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Jobisdone [24]
2 years ago
14

Given u = −8i − 3j and v = −12i − 7j, what is projvu?

Mathematics
1 answer:
8090 [49]2 years ago
7 0

Answer:

  (b)  -7.275i -4.244j

Step-by-step explanation:

The projection of vector u onto vector v is the product of the unit vector v, the magnitude of vector u, and the cosine of the angle between them.

__

The dot product gives the product of the magnitudes of the two vectors and the cosine of the angle between them. To find the projection, we must divide the dot product by the magnitude of v and multiply by the unit vector in the direction of v.

  proj(u,v)=(\vec{u}\cdot\vec{v})\cdot\dfrac{\vec{v}}{|\vec{v}|^2}=\dfrac{((-8)(-12)+(-3)(-7))(-12\vec{i}-7\vec{j})}{(-12)^2+(-7)^2}\\\\=\dfrac{-(96+21)(12\vec{i}+7\vec{j})}{144+49}=-\dfrac{117}{193}(12\vec{i}+7\vec{j})\approx\boxed{-7.275\vec{i}-4.244\vec{j}}

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Answer:

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Step-by-step explanation:

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7 0
2 years ago
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Answer:

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We need to check the conditions in order to use the normal approximation.

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Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

We know that n = 50 and p =0.78.

We need to check the conditions in order to use the normal approximation.

np=50*0.78=39  \geq 10

n(1-p)=50*(1-0.78)=11 \geq 10

Since both conditions are satisfied we can use the normal approximation and the distribution for the proportion is given by:

p \sim N (p, \sqrt{\frac{p(1-p)}{n}})

With the following parameters:

\mu_ p = 0.78

\sigma_p = \sqrt{\frac{0.78*(1-0.78)}{50}}= 0.0586

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Answer:

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hope this helps

brainliest appreciated

good luck! have a nice day!

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