Suppose you are climbing a hill whose shape is given by the equation z = 2000 − 0.005x2 − 0.01y2, where x, y, and z are measured in meters, and you are standing at a point with coordinates (60, 40, 1966). 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. At what rate? Correct: Your answer is correct. vertical meters per horizontal meter (b) If you walk northwest, will you start to ascend or descend? ascend descend Correct: Your answer is correct. At what rate? (Round your answer to two decimal places.) Correct: Your answer is correct. vertical meters per horizontal meter (c) In which direction is the slope largest? What is the rate of ascent in that direction? vertical meters per horizontal meter At what angle above the horizontal does the path in that direction begin? (Round your answer to two decimal places.)

Answers

Answer 1

Answer:

(a) Ascend at 0.8 vertical meter/meter

(b) Descend at -0.2·√2 vertical meter/meter

(c) In the (-0.6, -0.8) direction. The path begins at 45° to the horizontal

Explanation:

The given equation of the shape of the hill is z = 2000 - 0.005·x² - 0.01·y²

The current location = (60, 40, 1966)  

The direction of the positive x-axis = east

The direction of the positive y-axis = north

(a) Walking due south = Reducing the y-value 40

From the equation, the elevation varies inversely with the motion towards the north

Therefore, walking south increases the elevation, and we ascend

The rate is given by the partial derivative at in the -j direction, which is 0.02

The rate is therefore 40 × 0.02 = 0.8

(b)The unit vector in the northwest direction u = 1/√2·(-1, 1)

∴ The rate = (-0.01(60), -0.02(40))·u = (-0.6, -0.8)·1/√2·(-1, 1) = -0.2·√2

Therefore we descend

(c) The slope is largest in the grad of the function at the point (60, 40) which is given as follows;

d(2000 - 0.005·x² - 0.01·y² )/dx, d(2000 - 0.005·x² - 0.01·y² )/dy = (-0.6, -0.8)

Therefore, the direction is tan⁻¹(-0.8/-0.6) ≈ S 36.87° W

The slope =(√((-0.4)² + (-0.8)²) = 1

Therefore, the angle is 45° to the horizontal.


Related Questions

Please help A.S.A.P
If the bands in an igneous rock are dark. What kind of magma was present when it was formed?

Answers

Answer:

The magma, molten rock under the surface, and lava (molten rock on the surface) harden into igneous rock. The igneous rock then breaks apart over time through the process of weathering.

Explanation:

helpppp please I'm really stuck on this question

Answers

Is this a test? If it is, i’m not allowed to help as i would be seen as a bad person! I hope you pass, god bless.

The atomic mass of an atom do not contain electrons because

Electrons do not exist in all atoms.
Electrons are so small that it does not affect the mass of an atom.
Electrons are do not contain mass.
Electrons are not as important as protons and neutrons.

Answers

Answer:

Electrons are so small that it does not affect the mass of atom .

Explanation:

Electrons are much smaller in mass than protons, weighing only 9.11 × 10^-28 grams, or about 1/1800 of an atomic mass unit. Therefore, they do not contribute much to an element's overall atomic mass.

Answer:

Electrons are so small that it does not affect the mass of an atom

Explanation:

What is 9.14 m/s to m/s squared? Will mark as brainilest

Answers

1, = 0.001. 2, = 0.002. 3, = 0.003.

b) When the wave passes over the glass it refracts. State what will happen to each
of the following properties of the wave when it refracts: (3)
Velocity -
Wavelength -
Frequency -

Answers

LOVE THE DOG

Explanation:

Will give brainliest, 25 points:
A cannonball is launched straight up from the ground at 13.5 m/s. How much time is the cannonball in the air (hangtime)?

Answers

Answer:

Time in air t = 1.38 second (Approx)

Explanation:

Given:

Initial speed u = 0 m/s

Final speed v = 13.5 m/s

Find:

Time in air t

Computation:

v = u + gt

g = 9.8 m/s²

13.5 = 0 + (9.8)(t)

13.5 = 9.8 t

t = 13.5 / 9.8

t = 1.3777 second

Time in air t = 1.38 second (Approx)

why it's dangerous to jump from a moving bus?​

Answers

Answer:

A man jumping out from a moving bus holds the inertia of motion.As the man lands on the ground,feet came to rest instantly while the upper due to inertia of motion.Therefore the person may fall under bus.

I WILL GIVE BRAINLIEST A battery contains two metals that have different tendencies to attract electrons. If one is lithium with an electron affinity of −3.05, and the other is zinc with an electron affinity of −0.76, describe how the electrons will flow. Then, describe how you could make this an even stronger battery. (4 points)

Answers

Answer:

electrons will flow from lower (lithium) to higher (zinc)

You can make a stronger battery by having a larger electron affinity difference.

Hope this helps \(-._.-)/

A high school bus travels 240 km in 6.0 h. What is its average speed for the trip? (in km/h).

Answers

Answer:

40 km/h

Explanation:

First...

Look at the formula speed is equal to the distance over time or s = d/t.

