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3 years ago

Use Pascal's triangle to find the coefficient of the third term in the expansion of (a + b)2.

Mathematics

1 answer:

Alexxandr [17]3 years ago

4 0

Answer:

Step-by-step explanation:

(a+b)^2

using Pascal triangle

1 1

1 2 1

1 3 3 1

so the third term in the expansion of (a+b)^2

we use

1 2 1

a^2 + 2ab+b

hence the coefficient of third term is 1

option B is collect

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Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving

harina [27]

Answer:

The volume of the solid is 714.887 units³

Step-by-step explanation:

* Lets talk about the shell method

- The shell method is to finding the volume by decomposing

a solid of revolution into cylindrical shells

- Consider a region in the plane that is divided into thin vertical

rectangle

- If each vertical rectangle is revolved about the y-axis, we

obtain a cylindrical shell, with the top and bottom removed.

- The resulting volume of the cylindrical shell is the surface area

of the cylinder times the thickness of the cylinder

- The formula for the volume will be: V = $\int\limits^a_b {2\pi xf(x)} \, dx$ ,

where 2πx · f(x) is the surface area of the cylinder shell and

dx is its thickness

* Lets solve the problem

∵ y = $x^{\frac{5}{2}}$

∵ The plane region is revolving about the y-axis

∵ y = 32 and x = 0

- Lets find the volume by the shell method

- The definite integral are x = 0 and the value of x when y = 32

- Lets find the value of x when y = 0

∵ $y = x^{\frac{5}{2}}$

∵ y = 32

∴ $32=x^{\frac{5}{2}}$

- We will use this rule to find x, if $x^{\frac{a}{b}}=c, then=== x=c^{\frac{b}{a}}$ , where c

is a constant

∴ $x=(32)^{\frac{2}{5}}=4$

∴ The definite integral are x = 0 , x = 4

- Now we will use the rule

∵ $V = \int\limits^a_b {2\pi}xf(x) \, dx$

∵ y = f(x) = x^(5/2) , a = 4 , b = 0

∴ $V=2\pi \int\limits^4_0 {x}.x^{\frac{5}{2}}\, dx$

- simplify x(x^5/2) by adding their power

∴ $V = 2\pi \int\limits^4_0 {x^{\frac{7}{2}}} \, dx$

- The rule of integration of $x^{n} is ==== \frac{x^{n+1}}{(n+1)}$

∴ $V = 2\pi \int\limits^4_0 {x^{\frac{9}{2}}} \, dx=2\pi[\frac{x^{\frac{9}{2}}}{\frac{9}{2}}]$ from x = 0 to x = 4

∴ $V=2\pi[\frac{2}{9}x^{\frac{9}{2}}]$ from x = 0 to x = 4

- Substitute x = 4 and x = 0

∴ $V=2\pi[\frac{2}{9}(4)^{\frac{9}{2}}-\frac{2}{9}(0)^{\frac{9}{2}}}]=2\pi[\frac{1024}{9}-0]$

∴ $V=\frac{2048}{9}\pi=714.887$

* The volume of the solid is 714.887 units³

5 0

3 years ago

Draw the image of AABC under a dilation whose center is P and scale factor is 2.

Elan Coil [88]

Just use quizlet and you’ll get all the answers

5 0

3 years ago

What does the model predict for 1900?

vagabundo [1.1K]

Answer:

64.0% is the correct answer.

Step-by-step explanation:

As per the given scatter plot of voter turnout every year:

X axis represents the year and

Y axis represents the percentage of people who voted.

The model was predicted as per the equation:

$y = -0.1271x + 307.53$

<u>To find:</u> Prediction for the year 1900.

Putting the value of $x=1900$ , the value of y will be the predicted value of the model i.e. the value of percentage of voter turnout.

$\Rightarrow y = -0.1271\times (1900) + 307.53\\\Rightarrow y = -241.49 + 307.53\\\Rightarrow y = -64.04\%\\OR\\y \approx 64.0\%$

So, the model predicts $y \approx 64.0\%$ for the year 1900.

3 0

3 years ago

A hot air balloon rises an initial 525

ludmilkaskok [199]

Answer:

380ft

Step-by-step explanation:

Assuming the balloon rises 525ft from sea level (0ft), all we need to do is subtract both numbers to find the new height.

525 - 145 = 380ft

There could be many different scenarios though because if the question provides the height of land off sea level, you would have to take that into account as well.

Best of Luck!

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2 years ago

Evaluate the piece wise-defined function for the given values of x by matching the domain values with the range values

ss7ja [257]

Answer:

Step-by-step explanation:

3 0

3 years ago

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