Convert the mixed number to an improper fraction. enter your answer below using the slash mark ( / ) as the fraction bar

An airliner maintaining a constant elevation of 2 miles passes over an airport at noon traveling 500 mi/hr due west. At 1:00 PM,

butalik [34]

Answer:

$\frac{ds}{dt}\approx 743.303\,\frac{mi}{h}$

Step-by-step explanation:

Let suppose that airliners travel at constant speed. The equations for travelled distance of each airplane with respect to origin are respectively:

First airplane

$r_{A} = 500\,\frac{mi}{h}\cdot t\\r_{B} = 550\,\frac{mi}{h}\cdot t$

Where t is the time measured in hours.

Since north and west are perpendicular to each other, the staight distance between airliners can modelled by means of the Pythagorean Theorem:

$s=\sqrt{r_{A}^{2}+r_{B}^{2}}$

Rate of change of such distance can be found by the deriving the expression in terms of time:

$\frac{ds}{dt}=\frac{r_{A}\cdot \frac{dr_{A}}{dt}+r_{B}\cdot \frac{dr_{B}}{dt}}{\sqrt{r_{A}^{2}+r_{B}^{2}} }$

Where $\frac{dr_{A}}{dt} = 500\,\frac{mi}{h}$ and $\frac{dr_{B}}{dt} = 550\,\frac{mi}{h}$ , respectively. Distances of each airliner at 2:30 PM are:

$r_{A}= (500\,\frac{mi}{h})\cdot (1.5\,h)\\r_{A} = 750\,mi$

$r_{B}=(550\,\frac{mi}{h} )\cdot (1.5\,h)\\r_{B} = 825\,mi$

The rate of change is:

$\frac{ds}{dt}=\frac{(750\,mi)\cdot (500\,\frac{mi}{h} )+(825\,mi)\cdot(550\,\frac{mi}{h})}{\sqrt{(750\,mi)^{2}+(825\,mi)^{2}} }$

$\frac{ds}{dt}\approx 743.303\,\frac{mi}{h}$

6 0

2 years ago

Please help me answer #4, #5 and #6

Salsk061 [2.6K]

Answer:

4). The Washington Monument is 169.2-m tall.

Step-by-step explanation:

4). We know this because...

person 1.8 0.7

---------- = ----- = -------

Wash. x 65.8

We then know to cross-multiply to get:

1.8(65.8) = 0.7x

Which simplifies down to:

118.44 = 0.7x

x = 169.2

Answer:

5). The pond is 180ft wide.

Step-by-step explanation:

5). We know this because...

90 120

----- = -------

135 x

We then know to cross-multiply to get:

90x = 120(135)

Which simplifies down to:

90x = 16200

x = 180

Answer:

6). The height of the clock tower is 13ft 9in.

Step-by-step explanation:

6). We know this because...

person 5.5 4

---------- = -------- = -----

clock x 10

We then know to cross-multiply to get:

5.5(10) = 4x

Which simplifies down to:

55 = 4x

x = 13.75 (13 ft 9 in)

7 0

2 years ago

Help me please. i need to pass geometry

AleksandrR [38]

Answer:

1080°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 8, thus

sum = 180° × 6 = 1080°

8 0

3 years ago

What is the equation, in slope-intercept form, of the line that passes through (0, −2) and has a slope of −3?

Julli [10]

Answer:

y= -3x-2

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

A polygon has an angle sum of 360°, and each angle measures 90°. What is the polygon?

Brums [2.3K]

<span>A polygon has an angle sum of 360°, and each angle measures 90°. Let's find our what is the polygon.
=> 360 degrees polygon with 90 degree measure for each angles.
=> 360 degrees / 90 degrees = 4
Therefore the polygon is a square.</span>

3 0

2 years ago