All categories

3 years ago

How big of box is needed to pack 64 boxes that are 1ft x 1ft x 1ft

Mathematics

1 answer:

AVprozaik [17]3 years ago

7 0

Answer:

something with a volume of 64 ft³, such as a box 4 ft × 4 ft × 4 ft

Step-by-step explanation:

The volume of the smaller box is (1 ft)³ = 1 ft³. So 64 of them require a box with a volume of 64 ft³.

The most compact of such boxes is one that is cube-shaped itself. Such a box would have dimensions of ...

∛(64 ft³) = 4 ft

A box that is 4 ft × 4 ft × 4 ft would hold the 64 smaller boxes.

You might be interested in

A person stands 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 meters

In-s [12.5K]

Answer:

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

Step-by-step explanation:

Given that,

A person stand 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 m/s.

From Pythagorean Theorem,

(The distance between car and person)²= (The distance of the car from intersection)²+ (The distance of the person from intersection)²+

Assume that the distance of the car from the intersection and from the person be x and y at any time t respectively.

∴y²= x²+10²

$\Rightarrow y=\sqrt{x^2+100}$

Differentiating with respect to t

$\frac{dy}{dt}=\frac{1}{2\sqrt{x^2+100}}. 2x\frac{dx}{dt}$

$\Rightarrow \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}. \frac{dx}{dt}$

Since the car driving towards the intersection at 13 m/s.

so, $\frac{dx}{dt}=-13$

$\therefore \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}.(-13)$

Now

$\therefore \frac{dy}{dt}|_{x=24}=\frac{24}{\sqrt{24^2+100}}.(-13)$

$=\frac{24\times (-13)}{\sqrt{676}}$

$=\frac{24\times (-13)}{26}$

= -12 m/s

Negative sign denotes the distance between the car and the person decrease.

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

8 0

2 years ago

How does one find the inverse function of f(x)= <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3x-1%7D" id="TexFormula1" tit

lisabon 2012 [21]

Answer:

$\displaystyle f^{-1}(x)=\frac{1+x}{3x}$

Step-by-step explanation:

<u>The Inverse of a Function</u>

The procedure to find the inverse of the function is:

* Write the function as a two-variable equation:

$\displaystyle y=\frac{1}{3x-1}$

* Solve the equation for x.

Multiply by 3x-1

$y(3x-1)=1$

Divide by y:

$\displaystyle 3x-1=\frac{1}{y}$

Sum 1:

$\displaystyle 3x=\frac{1}{y}+1$

Operate the right side:

$\displaystyle 3x=\frac{1+y}{y}$

Divide by 3:

$\displaystyle x=\frac{1+y}{3y}$

* Swap the variables:

$\displaystyle y=\frac{1+x}{3x}$

Write back into function form:

$\boxed{\displaystyle f^{-1}(x)=\frac{1+x}{3x}}$

7 0

3 years ago

A plane descends by 4500 ft in 5 minutes. What is the change in the planes elevation each minute

beks73 [17]

The plane will descend 900 ft every minute

This is the case because we divide 4500 by 5

Hope this helps and have a great day!

3 0

2 years ago

Read 2 more answers

Write an algebraic expression to describe the combined number of posts for Jenny and Antonio after any given number of days

Charra [1.4K]

Suppose Jenny publishes X post per day, and Antonio publishes Y post per day.
So, the combined number of posts will be X+Y multiplied by the number of days.

For example, if the numbers of days is Z, Jenny and Antonio published Z(X+Y) posts.

3 0

2 years ago

Write an equation of the line, in point-slope form, that passes through the two given points.

EleoNora [17]

(-2,15)(9,-18)
slope = (-18 - 15) / (9 - (-2) = -33/11 = -3

There can be 2 answers to this question....
point slope form : y - y1 = m(x - x1)

(1) using points (-2,15)...
y - 15 = -3(x + 2) <== one possible answer

(2) using points (9,-18)
y + 18 = -3(x - 9) <== another possible answer

3 0

3 years ago