A particle is moving with the given data. Find the position of the particle. a(t) = 2t + 9, s(0) = 8, v(0) = −7

1 answer:

4 0

If you mean by a(t)=2t+9 is the acceleration function then we integrate...

v(t)=2t^2/2+9t+c where c is vo and we are told that that is -7 so

v(t)=t^2+9t-7 integrating again we get:

s(t)=t^3/3+9t^2/2-7t+c where c is the initial position which is 8 so

s(t)=t^3/3+9t^2/2-7t+8 which neatened up as

s(t)=(2t^3+27t^2-42t+48)/6

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The Smith family is designing new plans for an in-ground pool. Mr. Smith draws a rectangular shape with a length that is 5 feet

Vinil7 [7]

Answer:
total area = w^2 + 13w + 36 ft^2

Explanation:
The final pool and the sideways will be as shown in the attachment

1- We will get the area of the pool:
length of pool = w + 5
width of pool = w
area of pool = length * width
area of pool = w (w+5) square ft ...........> I

2- We will get the area of the sideways:
The side way is composed of the two blue rectangles and the two green ones
Therefore:
area of sideway = 2(area of blue rectangle) + 2(area of green rectangle)
a- getting the area of the blue rectangle:
length = w + 5 + 2 + 2 = w+9
width = 2
area of blue rectangle = length * width
area of blue rectangle = 2(w+9) square ft ..........> a
b- getting the area of the green rectangle:
length = w
width = 2
area of green rectangle = length * width
area of green rectangle = 2w square ft ..............> b
c- getting area of sideways:
as mentioned before:
area of sideways = 2(area of blue rectangle) + 2(area of green rectangle)
area of sideways = 2*equation a + 2*equation b
area of sideways = 2 (2(w+9)) + 2(2w)
area of sideways = 4(w+9) + 4w
area of sideways = 4w + 36 + 4w
area of sideways = 8w + 36 ...........> II

3- getting the total area:
total area = area of pool + area of sideways
total area = equation I + equation II
total area = w (w+5) + 8w + 36
total area = w^2 + 5w + 8w + 36
total area = w^2 + 13w + 36 ft^2

Hope this helps :)