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SVEN [57.7K]
2 years ago
5

Julissa is running a 10-kilometer race at a constant pace. After running for 18 minutes, she completes 2 kilometers. After runni

ng for 54 minutes, she completes 6 kilometers. Her trainer writes an equation letting t, the time in minutes, represent the independent variable and k, the number of kilometers, represent the dependent variable. Which equation can be used to represent k, the number of kilometers Julissa runs in t minutes?
Mathematics
2 answers:
77julia77 [94]2 years ago
7 0

Answer:

K-18 = 9(t-2)

Step-by-step explanation:

Softa [21]2 years ago
3 0

Find how fast she runs 1 km:

18/2 = 9 minutes.

So we know have K = 9t

Subtract 18 from both sides:

K-18 = 9t -18

Rewrite the right side:

K-18 = 9(t-2)

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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
3 years ago
0.12x - 1.5= 0.24x - 0.06
Sophie [7]

To solve this equation, lets move all of the variables to one side of the equation and the constants to the other.

0.12x - 1.5 = 0.24x - 0.06

Subtract 0.12x from both sides of the equation

-1.5 = 0.12x - 0.06

Add 0.06 to both sides of the equation

-1.44 = 0.12x

Divide both sides by 0.12 to isolate x

x = -12

5 0
3 years ago
Which of the following values are solutions to the inequality - 8 - 3x &gt; 2?
____ [38]

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

X< -10/3

Interval Notation:

(-∞, - 10/3)

Hope this is right :)

6 0
2 years ago
someone please answer this but no links because i have a school computer and it blocks the links so please dont send links
Otrada [13]

Answer:

just typed the whole in mathaway.com

Step-by-step explanation:

it's a better app for quadratic equation and you can use it on a school computer

7 0
2 years ago
In which situation would blinking be beneficial for a animal?
erik [133]

Answer:

D

Step-by-step explanation:

So you can protect your eyes.

7 0
3 years ago
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