Next...

Use the formula: 240/6.0

Finally...

Solve: 40

So the answer: 40 km/h


What affect does doubling the net force have on the acceleration of the object (when
the mass of the object stays the same)? Identify a set of two trials that support your answer to question 1

Answers

Answer: The acceleration doubles

===========================================================

Explanation:

Consider a mass of 10 kg, so m = 10

Let's say we apply a net force of 20 newtons, so F = 20

The acceleration 'a' is...

F = ma

20 = 10a

20/10 = a

2 = a

a = 2

The acceleration is 2 m/s^2. Every second, the velocity increases by 10 m/s.

---------------

Now let's double the net force on the object

F = 20 goes to F = 40

m = 10 stays the same

F = ma

40 = 10a

10a = 40

a = 40/10

a = 4

The acceleration has also doubled since earlier it was a = 2, but now it's a = 4.

---------------

In summary, if you double the net force applied to the object, then the acceleration doubles as well.

Acceleration is directly proportional to the net force on an object, and inversely proportional to its mass.

So if an object's mass stays the same while the net force on it doubles, then its acceleration will also double.

We don't know anything about the "trials".  This sounds like it might be a follow-up to a lab experiment that was performed when we weren't there.

We also don't know anything about "question 1".

What is energy?
the ability to do work
chemical change
force
force x distance

Answers

from my notes it’s the ability to do work

define the word prism

Answers

Answer:

a polyhedron with two polygonal faces lying in parallel planes and with the other faces parallelograms

Help plz I’m Cunfused !!

Answers

Explanation:

look up the coordinates or if they provide you with a map use that

Answer:

find each point in and draw a straight line until they touch and whatever is there is the country

Three people pull simultaneously on a stubborn donkey. Jack pulls directly ahead of the donkey with a force of 63.9 N63.9 N , Jill pulls with 79.1 N79.1 N in a direction 45° to the left, and Jane pulls in a direction 45° to the right with 183 N183 N . (Since the donkey is involved with such uncoordinated people, who can blame it for being stubborn?) Find the magnitude of the net force the people exert on the donkey.

Answers

Answer:

a) F = (137.4 i ^ + 185 j ^) N

b)    F = 230.2 N  ,  θ = 53.5º

Explanation:

In this exercise we ask to find the net force, for which we will define a coordinate system fix the donkey and use trigonometry to decompose the forces

Jack       F₁ₓ = 63.9 N

Jill          F₂ = 79.1 N with direction 45º to the left

              cos (180 -45) = F₂ₓ / F₂

              sin 135 = [tex]F_{2y}[/tex] / F₂

              F₂ₓ = F₂ cos 135

              F_{2y} = F₂ sin 135

              F₂ₓ = 79.1 cos 135 = -55.9 N

              F_{2y} = 79.1 sin 135 = 55.9 N

Jane      F₃ = 183 N direction 45th to the right

             cos 45 = F₃ₓ / F3

             sin 45 = F_{3y} / F3

             F₃ₓ = F₃ cos 45 = 183 cos 45

             F_{₃y} = F₃ sin 45 = 183 sin 45

             F₃ₓ = 129.4 N

             F_{3y} = 129.4 N

we add each component of the force

       Fₓ = F₁ₓ + F₂ₓ + F₃ₓ

       Fₓ = 63.9 + (-55.9) + 129.4

       Fₓ = 137.4 N

       F_{y} = F_{2y} + F_{3y}

       F_{2y} = 55.9 + 129.4

       F_{2y} = 185.3 N

we can give the result of the forms

 

a) F = (137.4 i ^ + 185 j ^) N

b) in the form of module and angle

         F = RA (Fₓ² + F_{y}²)

         F = Ra (137² + 185²)

         F = 230.2 N

         tan θ = F_{y} / Fₓ

         θ = tan⁻¹ F_{y} / Fₓ

        θ = tan⁻¹ (185/137)

        θ = 53.5º

What is the equation for momentum (p)?
O A. p = mgh
B. p = my
C. p = ma
O D. p = 127v2

Answers

p=mv. Im guessing theres a typo in choice b.

Which of the following describes an action-reaction pair?
O A. You push a car forward, and the car pulls you forward.
B. Earth's gravity pulls down on you, and your gravity pulls up on
Earth.
C. Friction slows you down, and the normal force holds you up.
D. Your hat pushes down on your head, and your feet push down on
the ground.

Answers

Answer:

B. Earth's gravity pulls down on you, and your gravity pulls up on

Earth

Explanation:

AYEPECKS

A Punnett square is used to determine the *

Answers

Answer:

predict the genotypes of a particular cross or breeding experiment

Explanation:

Answer:

A.

