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Ivanshal [37]
3 years ago
14

On the moon, the acceleration due to gravity is -1.6 meters per second per second. A stone is dropped from a cliff on the moon a

nd hits the surface of the moon 20 seconds later.a) How far did it fall?b) What was its velocity at impact?
Mathematics
1 answer:
zepelin [54]3 years ago
4 0

Answer:

How far did it fall? -320 meters

What was its velocity at impact? -32 m/s

Step-by-step explanation:

a) How far did it fall?

To calculate the distance traveled by the stone we must use the following formula:

d=\frac{gt^{2}}{2}

Sustituing the given values we have that:

d=\frac{-1.6\times 20^{2}}{2}\\ d=\frac{-1.6\times 400}{2}\\ d=\frac{-640}{2}\\ d=-320 m

The distance traveled by the stone was -320 meters under the released point

b) What was its velocity at impact?

To calculate the velocity we need to use the formula:

v=gt

Sustituing the given values we have that:

v=(-1.6)(20)\\v=-32 m/s

So the velocity is -32 meteres per second, the negative sign indicate that the object is going down

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Systems of linear equations ; elimination method<br><br><br> pls help&lt;3
Basile [38]
<h3>Answer:</h3>

System

  • 10s +25t = 11700
  • s -2t = 0

Solution

  • s = 520
  • t = 260
<h3>Explanation:</h3>

Let s and t represent single-entry and three-day tickets, respectively. These variables represent the numbers we're asked to find: "how many of each [ticket type] he sold."

We are given the revenue from each ticket type, and the total revenue, so we can write an equation based on the relation between prices, numbers sold, and revenue:

... 10s +25t = 11700 . . . . . equation for total revenue

We are also given a relation between the two number of tickets sold:

... s = 2t . . . . . . . . . . . . . . . twice as many single tickets were sold as 3-day

We can rearrange this second equation to put it into standard form. That makes it easier to see what to do to eliminate a variable.

... s -2t = 0 . . . . . . . . . . . . subtract 2t to put into standard form

So, our system of equations is ...

  • 10s +25t = 11700
  • s -2t = 0

<em>What </em>elimination<em> is all about</em>

The idea with "elimination" is to find a multiple of one (or both) equations such that the coefficients of one of the variables are opposite. Then, the result of adding those multiples will be to eliminate that variable.

Here, we can multiply the second equation by -10 to make the coefficient of s be -10, the opposite of its value in the first equation. (We could also multiply the first equation by -0.1 to achieve the same result. This would result in a non-integer value for the coefficient of t, but the solution process would still work.)

Alternatively, we can multiply the first equation by 2 and the second equation by 25 to give two equations with 50t and -50t as the t-variable terms. These would cancel when added, so would eliminate the t variable. (It seems like more work to do that, so we'll choose the first option.)

<em>Solution by elimination</em>

... 10s +25t = 11700 . . . . our first equation

... -10s +20t = 0 . . . . . . . second equation of our system, multiplied by -10

... 45t = 11700 . . . . . . . . .the sum of these two equations (s-term eliminated)

... t = 11700/45 = 260 . . . . . divide by the coefficient of t

... s = 2t = 520 . . . . . . . . . . use the relationship with s to find s

_____

<em>Solution using your number sense</em>

As soon as you see there is a relation between single-day tickets and 3-day tickets, you can realize that all you need to do is bundle the tickets according to that relation, then find the number of bundles. Here, 2 single-day tickets and 1 three-day ticket will bundle to give a package worth 2×$10 + $25 = $45. Then the revenue of $11700 will be $11700/$45 = 260 packages of tickets. That amounts to 260 three-day tickets and 520 single-day tickets.

(You may notice that our elimination solution effectively computes this same result, where "t" and the number of "packages" is the same value (since there is 1 "t" in the package).)

6 0
3 years ago
Can someone help me, please?
MrRa [10]

Answer:

For the first two you are right, the last two should be 1/10 and 9/10.

Step-by-step explanation:

The probability that you win is both blue and even number happen, which is 1/5 * 3/6 = 3/30 = 1/ 10, then the probability you not win is 1- 1/10 = 9/10.

If it is helpful, plz give me Brainliest.

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2 years ago
12 POINTS!!!<br><br><br> Find x. (Hint. Draw an auxiliary line
padilas [110]

Answer:

30

Step-by-step explanation:

x+50=180(संगत कोन भएकाले )

x=180-50

X=130

अब,

130-100=30

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Rút gọn M=[ căn x -2/x-1- căn x +2/x+2 căn x+ 1] nhân x bình-2x+1/2 với x&gt;0 x khác 1
Ymorist [56]

Answer:

Step-by-step explanation:

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3 years ago
Which is a solution to the equation?<br> (х-2)(х + 5) = 18?
jok3333 [9.3K]

\bf (x-2)(x+5)=18\implies \stackrel{\mathbb{F~O~I~L}}{x^2+3x-10}=18\implies x^2+3x-28=0 \\\\\\ (x-4)(x+7)=0\implies x= \begin{cases} 4\\ -7 \end{cases}

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2 years ago
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