All categories

3 years ago

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

You have a gift card for your favorite clothing store for the amount of $60. You have found a shirt you want for $15. You don't

Zolol [24]

Let

x--------> the amount you have left to spend

y--------> the cost of a shirt you want

z------> the amount of the gift card

we know that

$x+y \leq z$ --------> equation $1$

$y=\$ 15$ --------> equation $2$

$z=\$ 60$ --------> equation $3$

Substitute the equation $2$ and equation $3 in the equation [tex] 1$ [/tex]

$x+y \leq z$

$x+15 \leq 60$

therefore

<u>the answer is the option</u>

x+15 is less than or equal to 60

7 0

3 years ago

Read 2 more answers

Segment AB is completely rotated about the y-axis to form a 3-D figure. Find the volume of the figure. The

Lady bird [3.3K]

Answer:

The volume of the figure is 905 cubic units.

Step-by-step explanation:

Rotation is a method of solid transformation which involve turning a given line, or object about a reference point. In the given question, rotating segment AB completely about the y-axis would form a 3 dimensional figure of a sphere.

volume of a sphere = $\frac{4}{3}$ $\pi$ $r^{3}$

where r is the radius of the sphere.

Given that AB = 6, then the radius of the sphere = 6

volume of sphere = $\frac{4}{3}$ x $\frac{22}{7}$ x $(6)^{3}$

= $\frac{88}{21}$ x 216

= 905.14

volume of sphere = 905 cubic units

The volume of the figure is 905 cubic units.

3 0

3 years ago

What is the solution to the equation? Need help with both 3 and 4

In-s [12.5K]

3. -1
4. 19/4
hope i helped!

4 0

3 years ago

Read 2 more answers

9s in 9,905,482 place<br> C

Citrus2011 [14]

100 thousands is the answer good luck!

7 0

3 years ago

A candle burns down at the rate of 0.5 inches per hour. The original height of the candle was 9 inches.

Oksanka [162]

The ordered pairs would be,

(1, 8.5)
(2, 8)
(3, 7.5)
(4,7)
(5, 6.5)
(6, 6)

I got the ordered pairs from the question since it stated that the length of the candle decreased .5 every hour. I just corresponded the hour to the length of the candle.

I hope this helped!

Brainliest answer is always appreciated!

3 0

3 years ago

Read 2 more answers