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andrezito [222]

3 years ago

6

A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find th

e velocity and the speed when t = 4. f(t) = 12 + 35 t + 1

1 answer:

Igoryamba3 years ago

5 0

A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and the speed when t = 4. f(t) = 12t² + 35 t + 1

Answer:

Velocity = 131 m/s

Speed = 131 m/s

Explanation:

Equation of motion, s = f(t) = 12t² + 35 t + 1

To get velocity of the particle, let us find the first derivative of s

v (t) = ds/dt = 24t + 35

At t = 4

v(4) = 24(4) + 35

v(4) = 131 m/s

Speed is the magnitude of velocity. Since the velocity is already positive, speed is also 131 m/s

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2 years ago

Suppose that the inverse market demand for silicone replacement tips for Sony earbud headphones is p = pN - 0.1Q, where p is t

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Complete Question

The complete question is shown on the first uploaded image

Answer:

a

The effect of a change in the price of a new pair of headphones on the equilibrium price of replacement tips ( dp/dpN) is

$\frac{\delta p}{\delta p_N} =1$

b

The value of Q and p at equilibruim is

$Q_e = 250$ and $p_d =$ 5

The consumer surplus is $C= 3125$

The producer surplus is $P = 375$

Explanation:

From the question we are told that

The inverse market demand is $p_d = p_N -0.1Q$

The inverse supply function is $p_s = 2+ 0.012Q$

a

The effect of change in the price is mathematically given as

$\frac{\delta p}{\delta p_N}$

Now differntiating the inverse market demand function with respect to $p_N$

We get that

$\frac{\delta p}{\delta p_N} =1$

b

We are told that $p_N =$ $30

Therefore the inverse market demand becomes

$p_d = 30 -0.1Q$

At equilibrium

$p_d = p_s$

So we have

$30 -0.1Q_e = 2+ 0.012Q_e$

Where $Q_e$ is the quantity at equilibrium

$28 = 0.112Q_e$

$Q_e = \frac{28}{0.112}$

$Q_e = 250$

Substituting the value of Q into the equation for the inverse market demand function

$p_d = 30 - 0.1 (250 )$

$p_d =$ 5

Looking at the equation for $p_d \ and \ p_s$ we see that

For Q = 0

$p_d = 30$

$p_s =2$

And for Q = 250

$p_d = 5$

$p_s = 5$

Hence the consumer surplus is mathematically evaluated as

$C = \frac{1}{2} * Q_e * (30 -5)$

Substituting value

$C = \frac{1}{2} * 250 (30-5)$

$C= 3125$

And

The producer surplus is mathematically evaluated as

$P = \frac{1}{2} *250 * (5-2)$

$P = 375$

4 0

3 years ago