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2 years ago

Order the numbers 21 , 40, and 42 from least to greatest based on how many numbers are in their prime factorization.

Mathematics

1 answer:

lora16 [44]2 years ago

6 0

Answer:

21,40,42

Step-by-step explanation:

That's it.Wish it's correct.:D

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Area is 1/2•b•h so 25

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2 years ago

What is the answer to 41x 59 plus 8 divided by 6

Advocard [28]

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3/4log7(625)+2log7(x)=2 solve for x

sdas [7]

Simplifies to:
1.690196x+396.139706=2

Let's solve your equation step-by-step.
1.690196x+396.139706=2

Step 1: Subtract 396.139706 from both sides.

1.690196x+396.139706-396.139706=2-396.139706

1.690196x=-394.139706

Step 2: Divide both sides by 1.690196.
1.690196x/1.690196 -394.139706/1.690196

x= -233.191716
Answer: x= -233.191716

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3 years ago

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3 years ago

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How would I find the integral of <img src="https://tex.z-dn.net/?f=%5Cint%5Cfrac%7Btdt%7D%7Bt%5E4%2B2%7D" id="TexFormula1" title

kotegsom [21]

Let $t=\sqrt y$ , so that $t^2=y$ , $t^4=y^2$ , and $\mathrm dt=\dfrac{\mathrm dy}{2\sqrt y}$ . Then

$\displaystyle\int\frac t{t^4+2}\,\mathrm dt=\int\frac{\sqrt y}{2\sqrt y(y^2+2)}\,\mathrm dy=\frac12\int\frac{\mathrm dy}{y^2+2}$

Now let $y=\sqrt2\tan z$ , so that $\mathrm dy=\sqrt2\sec^2z\,\mathrm dz$ . Then

$\displaystyle\frac12\int\frac{\mathrm dy}{y^2+2}=\frac12\int\frac{\sqrt2\sec^2z}{(\sqrt2\tan z)+2}\,\mathrm dz=\frac{\sqrt2}4\int\frac{\sec^2z}{\tan^2z+1}\,\mathrm dz=\frac1{2\sqrt2}\int\mathrm dz=\dfrac1{2\sqrt2}z+C$

Transform back to $y$ to get

$\dfrac1{2\sqrt2}\arctan\left(\dfrac y{\sqrt2}\right)+C$

and again to get back a result in terms of $t$ .

$\dfrac1{2\sqrt2}\arctan\left(\dfrac{t^2}{\sqrt2}\right)+C$

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