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dedylja [7]
3 years ago
13

Suppose you are climbing a hill whose shape is given by the equation z = 1300 − 0.005x2 − 0.01y2, where x, y, and z are measured

in meters, and you are standing at a point with coordinates (120, 80, 1164). 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?

Mathematics
1 answer:
Varvara68 [4.7K]3 years ago
6 0

Answer:

  ascend

Step-by-step explanation:

There are a couple of ways to figure this. One is to look at the partial derivative ...

  \dfrac{\partial z}{\partial y}=-0.02y

The sign of it is negative, so when y decreases, z increases. Going south means decreasing the y-coordinate, so moving in that direction will cause you to ascend.

__

Another way to figure this is to evaluate z for some small movement in the southerly direction. In the attached, we find that moving 1 m south to (120, 79, 1165.59) causes an elevation increase of about 1.6 m. Walking south causes you to ascend.

Note that this is consistent with our first result, as -0.02y = -0.02(80) = -1.6. So a change in y of -1 should cause a change in z of about (-1.6)(-1) = 1.6.

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Lin ran 2 3/4 miles in 2/5 of an hour, Noah ran 8 2/3 miles in 4/3 of an hour, how far would Lin run in 1 hour?
Marizza181 [45]

Answer:

6\frac{7}{8}\ miles

Step-by-step explanation:

Given that Lil's distance in 2/5 hrs is 2 3/4hrs

-Let x be the distance ran in 1 hr.

#We equate and cross multiply to solve for x as follows:

\frac{2}{5}\ hrs=2\frac{3}{4}\\1\ hr=x\\\\\therefore x=2\frac{3}{4}/\frac{2}{5}\\\\=6\frac{7}{8}\ miles

Hence, Lil can run 6 7/8 miles in 1 hr.

5 0
3 years ago
there are 49 dogs signed up for the dog show. there are 36 more small dogs than large dogs. how many small dogs are signed up fo
pogonyaev
Okay, so total dogs are 49.
So we know if x=large dogs and y=small dogs, then x+y=49.
Next we are told that there are 36 MORE small dogs than large dogs. We can take that more meaning addition, and x being our value for large dogs. So y=x+36.
After that we now know what value we can plug in for y. So x+x+36=49.
We can then simplify it to 2x+36=49.
Subtracting the 36 from both sides, leaves you with 2x=13.
Followed by dividing both sides by 2, gives you x=6.5. Or 6.5 large dogs.
Now we can plug this into our formula for the small dogs (y=x+36) to give us y=6.5+36, which simplifies to y=42.5. Or 42.5 small dogs. Which is our answer.
We can double check it by adding the small and large dogs together, 6.5+42.5, which gives us 49, our total entries.
4 0
3 years ago
Read 2 more answers
A driver driving a business trip of 240 miles would have reached his destination if he'd been able to drive 12 mph faster than h
mariarad [96]

The average speed of his trip is = 12 mile/ hour

The total distance covered by the driver = 240 miles

The rate at which he traveled = 12 miles per hour

Therefore, the time he used to cover his distance

= 240/12

= 20 hrs

But average speed = distance/ time

= 240/ 20

= 12 miles/ hour

Therefore, the average speed of his trip is = 12 mile/ hour

Learn more here:

brainly.com/question/11753352

8 0
2 years ago
The difference between a number and 8 is less than -15
Olenka [21]

Answer:

x-8<-15

Step-by-step explanation:

8 0
3 years ago
okay hear this someone came into my shop and stole $100 without my knowledge they came back to the store and spent $70 in items
son4ous [18]
Well, you lost the original $100 and then you gained back $70 but gave away $70 worth of merchandise, so it evens out and you lost $100 in total
8 0
3 years ago
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