Please this is a quizzzz

A particle begins at point (1, 2) and is moving along the line segment joining (1, 2) to (3, 4). Initially, what is the rate of

Bumek [7]

Answer:

Initially, that is, at (1,2), the rate of increase of the function in the direction given = 0

Hence the function is neither increasing nor decreasing initially in the given direction.

Step-by-step explanation:

f(x,y) = 2x² - y²

Rate of Change of the function = ∇f = (fₓ, fᵧ)

And we're told to find the rate of change in a particular direction = ∇f.û

We first obtain the unit vector in that direction, û

Direction = (3,4) - (1,2) = (2,2)

Uni vector = vector/magnitude

Vector = 2î + 2j

magnitude = √(2² + 2²) = √8 = 2 √2

(2î + 2j)/(2√2) = (1/√2)î + (1/√2)j = û

Unit vector in the direction = (1/√2, 1/√2)

f = 2x² - y²

At (1,2)

fₓ = ∂f/∂x = 4x = 4

fᵧ = ∂f/∂y = -2y = -4

∇f = (4,-4)

∇f.û = (4î - 4j).((1/√2)î + (1/√2)j) = (4/√2) - (4/√2) = 0

If it was positive, then the function is increasing, if it was negative, the function is decreasing. Zero means neither of them.

Hence the function is neither increasing nor decreasing initially in the given direction.

7 0

3 years ago

A dance school allows a maximum of 15 students per class of 112 students signing up for class how many classes does the school n

STALIN [3.7K]

The school needs to offer 8 classes

7 0

3 years ago

Read 2 more answers

The length of a rectangle is 7 centimeters greater than the width.

Lisa [10]

Answer:

length = 17cm, width = 10cm

Step-by-step explanation:

2L + 2w = 54

L = w + 7

Substitute:

2(w + 7) + 2w = 54

2w + 14 + 2w = 54

4w = 40

w = 10

L = 10 + 7 = 17

7 0

3 years ago

your patient has a 2500 cc bag of irrigation solution hanging, and 750 cc of fluid has been infused. what percentage of irrigati

nlexa [21]

Answer: 30%

Step-by-step explanation:

Given : Patient has a 2500 cc bag of irrigation solution hanging.

Irrigation has been infused = 750cc

Then, the percentage of irrigation solution has been infused :

$\dfrac{\text{ fluid infused}}{\text{Total irrigation solution}}\times100\\\\=\dfrac{750}{2500}\times100\\\\= 30\%$

Hence, the percentage of irrigation solution has been infused = 30%

6 0

3 years ago

Annual starting salaries in a certain region of the U. S. for college graduates with an engineering major are normally distribut

defon

Answer:

0.8665 = 86.65% probability that the sample mean would be at least $39000

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .