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3 years ago

True or False 3 is a factor of n(n + 2)(n − 1) by mathematical induction. Explain why.

Mathematics

1 answer:

Crazy boy [7]3 years ago

8 0

Answer:

false

Step-by-step explanation:

this beacuse when is times with the base that shows the product thats the factor

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Which of the following functions is graphed below?

nikitadnepr [17]

Answer:

non of the above thanks

don't ask me again please

3 0

3 years ago

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What set of numbers are equivalent to 75%

VMariaS [17]

Answer:

Decimal= .75

fraction= 75/100; 3/4

Step-by-step explanation:

5 0

3 years ago

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Find the volume of the solid formed by revolving the region bounded by LaTeX: y = \sqrt{x} y = x and the lines LaTeX: y = 1 y =

Strike441 [17]

Answer:

The volume is:

$\displaystyle\frac{37\pi}{10}$

Step-by-step explanation:

See the sketch of the region in the attached graph.

We set the integral using washer method:

$\displaystyle\int_a^b\pi r^2dx$

Notice here the radius of the washer is the difference of the given curves:

$x-\sqrt{x}$

So the integral becomes:

$\displaystyle\int_1^4\pi(x-\sqrt{x})^2dx$

We solve it:

Factor $\pi$ out and distribute the exponent (you can use FOIL):

$\displaystyle\pi\int_1^4x^2-2x\sqrt{x}+x\,dx$

Notice: $x\sqrt{x}=x\cdot x^{1/2}=x^{3/2}$

So the integral becomes:

$\displaystyle\pi\int_1^4x^2-2x^{3/2}+x\,dx$

Then using the basic rule to evaluate the integral:

$\displaystyle\pi\left[\frac{x^3}{3}-\frac{2x^{5/2}}{5/2}+\frac{x^2}{2}\right|_1^4$

Simplifying a bit:

$\displaystyle\pi\left[\frac{x^3}{3}-\frac{4x^{5/2}}{5}+\frac{x^2}{2}\right|_1^4$

Then plugging the limits of the integral:

$\displaystyle\pi\left[\frac{4^3}{3}-\frac{4(4)^{5/2}}{5}+\frac{4^2}{2}-\left(\frac{1}{3}-\frac{4}{5}+\frac{1}{2}\right)\right]$

Taking the root (rational exponents):

$\displaystyle\pi\left[\frac{4^3}{3}-\frac{4(2)^{5}}{5}+\frac{4^2}{2}-\left(\frac{1}{3}-\frac{4}{5}+\frac{1}{2}\right)\right]$

Then doing those arithmetic computations we get:

$\displaystyle\frac{37\pi}{10}$

6 0

3 years ago

Company A had a loss of $255 in January. Company B had a profit of $162 in January. What was the difference between the profits

Julli [10]

Answer:

The difference of the profit of two companies is $ 417

Step-by-step explanation:

Given as :

The company A loss amount in January = $ 255

The company B profit amount in January = $ 162

Let the difference between there profits = x

So, x = company B profit - ( company A profit)

I.e x = company B profit - ( - company A loss)

Or, x = $ 255 + $162

∴ x = $ 417

Hence The difference of the profit of two companies is $ 417 . Answer

6 0

3 years ago

How does your cosine graph change when including the d-value?

fredd [130]

Answer:

Changing value of "d" changes the vertical shift of the cosine graph.

Step-by-step explanation:

Question says to find about how does your cosine graph change when including the d-value.

General equation of cosine function can be given as:

$y=a\cdot\cos\left(bx-c)\right)+d$

In that formula, value of "d" gives vertical shift.

So changing value of "d" changes the vertical shift of the cosine graph.

6 0

3 years ago