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Nina [5.8K]
3 years ago
9

An object moves along a coordinate axis so that its position at time t is given by s(t)=t3. Estimate its instantaneous velocity

at time t=2 by computing its average velocity over the time interval [2,2.001].
Mathematics
1 answer:
Mademuasel [1]3 years ago
6 0

If the position at time <em>t</em> is

<em>s(t)</em> = (1 m/s³) <em>t</em> ³

then the average velocity over <em>t</em> = 2 s and <em>t</em> = 2.001 s is

<em>v</em> (ave) = (<em>s</em> (2.001 s) - <em>s</em> (2 s)) / (2.001 s - 2 s)

<em>v</em> (ave) = ((1 m/s³) (2.001 s)³ - (1 m/s³) (2 s)³) / (2.001 s - 2 s)

<em>v</em> (ave) ≈ (8.01201 m - 8 m) / (0.001 s)

<em>v</em> (ave) ≈ 12.006 m/s

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Answer:

104 ft

Step-by-step explanation:

6 x 4 = 24

16 x 8 = 128

128 - 24 = 104 ft

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3 years ago
A field is a unit of data consisting of one or more ________.
san4es73 [151]
A field is a unit of data consisting of one or more characters(bytes).

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The number of defective components produced by a certain process in one day has a Poisson distribution with a mean of 20. Each d
liberstina [14]

Answer: 0.0516

Step-by-step explanation:

Given : The number of defective components produced by a certain process in one day has a Poisson distribution with a mean of \lambda=20.

The probability mass function for Poisson distribution:-P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}

For x= 15 and  \lambda=20 , we have

P(X=x)=\dfrac{e^{-20}(20)^{15}}{15!}=0.0516488535318\approx0.0516

Hence, the probability that exactly 15 defective components are produced in a particular day = 0.0516

7 0
3 years ago
Identify the expression that is equivalent to cot x/ csc x -1
Yuri [45]
Cotx = cosx/sinx
cscx = 1/sinx

If we plug these into your equation we get:
(cosx/sinx)/(1/sinx) - 1

Dividing by a number is the same as multiplying by its reciprocal so it can be rewritten as:
(cosx/sinx)(sinx) - 1 

The two sinx's cancel each other out so we end up with cosx - 1

8 0
3 years ago
Factorize:<br>(2a - b)² - (a - 2b)²​
bagirrra123 [75]

Answer:

3(a - b)(a + b)

Step-by-step explanation:

Factorize: (2a - b)² - (a - 2b)²​

  • Different of Perfect a Square rule: a²​ - b²​ = (a + b)(a - b)

(2a - b)² - (a - 2b)²​ = [(2a - b) + (a - 2b)] × [(2a - b) - (a - 2b)]

1. Distribute and Simplify:

Distribute the (+) sign on the first bracket and simplify: [(2a - b) + (a - 2b)] → 2a - b + a - 2b → (3a - 3b)

Distribute the (-) sign on the first bracket and simplify: [(2a - b) - (a - 2b)] → 2a - b – a + 2b → (a + b)

We now have:

(3a - 3b)(a + b)

2. Factor out the Greatest Common Factor (3) from 3a - 3b:

(3a - 3b) → 3(a - b)

3. Add "(a + b)" back into your factored expression:

3(a - b)(a + b)

Hope this helps!

7 0
2 years ago
Read 2 more answers
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