Find the rate of change of the area of a square with respect

1 answer:

4 0

Let the side length of the square be x, then A = x^2
but diagonal (z) = sqrt(2x^2)
z^2 = 2x^2
x^2 = 1/2 z^2

Thus, A = 1/2 z^2
dA/dz = 1/2 (2z) = z
The rate of change is z.

When z = 4, the rate is 4.

You might be interested in

.....................................

Tatiana [17]

Answers: A , B , and D are correct.
________________________________________________________
The following statements are true and correct:
____________________________________________________
[A]: y is a function of x .
____________________________________________________
[B]: The graph of the relationship is a line.
____________________________________________________
[D]: When the input is -2, the output is 3.
____________________________________________________

Note:
____________________________________________________
Choice: [C]: "When the input is -3, the output is 4 ." → is INCORRECT.

Note: When the input is -3, the output is "4 <span>⅓";
that is, when x = -3, y = 4 </span>⅓ .
_____________________________________________________
Choice: [E]: "The y-intercept of the relationship is: (0,1)." → is incorrect.

Note: The y-intercept refers to the value of "y" where the line crosses the "x" axis. From the equation; and form the graph, we see that the y-intercept is: "⅓" ; or, "(0, ⅓)" .
<span>________________________________________________________
</span>Here is the graph of the equation:
____________________________________________
y = $- \frac{4}{3} x + \frac{1}{3}$ ;
_____________________________________________

5 0

3 years ago

WHAT ARE ALL PRIME NUMBERS X WHICH ARE <img src="https://tex.z-dn.net/?f=5%5C%20%5Ctextless%20%5C%20x%5Cleq%2019" id="TexFormula

ella [17]

Answer:

7, 11, 13, 17, 19

All of these numbers only have 1 and themselves as factors, and every other number can be written as a product of two or more primes, making the remaining number composite:

$6=2\cdot3\\8=2^3\\9=3^2\\10=2\cdot5\\12=2^2\cdot3\\14=2\cdot7\\15=3\cdot5\\16=2^4\\18=2\cdot3^2$