Adjust the number into correct standard form.<br> 60 x 103

Find the surface area of the solid generated by revolving the region bounded by the graphs of y = x2, y = 0, x = 0, and x = 2 ab

Nikitich [7]

Answer:

See explanation

Step-by-step explanation:

The surface area of the solid generated by revolving the region bounded by the graphs can be calculated using formula

$SA=2\pi \int\limits^a_b f(x)\sqrt{1+f'^2(x)} \, dx$

If $f(x)=x^2,$ then

$f'(x)=2x$

and

$b=0\\ \\a=2$

Therefore,

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+(2x)^2} \, dx=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx$

Apply substitution

$x=\dfrac{1}{2}\tan u\\ \\dx=\dfrac{1}{2}\cdot \dfrac{1}{\cos ^2 u}du$

Then

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx=2\pi \int\limits^{\arctan(4)}_0 \dfrac{1}{4}\tan^2u\sqrt{1+\tan^2u} \, \dfrac{1}{2}\dfrac{1}{\cos^2u}du=\\ \\=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0 \tan^2u\sec^3udu=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0(\sec^3u+\sec^5u)du$

Now

$\int\limits^{\arctan(4)}_0 \sec^3udu=2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17})\\ \\ \int\limits^{\arctan(4)}_0 \sec^5udu=\dfrac{1}{8}(-(2\sqrt{17}+\dfrac{1}{2}\ln(4+\sqrt{17})))+17\sqrt{17}+\dfrac{3}{4}(2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17}))$

Hence,

$SA=\pi \dfrac{-\ln(4+\sqrt{17})+132\sqrt{17}}{32}$

3 0

2 years ago

Helpppppppppp meeeeeee pleaseeeeeeeee

zavuch27 [327]

Answer:

If you are rounding to the nearest tens the smallest number is 45. If you are rounding to the nearest whole number, the smallest number is 49.5

3 0

2 years ago

Read 2 more answers

Hi can you please help me with my work

babymother [125]

Hi yes I can:)
Its the first option. 3 1/2

5 0

2 years ago

Read 2 more answers

An office is divided into 8 cubicles. How many of the cubicles are carpeted if only 1/4 of the cubicles are carpeted?

Bas_tet [7]

1/4 of 8 is 2. So 2 of the cubicles are carpeted.

5 0

3 years ago

Read 2 more answers

Based on a survey, that 46% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the

Wewaii [24]

$n=5,x=3,p=0.46,q=0.54$ .

<u>Step-by-step explanation:</u>

Here we have , Based on a survey, that 46% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when five consumers are randomly selected, exactly three on them are comfortable with delivery by drones. We need to find the values of n,x,p,and q .Let's find out:

According to question , 46% of consumers are comfortable having drones deliver their purchases , So , Probability of success :

⇒ $p=0.46$

And , probability of failure :

⇒ $q=1-p =1-0.46$

⇒ $q=0.54$

Now , n = Number of people randomly selected = 5

x = Number of people exactly comfortable = 3

Therefore , $n=5,x=3,p=0.46,q=0.54$ .

4 0

3 years ago

Adjust the number into correct standard form. 60 x 103