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Debora [2.8K]
3 years ago
10

The position function of a particle in rectilinear motion is given by s(t) = 2t3 – 21t2 + 60t + 3 for t ≥ 0 with t measured in s

econds and s(t) measured in feet. Find the position and acceleration of the particle at the two instants when the particle reverses direction. Include units in your answer.
Mathematics
1 answer:
stepladder [879]3 years ago
6 0
When the direction is reversed  velocity = 0 

v = ds/dt =  6t^2 - 42t + 60 = 0

t^2 - 7t + 10 = 0

(t - 5)(t - 2) = 0

t = 2 s  and 5 s   which are the times when the direction is reversed
Position at t = 2 =  2(2)^3 - 21(2)^2 +60(2) + 3 =  55 feet
  at t = 5  position =  28 feet

Acceleration  = dv/dt = 12t - 42

At t = 2  acceleration =  -18 ft s-2
At  t = 5   ...............    = 18 ft s-2


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A pool company is creating a blueprint for a family pool and a similar dog pool for a new client. Which statement explains how t
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The statement that explains how the company can determine whether pool LMNO is similar to pool PQRS is;

B. Translate PQRS so that point Q of PQRS lies on point M of LMNO, then dilate PQRS by the ratio segment PQ over segment LM.

<h3>How to carry out Transformations?</h3>

Given that quadrilaterals ABCD and EFGH are similar:

The corresponding points on the quadrilaterals are:

P → L

Q → M

R → N

S → O

So, the first step is any of the following:

Translate point P to L

Translate point Q to M

Translate point R to N

Translate point S to O

Notice that the side lengths of PQRS are bigger than that of LMNO

This means that the Quadrilateral PQRS has to be dilated (compressed) by a ratio of side lengths of LMNO divided by side lengths of PQRS

For example, the point M is translated to point Q. The figure will then be dilated by a ratio of LM divided by PQ.

Read more about Transformations at; brainly.com/question/4289712

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3 0
2 years ago
The surface area of a cone is 54 square inches. What is the surface area of a similar cone that is three times as large?
12345 [234]

<u>Given</u>:

Given that the surface area of the cone is 54 square inches.

We need to determine the surface area of the cone that is similar to the cone three times large.

<u>Surface area of the similar cone:</u>

Let us determine the surface area of the similar cone.

The surface area of the similar cone can be determined by multiplying the surface area of the cone by 3. Because it is given that the similar cone is three times large.

Thus, we have;

SA = 3 \times 54

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Thus, the surface area of the similar cone is 162 square inches.

6 0
3 years ago
At the beginning of the week, a puppy weighed 5 1/4 pounds. During the week, the puppy gains 8 ounces.
lys-0071 [83]

Answer:

5 3/4

Step-by-step explanation:

8 ounces is half (1/2) of a pound

1/2 is equivalent to 2/4

So I added 5 1/4 and 2/4

Which gives us 5 3/4

5 0
3 years ago
Represent the relationship between the number of copies made and time in seconds in the table
alexdok [17]

Answer:

you need to put  the table

Step-by-step explanation:

7 0
3 years ago
Identify the ordered pair that represents the vector from a(-9,9) to b(7,3) and the magnitude of ab.
sveta [45]

Answer:

Answers below

Step-by-step explanation:

1. Order pair method

[(x2-x1) , (y2-y1)] = b-a = [(7--9) , (3-9)] = (16,-6)

2. Magnitude

|v| = \sqrt{16^2+-6^2}

v = |17.088|

7 0
3 years ago
Read 2 more answers
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