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nexus9112 [7]
2 years ago
15

State if the two vectors are parallel, orthogonal, or neither. u=18i+8j v=9i+4j

Mathematics
1 answer:
Iteru [2.4K]2 years ago
8 0

Answer:

Parallel, since \vec u = 2\cdot \vec v.

Step-by-step explanation:

The relation between both vectors is determined by the use of the dot product, whose expression is:

\cos \theta = \frac{\vec u \bullet \vec v}{\|\vec u\| \|\vec v\|}

Where:

\cos \theta = 1 if vectors are parallel to each other and \cos \theta = 0 if vectors are orthogonal. Then, norms and dot product are calculated hereafter:

\|\vec u\| = \sqrt{18^{2}+8^{2}}

\|\vec u\| \approx 19.698

\|\vec v \| = \sqrt{9^{2}+4^{2}}

\|\vec v\| \approx 9.849

\vec u \bullet \vec v = (18)\cdot (9) + (8)\cdot (4)

\vec u \bullet \vec v = 194

\cos \theta = \frac{194}{(19.698)\cdot (9.849)}

\cos \theta = 1

The two vectors are parallel to each other, which is also supported by the fact that one vector is multiply of the other one. That is,

18i + 8j = 2\cdot (9i + 4j)

\vec u = 2\cdot \vec v

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<u>Answer:</u>

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<u>Solution:</u>

It is given that the height of each cup is 20 cm.

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Since the first cup is 20 cm high, the height cannot be reduced. So the space to fit in the remaining cups in the stack is only 30-20 cm as that’s the remaining space in the dispenser

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As we know that addition of each adds 0.8 cm to the stack, the total number of cups that can be fit in the dispenser can be calculated by the following equation. Let the number of cups other than the first cup be denoted by ‘x’.

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8 0
2 years ago
The rate of change of the number of squirrels S(t) that live on the Lehman College campus is directly proportional to 30 − S(t),
pishuonlain [190]

Answer:

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Step-by-step explanation:

The rate of change of the number of squirrels S(t) that live on the Lehman College campus is directly proportional to 30 − S(t).

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Therefore:

S(t)=30-15e^{\frac{\ln(2/3)}{2}t}\\$When t=3$\\S(t)=30-15e^{\frac{\ln(2/3)}{2} \times 3}\\S(3)=21.8 \approx 22

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6 0
3 years ago
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