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Vedmedyk [2.9K]
3 years ago
15

A rock is thrown vertically upward from the surface of an airless planet. It reaches a height of s = 120t - 4t2 meters in t seco

nds. How high does the rock go? How long does it take the rock to reach its highest point?
Mathematics
1 answer:
12345 [234]3 years ago
6 0

Answer:

Step-by-step explanation:

Given that a rock is thrown vertically upward from the surface of an airless planet. It reaches a height of s(t) = 120t - 4t^2

where t is expressed in seconds

The rock goes upto a height where the velocity becomes 0 and then it starts falling down by gravity

Velocity at time t = s'(t) = 120-8t

This becomes 0 when t =15 seconds

Hence at 15th second the rock starts falling and upto

s(15) = 120(15)-4(15^2)\\= 900 metres high it goes

The time taken to reach highest point is = 15 seconds.

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A password is 4 characters long, consisting of 2 letters and 2 numbers. The password must begin and end with a
Kisachek [45]

Answer:

a.

65,000

Step-by-step explanation:

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It’s - ( - 3 ) because a negative times a negative equals a positive so it wouldn’t be - ( 3 ) because it would turn into a negative number and - ( - 3 ) would be positive
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Find the derivative of Y=2xcos2x​
Nastasia [14]

Answer:

Y' = -xsin(2x) + 2cos(2x)

Step-by-step explanation:

For this problem, we will need to use the product rule since you have two terms that contain the variable x.

The product rule is simply as follows:

The derivative of the function is the product of the first term times the derivative of the second term plus the derivative of the first term times the second term.

Note the derivative of 2x with respect to x, is 2.

Note the derivative of cos(2x) with respect to x is (-1/2) sin(2x).

With this in mind, let's find the derivative of our function with respect to x.

Y = 2xcos2x

Y = 2x * cos(2x)

Y' = 2x * (-1/2)sin(2x) + 2 * cos(2x)

Y' = (2x * -1 / 2) sin(2x) + 2 * cos(2x)

Y' = (-x)sin(2x) + 2cos(2x)

So the derivative of our function is Y' = -xsin(2x) + 2cos(2x) according to the application of the product rule.

Cheers.

3 0
2 years ago
In a geometric sequence, a4 = 54 and a7 = 1,458. what is the 12th term? <br><br> answer: B) 354,294
slamgirl [31]

Option B:

The 12th term is 354294.

Solution:

Given data:

a_4=54 and a_7=1458

To find a_{12}:

The given sequence is a geometric sequence.

The general term of the geometric sequence is a_n=a_1\ r^{n-1}.

If we have 2 terms of a geometric sequence a_n and a_k (n > K),

then we can write the general term as a_n=a_k\ r^{n-k}.

Here we have a_4=54 and a_7=1458.

So, n = 7 and k = 4 ( 7 > 4)

a_7=a_4\ .\ r^{7-4}

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This can be written as

$r^3=\frac{1458}{54}

$r^3=27

$r^3=3^3

Taking cube root on both sides of the equation, we get

r = 3

a_{12}=a_7\ .\ r^{12-7}

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2 years ago
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aleksklad [387]

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