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WyzAnt Tutoring Tutor Tutor United States

## Experienced Math Tutor

### Bethel, CT (06801)

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# Jyothi's Responses in WyzAnt Answers

#### Mean value theorem

Determine whether the Mean Value Thereom can be applied to f on the closed interval (a,b) .  If the MVT can be applied, find all values of c in the open interval (a,b) such that f'(c) =f(b)-f(a) / b - a.

f(x) = x 2/3, (0,1)

Note it's x to the 2/3 power

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Asked by Elaine from San Pedro, CA
20

Step 1 Differentiate the given function                   f(x)=x2/3

Use the power rule.                                   f'(x)=2/3x-1/3

Step 2 Evaluate the derivative of c.                      f'(c)=2/3c-1/3

Step 3 Find the slope over the entire interval.

Evaluate the function at b=1.                    f(b)= f(1)= 12/3= 1

Evaluate the function at a=0.                    f(a) = f(0)= 02/3 = 0

Substitute in slope formula.                       f(b)-f(a) / b-a =1-0 / 1-0

Step 4 Set the derivative (Step 2) equal to the slope (step 3).     2/3c-1/3= 1

c-1/3= 3/2

Raise both sides to the power -3.                                    (c-1/3)-3=(3/2)-3

Simplify.                                                                       c= (2/3)3

c= 8/27

Hope this helps.

#### choose one rule that applies to exponents, explain how the rule works, and provide an example for your classmates to solve.

choose one rule that applies to exponents, explain how the rule works, and provide an example for your classmates to solve.

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Asked by Deborah from Durant, OK
00

xm × xn=xm+N

ex:  22×23=22+3

=25 =32  (R.H.S)

L.H.S: 22=4,  23=8

=22×23=4×8=32

L.H.S =R.H.S

#### Traffic signs are regulated by the Manual on Uniform Traffic Control Devices (MUTCD).

The perimeter of a rectangular traffic sign is 72 inches. Also, its length is 12 inches longer than its width.

Find the dimensions of this sign.

The width of the sign is ? (inches)

The length of the sign is ? (inches)

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Asked by Jamal from Oregon, OH
00

Rectangle perimeter = 2(l+b)  =72

We have given Length is 12 inches longer than width = l=12+b

2(l+b)= 72

l+b=72/2= 36

We substitute for l in the above

12+b+b=36

2b=36-12=24

b=12, then we find for l by sub..

l=12+b=12+12=24

sol...  l=24  b=12

#### Complete the table for each solution. Than identify the solution to both equations.

x          0    1      2      3

y=x+2   ?    ?      ?      ?

y=6-x     ?    ?      ?      ?

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Asked by Jamal from Oregon, OH
00

Given values for x = 0 , 1, 2, 3

we find values for 'y'in equation.    y= x+2 by substituting values of x

For x=0  ,   y= x+2 = 0+2 =2

x=1            y= 1+2    =3

x=2           y= 2+2    =4

x=3          y=3+2     =5

again we sub substitute the values for x in y=6-x

x=0        y=6-0 =6

x=1       y=6-1   =5

x=2      y= 6-2  =4

x=3      y=6-3    =3

Sol.     x    0  1  2  3

y=x+2      2   3   4  5

y=6-x      6   5    4  3

#### find the distance between the points (-2,5) and (12,-1)

finding the distance

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Asked by Louis from Arlington, TX
00

The distance between two  points (x1,y1) and (X2,Y2) can be found by using the formula d =  √ (x2-X1)²+(Y2-y1)²

you can find the distance for the points (-2,5) and (12,-1) using the above formula

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