Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Emily convinced her mom to buy a giant box of her favorite cereal. Her mom doesn't think the box will fit on their shelf. The volume of the box is
10,000cm^(3). The base of the box is
25cm by
10cm.
How tall is the box of cereal?

cm

Emily convinced her mom to buy a giant box of her favorite cereal. Her mom doesn't think the box will fit on their shelf. The volume of the box is $10,000 \mathrm{~cm}^{3}$ . The base of the box is $25 \mathrm{~cm}$ by $10 \mathrm{~cm}$ . $\newline$ How tall is the box of cereal? $\newline$ $\square$ $\mathrm{cm}$

View step-by-step help

View step-by-step help

Pythagorean Theorem and its converse

Full solution

Q. Emily convinced her mom to buy a giant box of her favorite cereal. Her mom doesn't think the box will fit on their shelf. The volume of the box is

10,000 \mathrm{~cm}^{3}

. The base of the box is

25 \mathrm{~cm}

by

10 \mathrm{~cm}

.

\newline

How tall is the box of cereal?

\newline

\square

\mathrm{cm}

Understand Problem: Understand the problem and identify the formula for volume. $\newline$ The volume of a box (rectangular prism) is calculated by multiplying its length, width, and height. $\newline$ Volume = Length $\times$ Width $\times$ Height $\newline$ Given: Volume = $10,000$ cm $^3$ , Length = $25$ cm, Width = $10$ cm. $\newline$ We need to find the Height.
Volume Formula: Rearrange the volume formula to solve for height. $\newline$ $\text{Height} = \frac{\text{Volume}}{\text{Length} \times \text{Width}}$ $\newline$ Plug in the given values. $\newline$ $\text{Height} = \frac{10,000 \, \text{cm}^3}{25 \, \text{cm} \times 10 \, \text{cm}}$
Calculate Height: Perform the calculation to find the height. $\newline$ Height = $10,000 \, \text{cm}^3 \div (250 \, \text{cm}^2)$ $\newline$ Height = $40 \, \text{cm}$

More problems from Pythagorean Theorem and its converse

Question

Marco's class is painting a mural on the side of their school. The mural covers a

3 \frac{1}{2} \mathrm{~m}

high, rectangular wall. It has an area of

28 \mathrm{~m}^{2}

\newline

What is the length of the mural?

\newline

Posted 10 months ago

Question

A cup of hot coffee has been left to cool in a room with an ambient temperature of

21^{\circ} \mathrm{C}

\newline

The relationship between the elapsed time,

m

, in minutes, since the coffee was left to cool, and the temperature of the coffee,

T

{ }^{\circ} \mathrm{C}

, is modeled by the following function.

\newline

T(m)=21+74 \cdot 10^{-0.03 m}

\newline

What will the temperature of the coffee be after

10

\newline

Round your answer, if necessary, to the nearest hundredth.

\newline

{ }^{\circ} C

Posted 10 months ago

Question

Takumi plants a tree in his backyard and studies how the number of branches grows over time.

\newline

He predicts that the relationship between

N

, the number of branches on the tree, and

t

, the elapsed time, in years, since the tree was planted can be modeled by the following equation.

\newline

N=5 \cdot 10^{0.3 t}

\newline

According to Takumi's model, in how many years will the tree have

100

\newline

Give an exact answer expressed as a base

-10

\newline

Posted 10 months ago

Question

g(x)=2^{x}

\newline

Can we use the mean value theorem to say the equation

g^{\prime}(x)=16

has a solution where

3<x<5

\newline

1

\newline

(A) No, since the function is not differentiable on that interval.

\newline

(B) No, since the average rate of change of

g

over the interval

3 \leq x \leq 5

1 \overline{6}

\newline

(C) Yes, both conditions for using the mean value theorem have been met.

Posted 9 months ago

Question

\frac{d}{d x}\left(\frac{3 x^{2}-1}{x-2}\right)=

Posted 9 months ago

Question

\frac{d y}{d t}=2 t+3 \text { and } y(1)=6

\newline

t

y=0

\newline

Choose all answers that apply:

\newline

t=-1

\newline

t=-3

\newline

t=0

\newline

t=-4

\newline

t=1

\newline

t=-2

Posted 9 months ago

Question

\frac{d}{d x}\left(x^{\frac{3}{4}}\right)=

Posted 9 months ago

Question

y=x^{13}

\newline

\frac{d y}{d x}=

Posted 9 months ago

Question

y=x^{10}

\newline

\frac{d y}{d x}=

Posted 9 months ago

Question

\frac{d}{d x}\left[x^{6}\right]=

Posted 9 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant