Write the equation of the given circle.<br><br> center (1, -5)<br> radius of 10

A plane flying horizontally at an altitude of 1 mi and a speed of 470 mi/h passes directly over a radar station. Find the rate a

kiruha [24]

Answer:

407 mi/h

Step-by-step explanation:

Given:

Speed of plane (s) = 470 mi/h

Height of plane above radar station (h) = 1 mi

Let the distance of plane from station be 'D' at any time 't' and let 'x' be the horizontal distance traveled in time 't' by the plane.

Consider a right angled triangle representing the above scenario.

We can see that, the height 'h' remains fixed as the plane is flying horizontally.

Speed of the plane is nothing but the rate of change of horizontal distance of plane. So, $s=\frac{dx}{dt}=470\ mi/h$

Now, applying Pythagoras theorem to the triangle, we have:

$D^2=h^2+x^2\\\\D^2=1+x^2$

Differentiating with respect to time 't', we get:

$2D\frac{dD}{dt}=0+2x\frac{dx}{dt}\\\\\frac{dD}{dt}=\frac{x}{D}(s)$

Now, when the plane is 2 miles away from radar station, then D = 2 mi

Also, the horizontal distance traveled can be calculated using the value of 'D' in equation (1). This gives,

$2^2=1+x^2\\\\x^2=4-1\\\\x=\sqrt3=1.732\ mi$

Now, plug in all the given values and solve for $\frac{dD}{dt}$ . This gives,

$\frac{dD}{dt}=\frac{1.732\times 470}{2}=407.02\approx 407\ mi/h$

Therefore, the distance from the plane to the station is increasing at a rate of 407 mi/h.

6 0

4 years ago

You spend 15 minutes reading email. You then spend 3 hours watching television. Write the ratio of the amount of time spent read

timurjin [86]

The amount of time spent reading email to the amount of time spent watching television is 1/12

Step-by-step explanation:

Given

Time to read email = 15 minutes

Time on television = 3 hours = 3*60 minutes = 180 minutes

Ration is the fraction between two things. In this case, the ration is from the amount of time spent reading email to the amount of time spent watching television

So,

Required ratio will be: 15/180

Simplifying => 1/12

So,

The amount of time spent reading email to the amount of time spent watching television is 1/12

Keywords: Ratio, fractions

Learn more about ratio at:

#LearnwithBrainly

7 0

3 years ago

Solve each equation and check. Show all work please I need it ASAP

Tresset [83]

Answer: 16

Step-by-step explanation:

$-\frac{t}{2}=-8$

in order to get rid of the negative sign and the 2 to isolate t, we must multiply both sides by -2

$-2(-\frac{t}{2}) =-8(-2)$

$t=16$

Proof:

$-\frac{t}{2}=-8\\ -\frac{16}{2}=-8\\ -8=-8$

5 0

4 years ago

PLZ HELP !!!!!!!!!!!!!!!!!!!!!!!!!!

jonny [76]

I think is A 2x²+13x-23

5 0

3 years ago

What is the relationship between 21 and 22?

blsea [12.9K]

someone please help her or him please

4 0

3 years ago

Write the equation of the given circle. center (1, -5) radius of 10