Suppose you are climbing a hill whose shape is given by the equation z = 900 − 0.005x2 − 0.01y2, where x, y, and z are measured in meters, and you are standing at a point with coordinates (120, 80, 764). The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend or descend? ascend descend Correct: Your answer is correct.

Answers

Answer 1

Answer:

Answer:

Ascend

Step-by-step explanation:

In order to solve this problem, we are going to use some principles of vector calculation. The concepts we are going to use are Partial derivatives, gradient vector, velocity vector, direction vector, and directional derivative.

The gradient vector is a vector that describes how is the 'slope' in the space of a multivariable function at a specified point; it is built as a vector of partial derivatives. The vector velocity is a vector that describes the direction and speed of the movement of a body, if we make the velocity a unitary vector (a vector whose norm is 1), we obtain the direction vector (because we are not considering the real norm of the vector, just direction). Finally, the directional derivative is a quantity (a scalar) that describes the slope that we get on a function if we make a displacement from a particular point in a specific direction.

The problem we have here is a problem where we want to know how will be the slope of the hill if we stand in the point (120, 80, 764) and walk due south if the hill has a shape given by z=f(x,y). As you see, we have to find the directional derivative of z=f(x,y) at a specific point (120, 80, 764) in a given displacement direction; this directional derivative will give us the slope we need. The displacement direction 'u' is (0,-1): That is because 'y' axis points north and our displacement won't be to the east either west (zero for x component), just to south, which is the opposite direction of that which the y-axis is pointing (-1 for y component). Remember that the direction vector must be a unitary vector as u=(0,-1) is.

Let's find the gradient vector:

$z=900-0.005x^2-0.01y^2\n(\partial z)/(\partial x)=-0.005*2*x=-0.01x\n(\partial z)/(\partial y)=-0.01*2*y=-0.02y\n \nabla (z)=(-0.01x,-0.02y)$

Evaluate the gradient vector at (120,80) (764 is z=f(120,80); you may confirm)

$\nabla (z(120,80))=(-0.01*120,-0.02*80)=(-1.2,-1.6)$

Finally, find the directional derivative; if you don't remember, it can be found as a dot product of the gradient vector and the direction vector):

$D_(u,P_0)= \nabla (z)_(P_0)\cdot u\nD_(u,P_0)= (-1.2,-1.6)\cdot (0,-1)=1.6$

As you see, the slope we find is positive, which means that we are ascending at that displacement direction.

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The temperature, H, in °F, of a cup of coffee t hours after it is set out to cool is given by the following equation. H = 70 + 120(1/4)t (a) What is the coffee's temperature initially (that is, at time t = 0)? 190 °F What is the coffee's temperature after 1 hour? 100 °F What is the coffee's temperature after 2 hours? (Round your answer to one decimal place.) 2 °F (b) How long does it take the coffee to cool down to 85°F? (Round your answer to three decimal places.) 5 hr How long does it take the coffee to cool down to 75°F? (Round your answer to three decimal places.) 5 hr
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3is (4,-5) a solution of the graphed inequality?Choose 1 answer:Yes0No
Solve for x x/8−9=1x=

What is equation to find 24÷8

Answers

You have the equation

Answer:

Step-by-step explanation:

What is the quotient of 10?

Answers

A quotient is the result of dividing one number by another. For example, the quotient of 6 and 3 equals 6/3 or 2. In your problem above it is asking you to provide the quotient of 10 and 2 meaning you divide the 2 into the ten and end up with 10/2 or 5.

So I think the answer is 10/2 or 5

Victor collects data on the price of a dozen eggs at 8 different stores.median: $ 1.55
Find the lower quartile and upper quartile of
the data set.
lower quartile: $
upper quartile: S
?
$1.39 $1.40 $1.44 $1.50 $1.60 $1.63 $1.65 $1.80

Answers

Answer:

Lower quartile: $1.42

Upper quartile: $1.64

Step-by-step explanation:

The median is the middle value when all data values are placed in order of size.

The ordered data set is:

$1.39 $1.40 $1.44 $1.50 $1.60 $1.63 $1.65 $1.80

There are 8 data values in the data set, so this is an even data set.

