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3 years ago

How many equilateral triangles are there in a regular hexagon?A. SixB. FiveC. ThreeD. Eight

Mathematics

2 answers:

vesna_86 [32]3 years ago

7 0

There'd be 6 EQUILATERAL triangles in a REGULAR hexagon

faust18 [17]3 years ago

6 0

Answer:

It’s six

Step-by-step explanation:

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Midpoint: (3,5) and (-1, 7)

8_murik_8 [283]

To find the midpoint:
x=3-1/2= 1
y=5+7/2= 6

8 0

3 years ago

Diagram 5 shows a right cylinder with a diameter of 2xcm. Given that the total surface area of the cylinder is 96cm³.Find the ma

Paraphin [41]

Given:

The diameter of the right cylinder is 2x cm.

The total surface area is 96 cm cube.

The radius is calculated as,

$\begin{gathered} r=\frac{d}{2} \\ r=\frac{2x}{2} \\ r=x\text{ cm} \end{gathered}$

The total surface area is,

$\begin{gathered} S=2\pi rh+2\pi(r)^2 \\ 96=2\pi xh+2\pi(x^2) \\ h=\frac{96-2\pi(x^2)}{2\pi x} \end{gathered}$

Volume is,

$\begin{gathered} V=\pi(r)^2h \\ =\pi(x^2)\frac{96-2\pi(x^2)}{2\pi x} \\ =\frac{x(96-2\pi(x^2)}{2} \end{gathered}$

Now, differentiate with respect to x,

$\begin{gathered} \frac{dV}{dx}^{}=\frac{d}{dx}(\frac{x(96-2\pi(x^2)}{2}) \\ =\frac{d}{dx}\mleft(x\mleft(-\pi x^2+48\mright)\mright) \\ =\frac{d}{dx}\mleft(x\mright)\mleft(-\pi x^2+48\mright)+\frac{d}{dx}\mleft(-\pi x^2+48\mright)x \\ =1\cdot\mleft(-\pi x^2+48\mright)+\mleft(-2\pi x\mright)x \\ =84-3\pi(x^2)\ldots\ldots\ldots\ldots\text{.}(1) \end{gathered}$

Now,

$\begin{gathered} \frac{dV}{dx}=0 \\ 84-3\pi(x^2)=0 \\ x^2=\frac{16}{\pi} \\ x=\sqrt[]{\frac{16}{\pi}} \end{gathered}$

Now, differentiate (1) with respect to x again,

$\begin{gathered} \frac{d^2V}{dx^2}=\frac{d}{dx}(84-3\pi(x^2)) \\ =-6\pi x \\ At\text{ x=}\sqrt[]{\frac{16}{\pi}} \\ \frac{d^2V}{dx^2}=-6\pi\sqrt[]{\frac{16}{\pi}}$

Since, the double derivative is negative.

$So,\text{ the volume is maximum at }\sqrt[]{\frac{16}{\pi}}$

So, the volume becomes,

$\begin{gathered} V=\pi(x^2)h \\ V=\pi(\sqrt[]{\frac{16}{\pi}})^2h \\ V=\frac{16h}{\pi} \end{gathered}$

Answer: maximum volume of the cylinder is,

6 0

1 year ago

70 pages assigned to read , 90% read what is the number of pages read

Bezzdna [24]

Answer:

63 is 90% of 70

Step-by-step explanation:

multiply 70 x .9 or 70(.9)

5 0

3 years ago

Read 2 more answers

About how much farther is May's softball throw than Robert's throw?

Degger [83]

Answer: Mays throw was 9.67 feet farther than Roberts.

5 0

2 years ago

Solve through substitution

Talja [164]

Answer:

The above system of equation have NO INTERSECTION POINT.

Step-by-step explanation:

Here, the givens system of equation are:

-3 x + 3 y = 4

and y = x + 3

Now, for the intersection of the equations:

Put y = x + 3 in the given first equation:

-3 x + 3 y = 4 ⇒ -3x + 3 (x+ 3) = 4

or, - 3x + 3x + 9 = 4

⇒ 9 = 4 which gives A CONTRADICTION as 9 ≠ 4

Hence, the above system of equation have NO INTERSECTION POINT.

8 0

3 years ago