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2 years ago

3. A parking fee at SM Lucena costs P25.00 for the first two hours and an extra P5.00

Mathematics

1 answer:

kaheart [24]2 years ago

3 0

Answer:

p(t) = 25 + 5t if t ≤ 12

p(t) = 100 if t > 12

Step-by-step explanation:

Given

1. When time is not more than 12 hours.

Base amount = P25

Additional = P5 per hour

2. When time is more than 12 hours

Fee = P100 one time payment

Represent (1) as a function of t.

p(t) = Base Amount + Additional * t

p(t) = 25 + 5 * t

P(t) = 25 + 5t --- when t ≤ 12

Represent (2) as a function

P(t) = 100 ---- when t > 12

So, the complete function is

p(t) = 25 + 5t if t ≤ 12

p(t) = 100 if t > 12

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A child wanders slowly down a circular staircase from the top of a tower. With x,y,zx,y,z in feet and the origin at the base of

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c) Her speed at time t is 5 \sqrt[]{5} ft/minute

d) Her acceleration at time t is 10 ft/minute^2

Step-by-step explanation:

Consider the path described by the child as going down the tower to have the following parametrization $\gamma(t) = (10\cos t, 10 \sin t, 90-5t)$

a) Assuming that the child is at the top of the tower when she starts going down, we have that at the initial time (t=0) we will have the value of the height of the tower. That is z = 90-5*0 = 90 ft.

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c) Given the parametrization we are given, the velocity of the child at time t is given by $\frac{d\gamma}{dt}= (\frac{d}{dt}(10\cos t), \frac{d}{dt} (10 \sin t ), \frac{d}{dt}(90-5t)) = (-10 \sin t, 10 \cos t, -5)$ . The speed is defined as the norm of the velocity vector,

so, the speed at time t is given by $v = \sqrt[]{(-10 \sin t)^2+(10 \cos t)^2+(-5)^2} = \sqrt[]{100(\sin^2 t + \cos^2 t)+25} = \sqrt[]{125}= 5 \sqrt[]{5}$

d) ON the same fashion we want to know the norm of the second derivative of $\gamma$ .

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2 years ago

1.How much taller Porter is than Henry, given that Porter is n inches tall and Henry is m inches tall. 2.How many times as tall

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Answer:

Porter is $n-m$ inches taller than Henry.

Porter is $\frac{n}{m}$ times taller than henry.

Step-by-step explanation:

The difference in height can be found using subtraction.

Since Porter is taller than Henry, we'll subtract away Henry's height from Porter's height. This will leave us with only the difference between the heights.

n = Porter's height

m = Henry's height

Difference in height is thus:

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Answer: Porter is $n-m$ inches taller than Henry.

To find out how many times taller Porter is than Henry, we can use division.

An example: if Porter was 200cm, and Henry was 100cm, Porter is obviously 2 times as tall.

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Using our values, n and m, we'll divide n by m.

$\frac{n}{m}$

Answer: Porter is $\frac{n}{m}$ times taller than henry.

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2 years ago