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3 years ago

Niagara Falls is 51 meters high. If you dropped a ball off the ledge, how much time would it take it to hit the water?

2 answers:

5 0

Rounded the answer should be 6 seconds, because the gravity of earth accelerates objects at 9.8 meters per second, and then 51 divided by 9.8 is 5.21 rounded to get 6

Licemer1 [7]3 years ago

3 0

It takes a ball about 0.45 seconds to drop 1 meter so for a ball to drop about 51 meters would take 22.95 seconds. Multiply 51 by 0.45. Hope this helps

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Every map projection has some degree of distortion because

Sholpan [36]

A - a curved surface cannot be represented on a flat surface without distortion

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2 years ago

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True

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1 year ago

2. Find the solution of each differential equation. (a) y/2y-8y = 0 (b) 25y/- 20y + 4y = 0 (c) y + 2y + 2y = 0 2. Find the solut

jek_recluse [69]

Each of these ODEs is linear and homogeneous with constant coefficients, so we only need to find the roots to their respective characteristic equations.

(a) The characteristic equation for

$y'' - 2y' - 8y = 0$

$r^2 - 2r - 8 = (r - 4) (r + 2) = 0$

which arises from the ansatz $y = e^{rx}$ .

The characteristic roots are $r=4$ and $r=-2$ . Then the general solution is

$\boxed{y = C_1 e^{4x} + C_2 e^{-2x}}$

where $C_1,C_2$ are arbitrary constants.

(b) The characteristic equation here is

$25r^2 - 20r + 4 = (5r - 2)^2 = 0$

with a root at $r=\frac25$ of multiplicity 2. Then the general solution is

$\boxed{y = C_1 e^{2/5\,x} + C_2 x e^{2/5\,x}}$

$r^2 + 2r + 2 = (r + 1)^2 + 1 = 0$

with roots at $r = -1 \pm i$ , where $i=\sqrt{-1}$ . Then the general solution is

$y = C_1 e^{(-1+i)x} + C_2 e^{(-1-i)x}$

Recall Euler's identity,

$e^{ix} = \cos(x) + i \sin(x)$

Then we can rewrite the solution as

$y = C_1 e^{-x} (\cos(x) + i \sin(x)) + C_2 e^{-x} (\cos(x) - i \sin(x))$

or even more simply as

$\boxed{y = C_1 e^{-x} \cos(x) + C_2 e^{-x} \sin(x)}$

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1 year ago

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ioda

The biggest problem for racial integration is that people live in segregated areas: so simply a school can have a majority of children from one background because the area around the school is inhabited by people of this background.

So the correct answer is d. Segregated housing patterns are still common in many communities.

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3 years ago

Pavlova-9 [17]

Answer:

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Explanation:

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3 years ago