Explanation:

The connections of many simple pieces in the brain is evidence of the:
O A. lobes of the brain
B. brain's complexity
C. function of neurons
D. cerebral cortex

Answers

B. Brains Conplexity

Hope This Helps ♡

Answer:

B. brain's complexity

Explanation:

Ape.x

what is 1/2 / 1/4. Please help am getting two answers.idk the correct one.​

Answers

Answer:

2

hope this helps :)

State the forces acting on an object that is stationary/moving. Explain how acceleration changes when the same object is kicked with a great force and a small force. Describe the difference in the movement if the initial object now weighs 50 lbs and is acted on by a small force and a large force.​

Answers

Answer:

it all is force I the barly kick you then it won't do that much date but If the full force kick you then it might hurt.

Explanation:

i hope this helps

name six kinds of simple machines.

Answers

Answer:

the wheel and axle, the lever, the inclined plane, the pulley, the screw, and the wedge

Explanation:

The wheel, Axel, Lever, Inclined Pane, pulley, screw, and wedge!

Which of the following describes the way heat is transferred in a geyser?

Answers

Where’s the following questions ?

two same size anvils are dropped from different heights. Assume both anvils are made of the same material (iron) and there is no air resistance. Which anvil has the greatest acceleration during the fall? ​

Answers

Everything falls at the same rate.

A water park is designing a new water slide that finishes with the rider flying horizontally off the bottom of the slide. The slide is designed to end 1.2 m above the water level, and the average rider is estimated to leave the bottom of the slide at 25 m/s. How far will the rider fly through the air before hitting the water?

Answers

Answer: 12.62 meters

Explanation:

How can you tell the difference between a colloid and a suspension?

Answers

Answer: Particles in a suspension are usually more than 1,000 nm, while those in a colloid range from 1-1,000 nm. Unlike those in a suspension, particles in a colloid do not separate when sitting still. ... Particles in a suspension can be seen by the naked eye, but those in a colloid must be viewed using a light microscope.

hope this helps:)

Explanation:

A bomber is flying at a height of 9 km at 800 km/h. How far in front of the target should he drop his bombs?

Answers

Answer:

The distance in front of the target is 9.524 km

Explanation:

Given;

height of the bomber above the ground, h = 9 km = 9000 m

velocity of the bomber, v = 800 km/h = 222.22 m/s

The time the bomb will get to the target is given by;

[tex]t = \sqrt{\frac{2h}{g} } \\\\t = \sqrt{\frac{2*9000}{9.8} }\\\\ t = 42.857 \ s[/tex]

The lead distance or distance in front of the target is given by;

x = vt

x = (222.22 m/s) x (42.857 s)

x = 9523.68 m

x = 9.524 km

Therefore, the distance in front of the target is 9.524 km

In front of the target, the distance will be "9.524 km".

Distance and Height

According to the question,

Bomber's height, h = 9 km or,

                                = 9000 m

Bomber's velocity, v = 800 km/h or,

                                  = 222.22 m/s

Now,

The time will be:

→ t = [tex]\sqrt{\frac{2h}{g} }[/tex]

By substituting the values, we get

     = [tex]\sqrt{\frac{2\times 9000}{9.8} }[/tex]

     = [tex]\sqrt{\frac{18000}{9.8} }[/tex]

     = 42.857 s

hence,

The lead distance will be:

→ x = vt

By putting the values,

     = 222.22 × 42.857

     = 9523.68 or,

     = 9.524 km

Thus the above answer is correct.

Find out more information about distance here:

https://brainly.com/question/4931057

The frequency of a F-sharp sound wave in music is 370 Hz, and its wavelength is 0.93 m. what is the wave speed?

Answers

Answer:

wave speed =344.1 m/s

using v=fΠ

where v is the speed

The wave speed will be 344.1 m/sec. The wave speed is found as the product of the wavelength and the frequency of the wave.

What is wavelength?

The distance between two successive troughs or crests is known as the wavelength. The peak of the wave is the highest point, while the trough is the lowest.

The wavelength is also defined as the distance between two locations in a wave that have the same oscillation phase.

The given data in the problem is;

v is the speed = ?

f is the frequency= 370 Hz

λ is the wavelength of the wave=0.96 m

The relationship between the wave's wavelength, frequency, and speed is given as;

wavelength = speed of wave / frequency

[tex]\rm \lambda = \frac{v}{f} \\\\ v = \lambda \times f \\\\ v = 0.93 \times 370 \ Hz \\\\ v= 344.1 \ m/sec[/tex]

Hence, the wave speed will be 344.1 m/sec.

To learn more about the wavelength, refer to the link;

brainly.com/question/7143261

#SPJ2

1. An unbalanced force of 25N is applied to a 12kg mass. What is the acceleration of the mass?

Answers

Answer:

a=2.1 m/s^2

Explanation:

F=ma

a=F/m

a=25/12

a=2.1 m/s^2

What is the smallest animal on earth?

Answers

Answer:

Pa edo phr yne amanuensis

Explanation:

is a species of microhylid frog from Papua New Guinea. At 7.7 mm in snout–to–vent length, it is considered the world's smallest known vertebrate. The species was listed in the Top 10 New Species 2013 by the International Institute for Species Exploration for discoveries made during 2012

differences between distance and displacement.​

Answers

It is a vector quantity
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