Compute the volume of a sphere with a radius of 12 inches.

A circle is cut into congruent sections and arranged to form a figure that approximates a parallelogram. Find the approximate he

Solnce55 [7]

Answer:

<h2>The height is 3.43 centimeters, approximately.</h2>

Step-by-step explanation:

Notice that there are 16 pieces from the circle, which means each sector has an angle of

$\theta = \frac{360\°}{16}=22.5\°$

Where all sectors have equal area.

Now, the area of the whole circle is $12.25 \pi \ cm^{2}$ , if we use the formula of its area, we'll find the radius of the circle

$A= \pi r^{2}\\ 12.25\pi = \pi r^{2}\\ r=\sqrt{12.25} \approx 3.5$

Notice that each piece works as an isosceles triangle, because each side is the radius, that is, they have the same length. So far, we know the sides of the isosceles triangle and one internal angle.

To find the height of the one piece, we need to use trigonometric reasons, because the height divides a triangle in two equal right triangles.

$cos(11.25\°)=\frac{h}{3.5}\\ h=3.5 \times cos(11.25 \°)\\h \approx 3.43$

Therefore, the height is 3.43 centimeters, approximately.

6 0

3 years ago

A bottling plant produces bottles of 500 ml at the production rate of 10,000 bottles per hour. An inspector randomly picks up 10

galben [10]

Answer:

e.none of these

Step-by-step explanation:

Computations For CC for Fraction defective

Sample No d p=d/100

1 0 0

2 0 0

3 2 0.02

4 1 0.01

5 0 0

6 1 0.01

7 2 0.02

8 0 0

Total 0.06

$\overline{p} =\frac{1}{k}\sum p=\frac{0.06}{8} =0.0075$

$\overline{q} =1- 0.0075= 0.9925$

3 sigma control limits for p chart are given by:

$\overline{p} \pm 3\sqrt{\overline{p}\overline{q}/n}\Rightarrow 0.0075\pm 3\sqrt{\frac{0.0075*0.9925}{100}}$

$= 0.0075\pm0.0259\Rightarrow ( 0.0334,0 )$

hence option e is correct

6 0

3 years ago

Evaluate ƒ(x) when x = -9. <br><br><br>A. No solution <br><br>B. 488 <br><br>C. 12 <br><br>D. 110

kondaur [170]

Answer:

The answer to your question is: 12

Step-by-step explanation:

You have a function with two conditions,

- the first condition do not consider number nine, because it uses the symbol <, then we can not evaluate nine in this function.

- the second condition considers nine because uses the symbol ≤ which means that nine is considered here, but the function equals 12, so that is the solution.

6 0

3 years ago

How many quarter-pound (1/4) packets of plant food can a garden ahop make out of 8 pounds of the plant food?

Allisa [31]

You can make a total of 32 quarter pound packets by multiplying (8)(4) this leading for you to get 32 quarter packets. :P

6 0

3 years ago

Find the directional derivative of the function at the given point in the direction of the vector v. G(r, s) = tan−1(rs), (1, 3)

alexandr1967 [171]

The <em>directional</em> derivative of $f$ at the given point in the direction indicated is $\frac{5}{2}$ .

<h3>How to calculate the directional derivative of a multivariate function</h3>

The <em>directional</em> derivative is represented by the following formula:

$\nabla_{\vec v} f = \nabla f (r_{o}, s_{o})\cdot \vec v$ (1)

Where:

$\nabla f (r_{o}, s_{o})$ - Gradient evaluated at the point $(r_{o}, s_{o})$ .
$\vec v$ - Directional vector.

The gradient of $f$ is calculated below:

$\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{\partial f}{\partial r}(r_{o},s_{o}) \\\frac{\partial f}{\partial s}(r_{o},s_{o}) \end{array}\right]$ (2)

Where $\frac{\partial f}{\partial r}$ and $\frac{\partial f}{\partial s}$ are the <em>partial</em> derivatives with respect to $r$ and $s$ , respectively.

If we know that $(r_{o}, s_{o}) = (1, 3)$ , then the gradient is:

$\nabla f(r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{s}{1+r^{2}\cdot s^{2}} \\\frac{r}{1+r^{2}\cdot s^{2}}\end{array}\right]$

$\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{3}{1+1^{2}\cdot 3^{2}} \\\frac{1}{1+1^{2}\cdot 3^{2}} \end{array}\right]$

$\nabla f (r_{o}, s_{o}) = \left[\begin{array}{cc}\frac{3}{10} \\\frac{1}{10} \end{array}\right]$

If we know that $\vec v = 5\,\hat{i} + 10\,\hat{j}$ , then the directional derivative is:

$\nabla_{\vec v} f = \left[\begin{array}{cc}\frac{3}{10} \\\frac{1}{10} \end{array}\right] \cdot \left[\begin{array}{cc}5\\10\end{array}\right]$

$\nabla _{\vec v} f (r_{o}, s_{o}) = \frac{5}{2}$

The <em>directional</em> derivative of $f$ at the given point in the direction indicated is $\frac{5}{2}$ . $\blacksquare$

To learn more on directional derivative, we kindly invite to check this verified question: brainly.com/question/9964491

3 0

2 years ago