CPhill

De rien.....

-4 ( 7r + 7)  =

-4* 7r    +     - 4 * 7   =

-28r    -  28

17 + e^(7x) = 33     subtract 17 from both sides

e^(7x)  =  16           take the Ln of both sides

Ln e^(7x)  = Ln 16      and we can write

(7x) Ln e  = Ln 16         Ln e = 1.....so we  can ignore this

7x =  Ln 16         divide both sides by 7

x =  [ Ln 16 ]  / 7

AB = AC                                                        given

Angle 1 = Angle 2                                         given

Angle BAD is supplemental to Angle 1         supplementary pair

Angle CAD is supplemental to Angle 2         supplementary pair

Angle BAD  + Angle 1 = 180                         definition of supplemental

Angle CAD + Angle 2 = 180                          definition of supplemental

Angle BAD + Angle 1 = Angle CAD + Angle 2      substitution

Angle BAD = Angle CAD                                      subtraction property of equality

AD = AD                                                               reflexive property of equality

Triangle DAB congruent to Triangle DAC            SAS

Angle B  = Angle C                                            corresponding parts of congruent triangles are congruent

You are correct, EP.....I didn't see that we had 5 people...!!!!

Any 3 can finish 1st

And, after this, any 2 can finish second

So

3 x 2   =   6  possible finishing orders

4 (10)^(5x) = 200       divide both sides by 4

(10)^(5x) = 50          take the log of both sides

log 10^(5x) = log 50       and by a log property, we can write

(5x) log 10  =  log 50        log 10  = 1  ....so we can ignore this.....and we have

5x  =  log 50             divide both sides by 5

x =  [ log 50 ] / 5

Extrema.....=  high or low points on graph

They may be absolute or local

The absoute max or min is higher or lower than any other point on the graph

The  local min is lower than the surrounding points....but not the lowest point on the graph

The local max is higher than the surrounding points....but not the highest point on the graph

First one.....we only have a low point

As this graph shows : https://www.desmos.com/calculator/iplw9vvorn

.....the low point is    (-1, - 7)

This is known as a global minimum.....the absolute lowest point on the graph

We have no max because the graph just keeps increasing forever

Second one....we only have one "local"  max  and one "local" minimum

Look at the graph here : https://www.desmos.com/calculator/opsial98n0

The local max is at (-3, 5)

The local min is at (-1, 1)

There is no absolute min or max because the graph falls to - inf  and rises to inf

LOL!!!.....that's what we're here for....!!!!!

[ 10 + x ] - [ 10 - x]   =

2x