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3 years ago

10

Six angles share a vertex. Each of the angles has the same measure. The sum of the measures of the angles is 330 degrees. What i

s the measure of one angle?

1 answer:

JulsSmile [24]3 years ago

8 0

The measure of one angle is 55 because 330 divided by six is 55

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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

What is 1/4 times 2 -9

krek1111 [17]

Answer:

-8.5

Step-by-step explanation:

1/4 times 2= 0.5

0.5-9=-8.5

Hope this helps :D

5 0

4 years ago

Read 2 more answers

Archie earns $4 a week for doing choirs. How much will Archie warm in 2 months if there are four weeks in each month?

siniylev [52]

Hello! The answer for your question would be $32. This is because if Archie earns $4 a week and there are 4 weeks in each month, and he works for 2 months, then 4*4 for one week would equal $16. This times 2 would equal $32 therefore, Archie earned $32 dollars for 2 months of doing chores.

4 0

3 years ago

Two consecutive even numbers are such that five times the smaller number , subtracted from eight times the bigger gives 58. Find

olga55 [171]

Answer:

$14\text{ and }16$

Step-by-step explanation:

Let the smaller number be $x$ . Since they are consecutive even numbers, the larger number can be represented by $x+2$ .

Therefore, we have the following equation:

$8(x+2)-5x=58,\\8x+16-5x=58,\\3x=42,\\x=\boxed{14}$

Thus, the larger number is $x+2=\boxed{16}$

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3 years ago

Aisha thinks 1,275 rounded to the nearest hundread is 1,200 because 2 is less than 5 what might aisha misunderstand about roundi

lora16 [44]

For rounding, you look at the number to the right of it.

In this case, it would be 7

because 7 is greater than 5, it is rounded up (remember, 5 and up is round up, while 4 and lower is round down)
So her answer should be 1300

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3 years ago

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