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3 years ago

What is the correct choice

Mathematics

2 answers:

Mekhanik [1.2K]3 years ago

5 0

I think it would be A.

Maybe not because they are all negatives.

Sliva [168]3 years ago

5 0

The answer is B. By rotating it 90 degrees counterclockwise around the origin, you will switch your x and y values, and your new x value will now be positive, so (x,y) is now (-y,x). Then, you add 4 to each y value and you are matched with answer B.

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A) Expand and simplify (x + 4)(x-7)<br>

saveliy_v [14]

Answer:

Expanded:x²-7x+4x-28

Simplified: x²-3x-28

Step-by-step explanation:

7 0

3 years ago

1.) A triangle has two interior angle measures of 82º and 19º. Find the measure of

daser333 [38]

Answer:

79°

Step-by-step explanation:

A triangle has 180° in it so 180 - 82 =98- 19=79

4 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

Heyo. Can ya help me out?

borishaifa [10]

Answer:

yEAH MAN

Step-by-step explanation:

no doubt

8 0

3 years ago

Simplify 8/-3 divided -4/9

alexdok [17]

Answer:

Step-by-step explanation:

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2 years ago