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Trava [24]
3 years ago
5

Explain why ∠4 is equal to the sum of the measures of the two nonadjacent interior angles (Angle 1 and Angle 2).

Mathematics
1 answer:
Akimi4 [234]3 years ago
3 0
Angle 4 is 77 degrees. Since angles 1, 2, and 3 must add up to 180 degrees, and angles 3 and 4 must also add up to 180 degrees, angles 1 + 2 must be equal to angle 4
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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
11. Little Sally Walker has a choice between going to an in-state college where she would pay
nalin [4]

Answer:

Step-by-step explanation:

Lets calculate first for in state college

yearly tuition fees = $3,500

monthly living expense = $700

one year has 12 months so yearly living expense =$700 * 12 = $8,400

Yearly expense of the in state college = yearly tuition fees ($3,500 )+ yearly living expense($8,400)   = $3,500 + $8,400  = $11,900

____________________________________________________

Lets calculate first for  out of state college

yearly tuition fees = $6,000

monthly living expense = $400

one year has 12 months so yearly living expense =$400 * 12 = $4,800

Yearly expense of the out of state college = yearly tuition fees ($3,500 )+ yearly living expense($8,400)   = $6,000 + $4,800  = $10,800

____________________________________________________

3 0
2 years ago
Is will like to make this as simple as i can. -1 x 372 - -31= what
mario62 [17]
The answer is -403

The order of operations puts multiplication before subtraction. -1 x 372= -372, and -372-31= -403
5 0
3 years ago
Read 2 more answers
A right triangle has a height of 20 cm and a base of 10 cm. What is the area of the triangle? (A = 1/2 bh)
alisha [4.7K]

Answer:

100 because its way too ez

7 0
2 years ago
Read 2 more answers
Average speed is calculated by dividing total distance with the time it takes to complete it. True False
Aliun [14]

Answer:True

Step-by-step explanation:

Average speed refers to the total distance covered in a specific time . it also a scalar quantity (has magnitude but no direction)

Average speed=distance / time

-Speed is in kilometers/hours or meter/seconds

-distance is in kilometers or meters

-time is in hours or seconds

4 0
3 years ago
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