Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

noot: Additional Practice (LMS graded) $\newline$ of $2$ $\newline$ e surface area of a paper cup is defined by the function $\newline$ $s(h)=6\pi\sqrt{16+h^{2}}$ , where $\newline$ $h$ is the height of the cup. What is the domain and range of $\newline$ $s(h)$ ? $\newline$ Describe the domain. Select the correct choice below and, if necessary, fill in the answer box within your choice. $\newline$ A. The domain is $\newline$ \{h\mid h>-\}. $\newline$ (Type an inequality or a compound inequality. Simplify your answer. Type an exact answer, using $\newline$ $\pi$ as needed.) $\newline$ B. The domain is all real numbers.

View step-by-step help

View step-by-step help

Simplify radical expressions with variables I

Full solution

Q. noot: Additional Practice (LMS graded)

\newline

of

2

\newline

e surface area of a paper cup is defined by the function

\newline

s(h)=6\pi\sqrt{16+h^{2}}

, where

\newline

h

is the height of the cup. What is the domain and range of

\newline

s(h)

?

\newline

Describe the domain. Select the correct choice below and, if necessary, fill in the answer box within your choice.

\newline

A. The domain is

\newline

\{h\mid h>-\}

.

\newline

(Type an inequality or a compound inequality. Simplify your answer. Type an exact answer, using

\newline

\pi

as needed.)

\newline

B. The domain is all real numbers.

Define Domain of Function: The domain of a function is the set of all possible input values (in this case, the height $h$ ) that will produce a valid output (the surface area $s(h)$ ). Since the surface area cannot be negative and the square root function $\sqrt{16 + h^2}$ is defined for all real numbers (because the expression inside the square root is always positive), the domain of $s(h)$ is all real numbers.
Define Range of Function: The range of the function is the set of all possible output values. Since the square root function $\sqrt{16 + h^2}$ produces non-negative values and is multiplied by the positive constant $6\pi$ , the range of $s(h)$ is all non-negative real numbers.

More problems from Simplify radical expressions with variables I

Question

Order the expressions from least to greatest.

\newline

11^{1} \quad8^{2}-60 \quad 2^{2} \times 5

Posted 8 months ago

Question

Order the expressions from least to greatest.

\newline

2^{3}-2^{1} \quad 2^{1}+3^{1} \quad 3^{2}

Posted 8 months ago

Question

y=\sqrt{e^{x}}

\newline

\frac{d y}{d x}

\newline

1

\newline

\frac{\sqrt{e^{x}}}{2}

\newline

\sqrt{e^{x}}

\newline

x \sqrt{e^{x-1}}

\newline

\frac{1}{2 \sqrt{e^{x}}}

Posted 7 months ago

Question

What is the area of the region between the graphs of

f(x)=-x^{2}+2 x+12

g(x)=x^{2}-12

x=-3

x=4

\newline

1

\newline

7

\newline

\frac{343}{3}

\newline

\frac{83}{3}

\newline

\frac{52}{3} \sqrt{13}-1-32 \sqrt{3}

Posted 7 months ago

Question

What is the average value of

\frac{1}{x}

on the interval

4 \leq x \leq 8

\newline

1

\newline

\frac{3}{16}

\newline

\frac{1}{16}

\newline

\frac{\ln (32)}{4}

\newline

\frac{\ln (2)}{4}

Posted 7 months ago

Question

4

6

\newline

K

\newline

For the data given below, answer parts (a) through (f).

\newline

\begin{array}{cc}

\newline

x & y (\newline\)

-19

102

-16

122

-14

120

-13

132

-9

142

(\newline\)\end{array}

\newline

(a) Draw a scatter plot.

\newline

Choose the correct graph below.

\newline

\newline

\newline

\newline

\newline

(b) Find the equation of the line containing the first and the last data points.

\newline

y=4x+178

\newline

(Type an equation. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)

\newline

(c) Graph the line found in part (b) on the scatter plot.

\newline

Choose the correct graph below.

\newline

\newline

\newline

\newline

(d) Use a graphing utility to find the line of best fit.

\newline

y=\square x+\square

\newline

(Type integers or decimals rounded to four decimal places as needed)

Posted 7 months ago

Question

Determine the coefficient and degree of the monomial.

\newline

-7x^{2}y^{5}

\newline

The coefficient of the monomial is

\newline

\square

\newline

The degree of the monomial is

\newline

\square

Posted 6 months ago

Question

\frac{x}{3} + \frac{4x}{5} = \frac{1}{3}

Posted 6 months ago

Question

Consider the following polynomial.

\newline

q(x)=4x^{2}-3x+12

\newline

2

2

: Describe the behavior of the graph of

q(x)

x \rightarrow \pm\infty

\newline

q(x)\rightarrow \square

x \rightarrow -\infty

Posted 6 months ago

Question

\newline

How did Native Americans use their Natural Resources to obtain their basic needs?

\newline

\begin{tabular}{|l|l}

\newline

\hline Answor to Question & Extra Notes \\

\newline

\newline

Posted 23 hours ago

Related topics

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