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Ray Of Light [21]
2 years ago
13

The cost for a pack of 18 pencils is $3.24. Find the unit price in dollars per pencil. If necessary, round your answer to the ne

arest cent.
Mathematics
1 answer:
nexus9112 [7]2 years ago
4 0

Answer:

$0.18 per pencil.

Step-by-step explanation:

"Dollars per unit" means that you take the dollar amount and divide it by the amount of pencils, so you get 3.24/18, or .18.

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the cylinder has radius 4√3 and hight h. the total surface area of the cylinder is 56π√6. find the exact value of h giving the a
Arte-miy333 [17]

The area of the cylinder is a function of its height (h) and radius, (\mathbf{4\sqrt 3})

The exact value of h is: \mathbf{7\sqrt 2- 4\sqrt 3}

The given parameters are:

\mathbf{Area =56\pi\sqrt 6}

\mathbf{r=4\sqrt 3}

The surface area of a cylinder is calculated as:

\mathbf{Area = 2\pi rh + 2\pi r^2}

Substitute values for Area

\mathbf{56\pi\sqrt 6= 2\pi rh + 2\pi r^2}

Divide through by pi

\mathbf{56\sqrt 6= 2 rh + 2r^2}

Substitute value for r

\mathbf{56\sqrt 6= 2 (4\sqrt 3)h + 2(4\sqrt 3)^2}

\mathbf{56\sqrt 6= 8h\sqrt 3 + 2\times 48}

\mathbf{56\sqrt 6= 8h\sqrt 3 + 96}

Collect like terms

\mathbf{8h\sqrt 3 = 56\sqrt 6- 96}

Make h the subject

\mathbf{h = \frac{56\sqrt 6}{8\sqrt 3}- \frac{96}{8\sqrt 3}}

\mathbf{h = 7\sqrt 2- \frac{12}{\sqrt 3}}

Rationalize

\mathbf{h = 7\sqrt 2- \frac{12\sqrt 3}{3}}

\mathbf{h = 7\sqrt 2- 4\sqrt 3}

Hence, the exact value of h is: \mathbf{7\sqrt 2- 4\sqrt 3}

Read more about surface areas t:

brainly.com/question/25131428

5 0
2 years ago
The spokes of a bicycle wheel form 10 congruent central angles. The diameter of the circle formed by the outer edge of the wheel
N76 [4]

find the circumference and divide it by 10

c = d\pi \\ c = 18\pi \\ c = 56.548668... \\  \\ arc =  \frac{c}{10}  \\ arc = 5.654867... \\ arc = 5.7

4 0
3 years ago
Am I correct? I added them all.
max2010maxim [7]
Yes you are correct.
6 0
3 years ago
Read 2 more answers
Is there a trend in this data if there is please tell me and why ,thank u
pickupchik [31]
No thers not a trend because a trend need to be in a strait line and thers not a strait line in the photo

5 0
3 years ago
Read 2 more answers
The vertices of a parallelogram are A(x1,y1), B(x2,y2), C(x3,y3), D(x4,y4)
Tju [1.3M]
<span>For a parallelogram to be proven to be a rectange, the opposide sides must be parallel and the two adjacent sides must be perpendicular. For two parallel sides, the slope of the two sides is equal. Thus, for the parallelogram to be a rectangle, AB is parallel to CD. The slope of AB = (y2 - y1)/(x2 - x1) while the slope of CD = (y4 - y3)/(x4 - x3) Also, BC is perpedicular to CD. For two perpendicular sides, the product of the slopes is -1. The slope of BC is given by (y3 - y2)/(x3 - x2). Therefore, for the parallelogram to be a rectangle. (y2 - y1)/(x2 - x1) = (y4 - y3)/(x4 - x3) and (y4 - y3)/(x4 - x3) x (y3 - y2)/(x3 - x2) = -1. The third option is the correct answer.</span>
3 0
2 years ago
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