Simplify (8x^2 − 1 + 2x^3) − (7x^3 − 3x^2 + 1).

With which whole number is the square root of 130 closest to

kati45 [8]

Putting the square root of 130 in the calculator you would get around 11.4 which if rounded to the next whole number would be 11. The closest whole number to the square root of 130 is 11.

8 0

3 years ago

The total surface area of a closed cylinder is

Degger [83]

The maximum volume of the cylinder is 27147.355 at the maximum point $r = \frac{50}{\sqrt{3} }$ .

<h3>How do you find the maximum volume of the cylinder?</h3>

The formula for the volume of the cylinder v = $\pi$ $r^{2}$ h, To find the maximum volume of the cylinder we apply the condition of maxima $\frac{\mathrm{d} v}{\mathrm{d} r}$ = 0.

Let r cm be the radius and h cm be the height of the closed cylinder.

Then, Total surface area of the cylinder = $2\pi r(r+h)$

$5000$ = $2\pi r^{2} +2\pi rh$

$h$ = $\frac{5000-2\pi r^{2} }{2\pi rh}$ .............(1)

Volume of the cylinder v = $\pi r^{2} h$

Substitute the value of $h$ in the above equation

$\Rightarrow$ = $\pi r^{2}$ × $\left [ \frac{5000-2\pi r^{2}}{2\pi r} \right ]$

$\Rightarrow$ = $\frac{r}{2}$ × $(5000-2\pi r^{2} )$

$\Rightarrow$ v = $2500r-\pi r^{3}$ ..............(2)

Now, for the maximum volume of the cylinder $\frac{\mathrm{d} v}{\mathrm{d} r}$ = 0

$\Rightarrow$ $\frac{\mathrm{d} (2500r-\pi r^{3})}{\mathrm{d} r} = 0$

$\Rightarrow$ $3\pi r^{2} = 2500$

$\Rightarrow$ $r^{2} = \frac{2500}{3\pi }$

$\Rightarrow$ $r = \frac{50}{\sqrt{3\pi } }$

Volume is maximum for $r = \frac{50}{\sqrt{3\pi } }$

Then, v = $2500r-\pi r^{3}$

$\Rightarrow$ = $2500 \frac{50}{\sqrt{3\pi } } -\pi (\frac{50}{\sqrt{3\pi } } )^{3}$

$\Rightarrow$ = $\frac{125000}{\sqrt{3\pi } } - \frac{125000}{3\sqrt{3\pi } }$

$\Rightarrow$ = $\frac{125000}{\sqrt{3\pi } }$ × $\frac{2}{3}$

$\Rightarrow$ = $\frac{250000}{3\sqrt{3\pi } }$

$\Rightarrow$ v = 27147.355

Hence, The maximum volume of the cylinder is 27147.355 at the maximum point $r = \frac{50}{\sqrt{3} }$ .

To learn more about total surface area and volume of the cylinder from the given link

brainly.com/question/16095729

#SPJ4

3 0

2 years ago

CAN SOMEONE HELP ME IT'S POLYNOMIAL EXPRESSIONS AND I got it done to at least c or d if someone could look at this and double ch

Reptile [31]

Answer:

The option is D

$(n+4)^{2} - n^{2} = 8(n + 2)$

Step-by-step explanation:

Given

$(n+4)^{2} - n^{2} = 8(n + 2)$

put $n=1$ we get

$(1+4)^{2}- 1^{2}= 8(1+2)\\5^{2}- 1^{2}= 8\times 3 = 24$

Similarly,

put $n=2$ we get

$(2+4)^{2}- 2^{2} = 8(2+2)\\6^{2}- 2^{2}= 8\times 4 = 32$

put $n=4$ we get

$(4+4)^{2}- 4^{2} = 8(4+2)\\8^{2}- 4^{2} = 8\times 6 = 48$

7 0

4 years ago

Evaluate the expression: a(b – c) if a = -8, b = 12, and c = 4

Mariana [72]

3 0

4 years ago

Read 2 more answers

Estimate the circumference of a circle that has a diameter of 13 yards.

Natali [406]

Circumference= 2πr

Radius= diameter ÷ 2

C= 2(3.14)(13/2)
divide 2 into 13 first
C= 2(3.14)(6.5)
multiply
C= 40.82 yards

ANSWER:
The circumference is 40.82 yards, estimated to 41 yards.

Hope this helps! :)

7 0

3 years ago

Read 2 more answers