Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

We want to solve the following equation.

x^(2)-4=root(3)(2x)
One of the solutions is
x~~2.4.
Find the other solution.
Hint: Use a graphing calculator.
Round your answer to the nearest tenth.

x~~

We want to solve the following equation. $\newline$ $x^{2}-4=\sqrt[3]{2 x}$ $\newline$ One of the solutions is $x \approx 2.4$ . $\newline$ Find the other solution. $\newline$ Hint: Use a graphing calculator. $\newline$ Round your answer to the nearest tenth. $\newline$ $x \approx$

View step-by-step help

View step-by-step help

Scale drawings: word problems

Full solution

Q. We want to solve the following equation.

\newline

x^{2}-4=\sqrt[3]{2 x}

\newline

One of the solutions is

x \approx 2.4

.

\newline

Find the other solution.

\newline

Hint: Use a graphing calculator.

\newline

Round your answer to the nearest tenth.

\newline

x \approx

Write down the equation: First, let's write down the equation we need to solve: $\newline$ $x^{2} - 4 = \sqrt[3]{2x}$ $\newline$ We are given that one of the solutions is approximately $x \approx 2.4$ . We need to find the other solution.
Use graphing calculator: To find the other solution, we can use a graphing calculator to plot the two functions $y = x^{2} - 4$ and $y = \sqrt[3]{2x}$ and find their intersection points.
Find intersection points: After plotting the functions on the graphing calculator, we look for the $x$ -value of the intersection point that is not $x \approx 2.4$ . This will be the other solution to the equation.
Round to nearest tenth: Upon observing the graph, we find that the other intersection point occurs at an $x$ -value that we need to round to the nearest tenth to answer the question prompt.
Final answer: Assuming the graphing calculator gives us an accurate intersection point, we round this value to the nearest tenth to get our final answer.

More problems from Scale drawings: word problems

Question

A factory designs cylindrical cans

10 \mathrm{~cm}

in height to hold exactly

500 \mathrm{~cm}^{3}

of liquid. Which of the following best approximates the radius of these cans?

\newline

1

\newline

4 \mathrm{~cm}

\newline

8 \mathrm{~cm}

\newline

12.5 \mathrm{~cm}

\newline

15.9 \mathrm{~cm}

Posted 1 month ago

Question

A die is created by smoothing the corners of a plastic cube and carving indented pips. The original cube had an edge length of

2

(\mathrm{cm})

. The volume of the final die is

7.5 \mathrm{~cm}^{3}

. What is the volume of the waste generated by creating the die from the cube in

\mathrm{cm}^{3}

Posted 10 days ago

Question

We want to find the intersection points of the graphs given by the following system of equations:

\newline

\left\{\begin{array}{l} y=2 x-1 \\ x^{2}+y^{2}=1 \end{array}\right.

\newline

One of the intersection points is

(0,-1)

\newline

Find the other intersection point. Your answer must be exact.

Posted 2 months ago

Question

A(x)=(8+2 x)^{2}

\newline

Carmen wants to add a border around a square picture. The function shows the area of the picture in square inches if it has a border

x

inches wide. What are the dimensions of the picture without the border?

\newline

1

\newline

2

2

\newline

6

6

\newline

8

8

\newline

10

10

Posted 4 months ago

Question

s=-11.8(t-1.2)^{2}+17

\newline

The equation models the horizontal distance,

s

, in centimeters, of a particular image on a computer screen from the left-hand edge of the screen,

t

seconds after appearing. If the image moves in from the left-hand edge of the screen during an on-screen animation, how far to the right does the image travel?

\newline

1

\newline

1

2

\newline

5

2

\newline

17

\newline

34

Posted 4 months ago

Question

A soap company changes the design of its soap from a cone to a sphere. The cone had a height of

3

(\mathrm{cm})

and a radius of

2 \mathrm{~cm}

. The sphere has a diameter of

3 \mathrm{~cm}

. The new design contains

\frac{\pi}{f}

cubic centimeters more soap than the old design. What is the value of

f

Posted 25 days ago

Question

Mindy is a sculptor. She has a cylinder of stone with a radius of

3

(\mathrm{m})

and a height of

2 \mathrm{~m}

. She needs to carve out a sphere of radius

1 \mathrm{~m}

from the cylinder. Mindy must cut away

\frac{v}{3} \pi

\left(\mathrm{m}^{3}\right)

of stone from the cylinder in order to be left with the sphere. What is the value of

v

Posted 28 days ago

Question

A cylindrical soda can has a volume of

108 \pi

cubic centimeters

\left(\mathrm{cm}^{3}\right)

and a height of

12 \mathrm{~cm}

. What is the surface area of the soda can in square centimeters?

\newline

1

\newline

18 \pi \mathrm{cm}^{2}

\newline

36 \pi \mathrm{cm}^{2}

\newline

72 \pi \mathrm{cm}^{2}

\newline

90 \pi \mathrm{cm}^{2}

Posted 2 months ago

Question

\mathrm{Cleo}

are looking for a location to open their new yoga studio. A fellow studio owner suggests a location that will fit

28

756

square foot area. Assuming that each student has a spot

x

3

times as long, what is the length, in feet, of the space they are allotting to each student?

\newline

1

\newline

1

\newline

3

\newline

9

\newline

27

Posted 19 days ago

Question

Morgan is designing a rectangular quilt. The quilt will be

1 \frac{3}{5} \mathrm{~m}

wide and will have an area of

6 \mathrm{~m}^{2}

\newline

How long is the quilt?

\newline

Posted 2 months ago