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4vir4ik [10]
3 years ago
13

Two airplanes are flying in the air at the same height: airplane a is flying east at 250 mi/h and airplane b is flying north at

300mi/h.300mi/h. if they are both heading to the same airport, located 30 miles east of airplane a and 40 miles north of airplane b, at what rate is the distance between the airplanes changing?
Mathematics
1 answer:
Marta_Voda [28]3 years ago
3 0
If the airport is located at the origin, for units of miles and hours, we can write the equations of position for airplanes "a" and "b" in rectangular coordinates as
  a = (-30 +250t, 0)
  b = (0, -40 +300t)

The distance between these (moving) points can be computed in the usual way using the Pythagorean theorem.
  d = √((-30 +250t - 0)² +(0 - (-40 +300t))²)
  d = √(2500 -39000t +152500t²)

Then the rate of change of d is the derivative of this.
  d'(t) = (-19500 +152500t)/√(2500 -39000t +152500t²)

At the present time (t=0), the rate of change of distance between the planes is
  d'(0) = -19500/√2500 = -390

The distance between the planes is decreasing at 390 mi/h.
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Answer:

children = 177, adults =215

Step-by-step explanation:

im too lazy to write but solve this with a systeme

x(children),y(adults)

x+y=392

x=392-y

2.5y+1.25x=758.75

2.5y+1.25(392-y)=758.75

2.5y+490-1.25y=758.75

490+1.25y=758.75

1.25y=758.75-490

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y=268.75/1.25

y=215

x=392-215=177(number of kids)

6 0
2 years ago
Delilah does 184 jumping jacks in 44 minutes. She does her jumping jacks at a constant rate. How many jumping jacks can Delilah
MariettaO [177]

Answer:

4

Step-by-step explanation:

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6 0
4 years ago
Read 2 more answers
The measure of angle 1 is 3x + 10 and the measure of angle 4 is (4x-15). What is the measure of angle 7
Alex_Xolod [135]
<u><em>Answer:</em></u>
∠7 = 95°

<u><em>Explanation:</em></u>
<u>1- getting the value of x:</u>
In the given figure, angle 1 and angle 4 are vertically opposite angles.
Therefore, they are equal in measurement
This means that:
3x + 10 = 4x - 15
4x - 3x = 10 + 15
x = 25

<u>2- getting the value of angle 4:</u>
We know that:
x = 25 and ∠4 is 4x-15
This means that:
∠4 = 4(25) - 15
∠4 = 85°

<u>3- getting the value of ∠6:</u>
From the given figure, we can see that ∠4 and ∠6 are supplement angles, this means that their summation is 180°.
We have calculated that ∠4 is 85°, therefore:
180 = ∠4 + ∠6
∠6 = 180 - ∠4
∠6 = 180 - 85
∠6 = 95°

<u>4- getting the value of angle 7:</u>
From the drawing, we can note that ∠6 and ∠7 are vertically opposite angles. This means that they are equal in measurements.
Therefore:
∠7 = ∠6 = 95°

Hope this helps :)
5 0
4 years ago
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You buy a new car for $30,000. It depreciates (decreases in value) 10% every year. In your notes, complete the table below. What
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Step-by-step explanation:

8 0
4 years ago
Suppose you deposit $1,500 in a savings account that pays interest at an annual rate of 5%. If no money is added or withdrawn fr
forsale [732]

Answer:

The solution is given below.

Step-by-step explanation:

Given that

Deposited amount = $1,500

Rate of interest = 5%

We need to find out the following things

a. The account after 4 years i.e. future value

As we know that

Future value = Present value × (1 + rate)^time period

Future value = $1,500 × (1 + 0.05)^4

Future value = $1,500 × (1.05)^4

Future value = $1,823.26

b. The account after 16 years i.e. future value

As we know that

Future value = Present value × (1 + rate)^time period

Future value = $1,500 × (1 + 0.05)^16

Future value = $1,500 × (1.05)^16

Future value = $3,274.312

c. The number of years that contain the amount of $2,000

Here

PV = $1,500

FV = $2,000

PMT = $0

RATE = 5%

The following formula should be applied

= NPER(RATE;PMT;-PV;FV;TYPE)

After applying the above formula, the time period is 4.94 years

d. The number of years that contain the amount of $2,500

Here

PV = $1,500

FV = $2,000

PMT = $0

RATE = 5%

The following formula should be applied

= NPER(RATE;PMT;-PV;FV;TYPE)

After applying the above formula, the time period is 8.77 years

7 0
3 years ago
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