Keisha solved the following equation:

A container is shaped like a cylinder with half spheres on each end. The cylinder has a length of 30 centimeters and a radius is

Crank

The cubic centimeter one container can hold is 2,878.33 cm³.

<h3>What is the cubic centimeter one container can hold ?</h3>

In order to determine the cubic centimeter one container can hold, the volume of the container has to be determined.

Volume of the container = volume of the cylinder + (2 x volume of the hemisphere)

Volume of the cylinder = πr²h

Where:

π = 3.14
r = radius
h = height

3.14 x 5² x 30 = 2355 cm³

Volume of a hemisphere = (2/3) x π x r³

2 x (2/3 x 3.14 x 5³) = 523.33 cm³

Volume of the container = 523.33 cm³ + 2355 cm³ = 2,878.33 cm³

To learn more about the volume of a hemisphere, please check: brainly.com/question/26840364

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7 0

2 years ago

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example tha

frosja888 [35]

Answer:

False

Step-by-step explanation:

the dot product between two vectors A and B is:

A·B=AB $cos\theta$

where $\theta$ is the angle between the vectors, if they are parallel, this angle is zero. so $\theta=0$

and so the dot product is:

A·B =AB $cos(0)$

and since $cos (0)=1$

the dot product is equal to

A·B=AB

The dot product of parallel vectors is NOT zero

5 0

2 years ago

Which of the following graphs shows the solution set for the inequality below? 3|x + 1| < 9

Bas_tet [7]

Step-by-step explanation:

The absolute value function is a well known piecewise function (a function defined by multiple subfunctions) that is described mathematically as

$f(x) \ = \ |x| \ = \ \left\{\left\begin{array}{ccc}x, \ \text{if} \ x \ \geq \ 0 \\ \\ -x, \ \text{if} \ x \ < \ 0\end{array}\right\}$ .

This definition of the absolute function can be explained geometrically to be similar to the straight line $\textbf{\textit{y}} \ = \ \textbf{\textit{x}}$ , however, when the value of x is negative, the range of the function remains positive. In other words, the segment of the line $\textbf{\textit{y}} \ = \ \textbf{\textit{x}}$ where $\textbf{\textit{x}} \ < \ 0$ (shown as the orange dotted line), the segment of the line is reflected across the x-axis.

First, we simplify the expression.

$3\left|x \ + \ 1 \right| \ < \ 9 \\ \\ \\\-\hspace{0.2cm} \left|x \ + \ 1 \right| \ < \ 3$ .

We, now, can simply visualise the straight line, $y \ = \ x \ + \ 1$ , as a line having its y-intercept at the point $(0, \ 1)$ and its x-intercept at the point $(-1, \ 0)$ . Then, imagine that the segment of the line where $x \ < \ 0$ to be reflected along the x-axis, and you get the graph of the absolute function $y \ = \ \left|x \ + \ 1 \right|$ .

Consider the inequality

$\left|x \ + \ 1 \right| \ < \ 3$ ,

this statement can actually be conceptualise as the question

$``\text{For what \textbf{values of \textit{x}} will the absolute function \textbf{be less than 3}}"$ .

Algebraically, we can solve this inequality by breaking the function into two different subfunctions (according to the definition above).

Case 1 (when $x \ \geq \ 0$ )

$x \ + \ 1 \ < \ 3 \\ \\ \\ \-\hspace{0.9cm} x \ < \ 3 \ - \ 1 \\ \\ \\ \-\hspace{0.9cm} x \ < \ 2$

Case 2 (when $x \ < \ 0$ )

$-(x \ + \ 1) \ < \ 3 \\ \\ \\ \-\hspace{0.15cm} -x \ - \ 1 \ < \ 3 \\ \\ \\ \-\hspace{1cm} -x \ < \ 3 \ + \ 1 \\ \\ \\ \-\hspace{1cm} -x \ < \ 4 \\ \\ \\ \-\hspace{1.5cm} x \ > \ -4$

*remember to flip the inequality sign when multiplying or dividing by

negative numbers on both sides of the statement.

Therefore, the values of x that satisfy this inequality lie within the interval

$-4 \ < \ x \ < \ 2$ .

Similarly, on the real number line, the interval is shown below.

The use of open circles (as in the graph) indicates that the interval highlighted on the number line does not include its boundary value (-4 and 2) since the inequality is expressed as "less than", but not "less than or equal to". Contrastingly, close circles (circles that are coloured) show the inclusivity of the boundary values of the inequality.