = 0

Mathematics
1 answer:
katen-ka-za [31]3 years ago
4 0
6x² + 23x - 18 = 0
(3x - 2)(2x + 9) = 0
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An air traffic controller spots two airplanes at the same altitude converging to a point as they fly at right angles to each oth
sattari [20]
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 :)


7 0
2 years ago
I don’t know it tried solving it but couldn’t find it
Hitman42 [59]

8f - 25 = 47. Add 25 to both sides.

8f = 72. Divide each side by 8.

f = 9.

4 0
3 years ago
Read 2 more answers
10 to the power of 16 times 10 to the power of -3
rodikova [14]

Answer:

the answer is the Scientific notation of 1×10^13

3 0
3 years ago
4x + 7y = 12<br> -8x - 14y = -24
Masteriza [31]

Answer:

x = 3

y = 0

Step-by-step explanation:

4(3) + 7(0) = 12

-8(3) - 14(0) = -24

8 0
2 years ago
Can you please help me?
d1i1m1o1n [39]

Answer:

C / (2 pi) = r

Step-by-step explanation:

C = 2 pi r

Divide each side by 2 pi

C / (2 pi) = 2 pi r/ (2 pi)

C / (2 pi) = r

3 0
2 years ago
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