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Nezavi [6.7K]
3 years ago
9

Find the area of the composite shape lable your answer in square in

Mathematics
1 answer:
Lelechka [254]3 years ago
4 0

Answer:

Step-by-step explanation:

A = 6(12) + ½(12)(3) = 90 in²

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Find the velocity and position vectors of a particle that has the given acceleration and the given initial velocity and position
stira [4]

Answer:

v(t) = (2t+1) \mathbb{i} +3t^2 \mathbb{j} +4t^3 \mathbb{k}

r(t) = (t^2+t) \mathbb{i} +(t^3+2) \mathbb{j} +(t^4 - 3) \mathbb{k}

Step-by-step explanation:

The velocity vector is the integral of the acceleration vector i.e.

v(t) = \int a(t) dt

v(t) = \int (2 \mathbb{i}+6t \mathbb{j} 12t^2 \mathbb{k}) dt

v(t) = 2t \mathbb{i}+3t^2 \mathbb{j} 4t^3 \mathbb{k} + C_1

When t=0, v(0) = \mathbb{i}. Inserting these values in v(t),

C_1= \mathbb{i}

v(t) = 2t \mathbb{i}+3t^2 \mathbb{j} 4t^3 \mathbb{k} + \mathbb{i}

v(t) = (2t+1) \mathbb{i}+3t^2 \mathbb{j} 4t^3 \mathbb{k}

The position vector is the integral of the velocity vector i.e.

r(t) = \int v(t) dt

r(t) = \int ((2t+1) \mathbb{i}+3t^2 \mathbb{j} 4t^3 \mathbb{k}) dt

r(t) = (t^2+t) \mathbb{i}+t^3 \mathbb{j} t^4 \mathbb{k} + C_2

When t=0, r(t) =2\mathbb{j}-3\mathbb{k}. Inserting these values in r(t),

C_2=2\mathbb{j}-3\mathbb{k}

r(t)= (t^2+t) \mathbb{i}+t^3 \mathbb{j}+ t^4 \mathbb{k} + 2\mathbb{j}-3\mathbb{k}

r(t) = (t^2+t) \mathbb{i}+(t^3+2) \mathbb{j}+ (t^4-3) \mathbb{k}

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Answer:

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Step-by-step explanation:

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