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 (100, 120, 1106). 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

Answers

Answer 1

Answer:

Answer:

a) "ascend"

Step-by-step explanation:

The equation is $z = 1300-0.005x^2-0.01y^2$

This question is asking for the value of the directional derivative in the direction of -j [since south that's y negative]

So, this is the negative of partial derivative of y. Thus we have:

$z = 1300-0.005x^2-0.01y^2\nz_y=-0.02y$

Now we are at (100,120,1106), we take y value of 120 and put it in the partial:

$z_y=-0.02y\nz_y=-0.02(120)\nz_y=-2.4$

We take the negative, that is -(-2.4) = 2.4

Since this is positive, we can say the hill is sloping upward at this point, so you will start to ascend.

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Solbe for x : x-1/x+3x+3=0

Find the quotient of 2/5 and 4/5
Give your answer as a fraction in its simplest form.

Answers

What is the quotient?

The quotient is the number which is generated when we perform division operations on two numbers.

The quotient of 2/5 and 4/5.

The quotient of 2/5 and 4/5 is determined in the following steps given below.

$\rm Quotient =((2)/(5))/((4)/(5))\n\nQuotient =(2)/(5)* (5)/(4)\n\n Quotient =(2)/(4)\n\nQuotient =(1)/(2)$

Hence, the quotient of 2/5 and 4/5 is 1/2.

Learn more about quotient here;

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Answer:

$(1)/(2)$

Step-by-step explanation:

The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume 360 days in a year. P=$4000, r=5% t= 1 year

Answers

9514 1404 393

Answer:

$200

Step-by-step explanation:

The interest is given by ...

I = Prt

I = ($4000)(0.05)(1) = $200

The simple interest owed is $200.

Place parentheses in the expression so that it equals the given value 12 = 2 X 23; value: 120

Answers

No the value answer is 48

What percent is equivalent to 2/366 1/3

66 3/5

66 2/3

66 7/10

Answers

$\huge\text{Hey there!}$

$\huge\textbf{Question reads....}$

$\large\textbf{What percent is equivalent to }\rm{\bf (2)/(3)}\large\textbf{ ?}$

$\huge\textbf{Let's simplify the current fraction}\n\huge\textbf{to find the overall result to this question.}$

$\mathbf{(2)/(3)}$

$\mathbf{= 2/3}$

$\mathbf{= 0.66666667}$

$\mathbf{= 0.66666667 * 100}$

$\mathbf{= 66.6666667\%}$

$\mathbf{\approx 66.67\%}$

$\huge\textbf{Let's do process of elimination to find}\n\huge\textbf{the fraction that is equivalent to yours.}$

$\huge\textsf{Option A.}$

$\mathbf{66 (1)/(3)}$

$\mathbf{= (66*3+1)/(3)}$

$\mathbf{= (198 +1)/(3)}$

$\mathbf{= (199)/(3)}$

$\mathbf{= 199/3}$

$\mathbf{= 66.3333333}$

$\mathbf{= 66.3333333 *100}$

$\mathbf{= 6,633.33333\%}$

$\mathbf{\approx 6,633.33\%}$

$\huge\textsf{This eliminates Option A. as your result.}$

$\huge\textsf{Option B.}$

$\mathbf{66 (3)/(5)}$

$\mathbf{= (66*5 + 3)/(5)}$

$\mathbf{= (330 + 3)/(5)}$

$\mathbf{= (333)/(5)}$

$\mathbf{= 333/5}$

$\mathbf{= 66.6}$

$\mathbf{= 66.6 * 100}$

$\mathbf{= 6,660}$

$\mathbf{\approx 6,660\%}$

$\huge\textsf{This eliminates Option B. as your result.}$

$\huge\textsf{Option C.}$

$\mathbf{66 (2)/(3)}$

$\mathbf{= (66*3+2)/(3)}$

$\mathbf{= (198 + 2)/(3)}$

$\mathbf{= (200)/(3)}$

$\mathbf{= 200/3}$

$\mathbf{= 66.6666667}$

$\mathbf{= 66.6666667*100}$

$\mathbf{= 6,666.66667}$

$\mathbf{\approx 6,666.67\%}$

$\huge\textsf{This eliminates Option C. as your result.}$

$\huge\textsf{Option D.}$

$\mathbf{66(7)/(10)}$

$\mathbf{= (66*10 +7)/(10)}$

$\mathbf{= (660 + 7)/(10)}$

$\mathbf{= (667)/(10)}$

$\mathbf{= 667/10}$

$\mathbf{= 6.67}$

$\mathbf{= 6.67*100}$

$\mathbf{= 6,670}$

$\mathbf{\approx 6,670\%}$

$\huge\textsf{This eliminates Option D. as your result.}$

$\huge\textbf{It seems like none of the above matches }\n\huge\textbf{the original fraction, so we will use the}\n\huge\textbf{that is close to the original answer.}$