Equation for line passing through (4,3) perpendicular to y=5x+4

A cereal company is exploring new cylinder-shaped containers. Two possible containers are shown in the diagram.x is 6 and r=4.5

KatRina [158]

Answer:

Container $\rm X$ will have less label area than container $\rm Y$ by about $9\; \rm in$ .

Step-by-step explanation:

A rectangular sheet of paper can be rolled into a cylinder. Conversely, the lateral surface of a cylinder can be unrolled into a rectangle- without changing the area of that surface.

Indeed, the width of that rectangle will be the same as the height of the cylinder. On the other hand, the length of that rectangle should be exactly equal to the circumference of the circles on the top and the bottom of the cylinder. In other words, if a cylinder has a height of $h$ and a radius of $r$ at the top and the bottom, then its lateral surface can be unrolled into a rectangle of width $h$ and length $2\,\pi\, r$ .

Apply this reasoning to both cylinder $\mathrm{X}$ and $\rm Y$ :

For cylinder $\mathrm{X}$ , $h = 6\; \rm in$ while $r = 4.5\; \rm in$ . Therefore, when the lateral side of this cylinder is unrolled:

The width of the rectangle will be $6\; \rm in$ , while
The length of the rectangle will be $2 \, \pi \times 4.5\; \rm in = 9\, \pi\; \rm in$ .

That corresponds to a lateral surface area of $54\, \pi\; \rm in^2$ .

For cylinder $\rm Y$ , $h = 10.5\; \rm in$ while $r = 3\; \rm in$ . Similarly, when the lateral side of this cylinder is unrolled:

The width of the rectangle will be $10.5\; \rm in$ , while
The length of the rectangle will be $2\pi\times 3\; \rm in = 6\,\pi \; \rm in$ .

That corresponds to a lateral surface area of $63\,\pi \; \rm in^2$ .

Therefore, the lateral surface area of cylinder $\rm X$ is smaller than that of cylinder $\rm Y$ by $9\,\pi\; \rm in^2$ .

5 0

3 years ago

Suppose that there are 15 antennas in a store, of which 3 are defective. Assume all the defectives and all the functional antenn

ohaa [14]

Answer:

Step-by-step explanation:

Total number of antenna is 15

Defective antenna is 3

The functional antenna is 15-3=12.

Now, if no two defectives are to be consecutive, then the spaces between the functional antennas must each contain at most one defective antenna.

So,

We line up the 13 good ones, and see where the bad one will fits in

__G __ G __ G __ G __ G __G __ G __ G __ G __ G __ G __ G __G __

Each of the places where there's a line is an available spot for one (and no more than one!) bad antenna.

Then,

There are 14 spot available for the defective and there are 3 defective, so the arrange will be combinational arrangement

ⁿCr= n!/(n-r)!r!

The number of arrangement is

14C3=14!/(14-3)!3!

14C3=14×13×12×11!/11!×3×2

14C3=14×13×12/6

14C3=364ways

7 0

3 years ago

Sample annual salaries (in thousands of dollars) for employees at a company are listed. 42 36 48 51 39 39 42 36 48 33 39 42 45 (

Sonja [21]

Answer:

a) Data given: 42 36 48 51 39 39 42 36 48 33 39 42 45

$\bar X = 41.538$

$s = 5.317$

b) 44.1, 37.8, 50.4, 53.55, 40.95, 44.1, 37.8, 50.4 ,34.65, 40.95, 44.1, 47.25

$\bar X = 43.615$

$s= 5.583$

c) 3.5, 3, 4, 4.25, 3.25, 3.25, 3.5, 3, 4, 2.75, 3.25, 3.5, 3.75

$\bar X= 3.462$

$s = 0.443$

d) As we can see, the average of part b is 1.05 times the average of part a (1.05 * 41.538 = 43.615) and the average of part c is equal to the average obtained in part a divided by 12 (41.538 / 12 = 3.462).

And that happens because we create linear transformations for the parts b and c and the linear transformation affects the mean.

And you have the same interpretation for the deviation, it is affected by the linear transformation as the mean.

Step-by-step explanation:

For this case we can use the following formulas for the mean and standard deviation:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

Part a

Data given: 42 36 48 51 39 39 42 36 48 33 39 42 45

And if we calculate the mean we got:

$\bar X = 41.538$

$s = 5.317$

Part b

For this case we know that each value present a 5% of rise so we just need to multiply each value bu 1.05 and we have this new dataset:

44.1, 37.8, 50.4, 53.55, 40.95, 44.1, 37.8, 50.4 ,34.65, 40.95, 44.1, 47.25

And if we calculate the new mean and deviation we got:

$\bar X = 43.615$

$s= 5.583$

Part c

The new dataset would be each value divided by 12 so we have:

3.5, 3, 4, 4.25, 3.25, 3.25, 3.5, 3, 4, 2.75, 3.25, 3.5, 3.75

And the new mean and deviation would be:

$\bar X= 3.462$

$s = 0.443$

Part d

As we can see, the average of part b is 1.05 times the average of part a (1.05 * 41.538 = 43.615) and the average of part c is equal to the average obtained in part a divided by 12 (41.538 / 12 = 3,462).

And that happens because we create linear transformations for the parts b and c and the linear transformation affects the mean.

And you have the same interpretation for the deviation, it is affected by the linear transformation as the mean.

5 0

3 years ago

The length of a regulation soccer field is 110 meters. The diagonal length of the same soccer field is about 133.14 meters. Abou

dexar [7]

Answer:

D

Step-by-step explanation:

Imagine this as a right angle triangle, where the diagonal length is the hypotenuse, the length is one side, and the width is the other.

We can therefore use Pythagoras' Theorem (or Pythagorean Theorem) to solve. The formula for this is a²+b²=c², where c is the hypotenuse, and a and b are the sides.

We can input the values we know to this formula to get the width. This gives 110²+b²=133.14² or 12100+b²=17 726.2596.

From there subtracting 12100 from both sides gives b²=5626.2596.

Square rooting b isolates it, leaving b=75.0083969.

Since the value of the diagonal was approximate, this can be assumed the b is 75m.

**This content involves Pythagoras' Theorem/Pythagorean Theorem, which you may wish to revise. I'm always happy to help!

8 0

3 years ago

Fine the area of a parallelogram with base b and height h.<br> b = 82 cm<br> h = 16.6 cm

Alona [7]

I just added an answer to a question exactly like that. The answer would be 1, 361.2. To find area you need to multiply the base and height together. Just think, b*h=a. Base times height equals area. Good luck!

3 0

3 years ago

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