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3 years ago

A dozen plain hats cost 3.60,what is the unit rate of a hat?

Mathematics

2 answers:

deff fn [24]3 years ago

7 0

I think the answer should be 12.

madreJ [45]3 years ago

7 0

$3.60/12 = $0.30! You just take the total cost and divide by the total amount to find the cost of one hat

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Using polygon STUVW what is m angle U ?

bija089 [108]

Answer:

The m∠ U is 72°.

Step-by-step explanation:

Given:

$\angle S = 90\\\angle T = 2x\\\angle U = x\\\angle V = 2x\\\angle W = 90\\$

To find :

$\angle U = x = ?$

Solution:

The sum of the measures of the interior angles of a polygon with 'n' sides is given as

$\textrm{sum of the measures of angle of a polygon with 'n' sides} = (n - 1)\times 180$

Here we have n = 5 on substituting the values we get

$\angle S +\angle T + \angle U +\angle V + \angle W = (5 -2)\times 180\\90 + 2x + x + 2x + 90 = 3\times 180\\5x + 180 = 540\\5x = 540-180\\5x = 360\\x = \frac{360}{5}\\x = 72$

Therefore,

m∠ U is 72°.

4 0

3 years ago

A cylindrical can without a top is made to contain 25 3 cm of liquid. What are the dimensions of the can that will minimize the

Basile [38]

Answer:

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

Step-by-step explanation:

Given that, the volume of cylindrical can with out top is 25 cm³.

Consider the height of the can be h and radius be r.

The volume of the can is V= $\pi r^2h$

According to the problem,

$\pi r^2 h=25$

$\Rightarrow h=\frac{25}{\pi r^2}$

The surface area of the base of the can is = $\pi r^2$

The metal for the bottom will cost $2.00 per cm²

The metal cost for the base is =$(2.00× $\pi r^2$ )

The lateral surface area of the can is = $2\pi rh$

The metal for the side will cost $1.25 per cm²

The metal cost for the base is =$(1.25× $2\pi rh$ )

$=\$2.5 \pi r h$

Total cost of metal is C= 2.00 $\pi r^2$ + $2.5 \pi r h$

Putting $h=\frac{25}{\pi r^2}$

$\therefore C=2\pi r^2+2.5 \pi r \times \frac{25}{\pi r^2}$

$\Rightarrow C=2\pi r^2+ \frac{62.5}{ r}$

Differentiating with respect to r

$C'=4\pi r- \frac{62.5}{ r^2}$

Again differentiating with respect to r

$C''=4\pi + \frac{125}{ r^3}$

To find the minimize cost, we set C'=0

$4\pi r- \frac{62.5}{ r^2}=0$

$\Rightarrow 4\pi r=\frac{62.5}{ r^2}$

$\Rightarrow r^3=\frac{62.5}{ 4\pi}$

⇒r=1.71

Now,

$\left C''\right|_{x=1.71}=4\pi +\frac{125}{1.71^3}>0$

When r=1.71 cm, the metal cost will be minimum.

Therefore,

$h=\frac{25}{\pi\times 1.71^2}$

⇒h=2.72 cm

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

6 0

3 years ago

A conical tent made of canvas has a base that is 34 feet across and a slant height of 12 feet to the nearest whole unit what is

RideAnS [48]

Check the picture below.

$\bf \textit{total surface area of a cone}\\\\
SA=\pi r\sqrt{r^2+h^2}+\pi r^2~~
\begin{cases}
r=radius\\
h=height\\
-------\\
r=17\\
\sqrt{r^2+h^2}=12
\end{cases}
\\\\\\
SA=\pi (17)(12)+\pi (17)^2\implies SA=204\pi +289\pi \implies SA=493\pi$