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3 years ago

Select all that apply to the given number.

Mathematics

2 answers:

Olenka [21]3 years ago

6 0

Answer:

2/3 can be classified as..

rational

Step-by-step explanation:

It can be classified as a rational number because it can be in the form of p/q as of fraction and is made up of two integers making p the numerator and for q a denominator not involving a zero.

Rudik [331]3 years ago

4 0

Answer:

real

rational

Step-by-step explanation:

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Harlamova29_29 [7]

I typed right on the problem set.

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3 years ago

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,

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

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3 years ago

A rectangle has a length of 4 mm has an area is 44 mm² width of the rectangle is

nordsb [41]

The answer is : w=1.1×10^7mm

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2 years ago

Read 2 more answers

Mr. Sasha teaches 4 math classes, with the same number of students in each class. Of those students, 80 are sixth graders and 40

STatiana [176]

80=6th graders
40=5th graders

80+40=120
120/22= 60/11
120/25=24/5
120/30= 4

There are 30 students in each class because he teaches 4 class and 120/30 will give you 4.

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4 years ago

How do you solve 2x^2+4x=3+3x^2?

allochka39001 [22]

Answer:

5x^2+4x=3

Step-by-step explanation:

You add the like terms: 3x^2 and 2x^2, you get 5x^2. You can't do anything else because there are no more terms that are alike.

So the answer would be 5x^+4x=3

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4 years ago