Mathematics: Write a formula that estimates the change in the volume Vx of a cube when the edge lengths change from a to ax. Then use the formula to estimate the change in volume when x changes from cm to cm.

Write a formula that estimates the change in the

Ответ:

tyeni2crazylolp7a3hk

16.03.2022

Mathematics

a. $dV = 3x^2\ dx$

b. See Explanation

Step-by-step explanation:

Given

Shape: Cube

Solving (a); Formula that estimates the change in edge length

The volume (V) of a cube is:

V = x^3

Where

$x = edge\ length$

The change in volume is got by:

$dV = \frac{d}{dx}(x^3)$

Differentiate x^3

$dV = 3x^2\ dx$

Where

dx = x_2 - x_1 i.e. change in x

Solving (b):

The initial and final edge lengths are not given.

In order to solve this question, I'll assume that x changes from 5cm to 5.01cm

So, we have:

x = x_1 = 5cm

x_2 = 5.01cm

Substitute these values in $dV = 3x^2\ dx$

dV = 3 * (5cm)^2 * (5.01cm - 5cm)

dV = 3 * (5cm)^2 * 0.01cm

dV = 3 * 25cm^2 * 0.01cm

dV = 075cm^3

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Ответ:

webbjalia04

23.04.2023

Mathematics

Andrea can only buy 1 snack

Okay so since she had 18 dollars at first write it down. So now,you would write down $18 and then Andrea spent $6.50 on a notebook. write that down as well. so now you do $18 - $6.50. that equals $11.50. but Andrea needs to save $5.75. so, subtract that from the $11.50 that you wrote $6.50. write $18-$6.50=$11.50 okay so now that you have that $11.50 written down, subtract 5.75 (for Andrea's savings) and then $11.50 - $5.75 = $5.75. So she can only buy 1 snack.

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Write a formula that estimates the change in the volume Vx of a cube when the edge lengths change from a to ax. Then use the formula to estimate the change in volume when x changes from cm to cm.

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