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labwork [276]
3 years ago
12

You start a small business making lamps. You decide to invest $3,150 of your own money to start

Mathematics
1 answer:
Reptile [31]3 years ago
4 0

Answer:

100

Step-by-step explanation:

the first you have to use Lebara

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Marcus has a square shaped garden that has an area of 4(x^2-y^2) square feet. If the garden has four equal sections, what is the
SpyIntel [72]

Answer:

x^2-y^2

Step-by-step explanation:

took a quiz and got it right

8 0
2 years ago
Peyton is taking a multįple choice test with a total of 20 points available. Each
OleMash [197]

Answer:

if she got 4 questions wrong it would be 12

her score if she got x questions wrong it would be 20-2x

6 0
3 years ago
Joshua Bennett purchased a television for $245.95 with 40.25% down. He will make 6 payments of $25.83 each. What is the total am
brilliants [131]
(245.95×0.4025)+(6×25.83)=253.97

253.97-245.95=8.02

4 0
3 years ago
Read 2 more answers
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
When is the absolute value of a difference equal to the difference of the absolute values?
marshall27 [118]
<span>ax(d) = absolute value of the difference = ax(a-b).
d(ax) = difference of the absolute value = ax(a) - ax(b).
ax(a-b) = absolute value of (a - b).
ax(a) - ax(b) = absolute value of (a) minus absolute value of (b).

Hope this works :)</span>
7 0
3 years ago
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