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Pie
3 years ago
13

Select the correct answer.

Mathematics
2 answers:
11Alexandr11 [23.1K]3 years ago
5 0

Answer:

The answer is D). x=-4 \pm \sqrt{13}

Step-by-step explanation:

Just use the quadratic formula and plug in for solution.

For reference:

x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a} is the quadratic formula.

In this equation: a = 1, b = 8, and c = 3

enot [183]3 years ago
4 0

Answer:

B

Step-by-step explanation:

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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
PLEASE HELPPP, its timed. NO BOTS please i want serious answers.
Rzqust [24]
CDAB

4.2 (convert to frac on ur own)

12.5=x

CB= 14.5

AB= 8.82
6 0
2 years ago
Answer me step by step detailed
KengaRu [80]

Answer:

$11.25

Step-by-step explanation:

When finding a discount that has a percentage, we have to multiply the amount of the specific item being discounted and the percentage of the discount. In this case, we have a forty-five dollar headset at a twenty-five percent discount rate. To find the price, multiply the amount of the headset by the percentage of the discount.

$45 * 25%

$11.25

Meaning that the price of the discount will be eleven dollars and twenty five cents.

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1 year ago
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Answer:

21

Step-by-step explanation:

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2 years ago
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Please help!!!!! Fast please
7nadin3 [17]

3/1 cup is the answer!

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2 years ago
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