Therefore, the median is the mean of the middle two values:

$\implies \sf Median\;(Q_2)=(\$1.50+\$1.60)/(2)=\$1.55$

Place "||" in the middle of the data set to signify where the median is:

$1.39 $1.40 $1.44 $1.50 ║ $1.60 $1.63 $1.65 $1.80

The lower quartile (Q₁) is the median of the data points to the left of the median. As there is an even number of data points to the left of the median, the lower quartile is the mean of the the middle two values:

$\implies \sf Lower\;quartile\;(Q_1)=(\$1.40+\$1.44)/(2)=\$1.42$

The upper quartile (Q₃) is the median of the data points to the right of the median. As there is an even number of data points to the right of the median, the upper quartile is the mean of the the middle two values:

$\implies \sf Upper \;quartile\;(Q_1)=(\$1.63+\$1.65)/(2)=\$1.64$

Answer:

to find the lower quartile and upper quartile of the given dataset, we need to first arrange the data in ascending order:

$1.39, 1.40, 1.44, 1.50, 1.60, 1.63, 1.65, 1.80$

The median of the dataset is given as $1.55$. Since there are an even number of data points, the median is the average of the two middle values, which in this case are $1.50$ and $1.60$.

Now, we need to find the lower quartile and upper quartile. The lower quartile is the median of the lower half of the data set, and the upper quartile is the median of the upper half of the data set.

The lower half of the dataset is $1.39, 1.40, 1.44, 1.50$. The median of this half is the average of the middle two values, which are $1.40$ and $1.44$.

Therefore, the lower quartile is $1.42$.

The upper half of the dataset is $1.60, 1.63, 1.65, 1.80$. The median of this half is the average of the middle two values, which are $1.63$ and $1.65$.

Therefore, the upper quartile is $1.64$.

Hence, the lower quartile of the dataset is $1.42$ and the upper quartile is $1.64$.

A bell tower casts a 60 cm shadow. At the same time a sculpture that is 4.5 meters tall casts a 15 cm shadow. How tall is the bell tower

Answers

Answer: 18

Step-by-step explanation:

x/4.5= 60/15

15x=270

X = 18cm

Suppose that weekly income of migrant workers doing agricultural labor in Florida has a distribution with a mean of $520 and a standard deviation of $90. A researcher randomly selected a sample of 100 migrant workers. What is the probability that sample mean is less than $500

Answers

Answer:

$z = (500-520)/((90)/(√(100)))= -2.22$

And we can find this probability using the normal standard distribution and we got:

$P(z<-2.22) =0.0132$

Step-by-step explanation:

For this case we have the foolowing parameters given:

$\mu = 520$ represent the mean

$\sigma =90$ represent the standard deviation

$n = 100$ the sample size selected

And for this case since the sample size is large enough (n>30) we can apply the central limit theorem and the distribution for the sample mean would be given by:

$\bar X \sim N(\mu , (\sigma)/(√(n)))$

And we want to find this probability:

$P(\bar X <500)$

We can use the z score formula given by:

$z = (500-520)/((90)/(√(100)))= -2.22$

And we can find this probability using the normal standard distribution and we got:

$P(z<-2.22) =0.0132$

The American Community Survey is an ongoing survey that provides data every year to give communities the current information they need to plan investments and services. The 2010 American Community Survey estimates that 14.6% of Americans live below the poverty line, 20.7% speak a language other than English (foreign language) at home, and 4.2% fall into both categories. a. Draw a Venn diagram summarizing the variables and their associated probabilities
b. What percent of Americans live below the poverty line and only speak English at home?
c. What percent of Americans live below the poverty line or speak a foreign language at home?

Answers

Answer:

b. 10.4

c. 26.9

Step-by-step explanation:

Let the universal set U = 100% which is the total no of people in the American community

Let A = 14.6% which is the total no of people living below poverty line

Let B = 20.7% which is the total no of people speaking foreign Language

C = 4.2% no of people who both speak foreign language and live below poverty line

X = no of people who neither live below poverty line nor speak foreign language

P (A) = 14.6%

P (B) = 20.7%

P (C) = P (A ∩ B) = 4.2%

P (A – C) = P (A ∩ U) = 14.6 – 4.2 = 10.4%

P (B – C) = P (B ∩ U) = 20.7 – 4.2 = 16.5%

P (X) = P (A ᴜ B) c =100 – (10.4 + 4.2 + 16.5) = 68.9%

a. The venn diagram is as shown above

b. Percent of Americans who live below poverty line and Speak English at home(minus foreign lang speakers living below poverty line) that is A only

= A – C

= 14.6 – 4.2

= 10.4%

c. Percentage of Americans Living below poverty line or Speaking foreign language

= A only + B only

A only = A – C ( People living below poverty line only)

= 14.6 -4.2

= 10.4%

B only = B – C ( people speaking foreign languages only)

= 20.7 – 4.2

= 16.5%

Hence

A only + B only = 10.4 + 16.5 = 26.9%

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