CPhill

I'll do 12, Nataszaa...the rest use exactly the same process......

12) y=3x+1

First ....get x by itself  by subtracting 1 from both sides

y - 1  = 3x      divide both sides by 3

(y - 1) / 3   = x

Now...."switch" x and y

(x - 1) / 3  = y     now, for "y"...write f^-1(x).....so we have...

f^-1(x) = (x - 1) / 3      ....and that's the inverse function.....

#58 5(x2/3)^7-6

I'm assuming that we have this???......... 5[x^(2/3)]^(7-6)   = 5[x^(2/3)]^(1) = 5[x^(2/3)] = 5x^(2/3).......I'm not too sure that I've answered what was actually asked on this one, Nataszaa !!!! If it's not....maybe you could provide more info to us ????

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#59 (-27x^-9)1/3

So we have....

-3x^(-3)

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#60 (-32y^15)1/5

So we have....

-2y^3

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And that's it!!!

The orange circle is those who like cricket

The blue is those who like baseball

The "9" outside represents the number of those who like neither sport.....

(5/8) x 300 =

1500/8  = 750/4 = 375/2 = 187.5

Just use the on-site calculator.....it will even "reduce" this for you....magic!!!

OOPS...sorry ND....I didn't know you were posting on this one, too!!

Well, anyway...yours was a more complete explanation....

I gave both of us points, but I'm thinking about rescinding mine !!!

9^867 x 9^428 x 3^-358 x 3^-2228

Let's get everything to the same base

Note that 9 = 3²    so we can write...

(3²)⁸⁶⁷ x (3²)⁴²⁸ x (3)^-358 x (3)^-2228    ...and by an exponent law, we have..

3¹⁷³⁴ x 3⁸⁵⁶ x 3^-358 x 3^-2228 

Now, just "keep" the base - (3) - and add/subtract the exponents and that will give you your answer.....!!!

∫(x/2) dx  =

(1/2)∫(x) dx  =

(1/2)  (x² / 2) + C  =

(1/4) x²  + C

You should check that the derivative of this returns the original function in the integrand..

Yep...Melody is correct.......we told the person how to build a clock and all they wanted to know is how to tell the time!!!

I'll have to admit it......I'm a little lax on "calculator instruction"

The other leg is found by taking the square root of the difference between the hypoteneuse squared and the other leg squared......i.e, ........

√(85² - 53²)  ≈ 66.5  ......rounded to the nearest tenth....

And that's it!!!