Solve for angle B in right triangle ABC. <br><br> I got 53, is it right?

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

3 years ago

Last Sunday a certain store sold copies of 256 Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the stor

Marat540 [252]

Answer:

D. $\frac{400p}{500-p}$

Step-by-step explanation:

let's call A the number of copies sold of newspaper A and B the number of copies sold of newspaper B.

So, we can formulate the following equations from the sentence: a certain store sold copies of 256 Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each as:

A + B = 256 (1)

1A + 1.25 B = Total Revenue (2)

Then, r and p are equal to:

$r=\frac{A}{Total Revenue}*100=\frac{100A}{A+1.25B}$ (3)

$p=\frac{A}{256} *100=\frac{100A}{256}$ (4)

Isolating A from (4) and B from (1), we get:

$A=\frac{256p}{100} =2.56p$ (5)

$B=256-A=256-2.56p$ (6)

Finally, replacing (5) and (6) in (3), we get:

$r=\frac{100A}{A+1.25B}=\frac{100(2.56p)}{2.56p+1.25(256-2.56p)}\\\\r=\frac{256p}{2.56p+320-3.2p}=\frac{256p}{320-0.64p}\\\\r=\frac{256p/0.64}{(320-0.64p)/0.64}=\frac{400p}{500-p}$

7 0

4 years ago

What is a variable in mathematics?

Dmitrij [34]

Answer:

variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).

7 0

2 years ago

Read 2 more answers

A tent in the shape of a triangular prism is set up at a camping site. Use the measurements to calculate the volume of the tent.

nlexa [21]

It’s d
It’s d Bc I make more sense

3 0

3 years ago

Which function has an inverse function?

joja [24]

Answer:

x=25.y2+755

y=x/25.2+755

4 0

3 years ago

Solve for angle B in right triangle ABC. I got 53, is it right?