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1 year ago

Scientists studying dolphin echolocation simulate the projection of a bottlenose dolphin's clicking sounds using computer

Mathematics

1 answer:

lina2011 [118]1 year ago

4 0

Step-by-step explanation:

The equation of a parabola with focus at (h, k) and the directrix y = p is given by the following formula:

(y - k)^2 = 4 * f * (x - h)

In this case, the focus is at the origin (0, 0) and the directrix is the line y = -1.3, so the equation representing the cross section of the reflector is:

y^2 = 4 * f * x

= 4 * (-1.3) * x

= -5.2x

The depth of the reflector is the distance from the vertex to the directrix. In this case, the vertex is at the origin, so the depth is simply the distance from the origin to the line y = -1.3. Since the directrix is a horizontal line, this distance is simply the absolute value of the y-coordinate of the line, which is 1.3 inches. Therefore, the depth of the reflector is approximately 1.3 inches.

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3 years ago

Read 2 more answers

At 1 P.M., ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast i

Evgen [1.6K]

The distance between the ships is changing at a rate of 21.393 km/h

Step 1: First, you must draw an image to help better understand the problem

The reason that ship A is moving -35km/h is because ship B acts as an "origin" and as things move closer to the "origin" they become negative and as things move away from the "origin" they become positive.

We know that the rate of Ship A is expressed as dAdt=−35 and the rate of Ship B is expressed as dBdt=25

Step 2: We want to figure out how many km Ship A and Ship B traveled in 4 hours

ShipA:−35kmh⋅4hr=−140km

Now if we take this −140km and add it to the 150km we can see that Ship A is now only 10km away from where Ship B began

ShipB:25kmh⋅4hr=100km

This means that Ship B is now 100km from where it originally started

We can now redraw our information

Step 3: We must use the Pythagorean Theorem to find the third side of the triangle

x2+y2=z2→102+1002=z2

z=√102+1002

Step 4: Now that we know z, we must differentiate the original equation in order to find the rate at which z in changing

x2+y2=z2→2xdxdt+2ydydt=2zdzdt

We can simplify by canceling out the 2's

xdxdt+ydydt=zdzdt

Step 5: Write down all the information and then plug into equation

x=10anddxdt=−35
y=100anddydt=25
z=√102+1002anddzdt=?

Now plug in the information

xdxdt+ydydt=zdzdt

10(−35)+100(25)=√102+1002dzdt

−350+2500=√102+1002dzdt

2150=√102+1002dzdt

21.393=dzdt

The distance between the ships are increasing at a rate of 21.393 km/h

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3 years ago

The Falcons had 3 fewer than twice as many Bears players. If the Falcons had 11 players, how many players were on the Bears?

Dmitry [639]

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2 years ago

Determine the equations of the vertical and horizontal asymptotes, if any, for y=x^3/(x-2)^4

djverab [1.8K]

Answer:

Option a)

Step-by-step explanation:

To get the vertical asymptotes of the function f(x) you must find the limit when x tends k of f(x). If this limit tends to infinity then x = k is a vertical asymptote of the function.

$\lim_{x\to\\2}\frac{x^3}{(x-2)^4} \\\\\\lim_{x\to\\2}\frac{2^3}{(2-2)^4}\\\\\lim_{x\to\\2}\frac{2^3}{(0)^4} = \infty$

Then. x = 2 it's a vertical asintota.

To obtain the horizontal asymptote of the function take the following limit:

$\lim_{x \to \infty}\frac{x^3}{(x-2)^4}$

if $\lim_{x \to \infty}\frac{x^3}{(x-2)^4} = b$ then y = b is horizontal asymptote

Then:

$\lim_{x \to \infty}\frac{x^3}{(x-2)^4} \\\\\\lim_{x \to \infty}\frac{1}{(\infty)} = 0$

Therefore y = 0 is a horizontal asymptote of f(x).

Then the correct answer is the option a) x = 2, y = 0

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3 years ago

Read 2 more answers

14 and 15, please :p explanation would also be appreciated!!

liraira [26]

14. B (4, -2)
15. I am not exactly sure about this one but I would say either A or B.

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3 years ago