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Excellent, EW!!!

Don't know about this, SydSu.....I haven't ever seen this, but maybe someone else knows!!!

First one (-8, -6) is correct

Note that (-2, 4)  is the other interval

Second one....the maximum is the "highest"  y value on the graph

This is  y = 4

Third one

Excellent....!!!

Fourth one....a function is constant where it is parallel to the x axis

Note this is ( -6, 0 )

Lastly

Excellent !!!!

\(c = \lambda \nu = (0.3m)(100s^{-1}) = 30\dfrac m s\)

just to add to this it is 7 too

x      f(x)

2      39

3     125

4      287

5     549

6     935

7    1469

The numbers above is the table it's just not in a proper table chart. 

I assume that you probably want to know the height of the balloon???

If so...call the ground distance from the balloon to the soccer field on the right side = x

And on the other side  ....let the grouhd distance to he football field = 4 - x

So we have that

tan  (20° 15') =  height / x

Note that 15' = (15/60)° = (1/4)° = .25°

So

tan (20.25°) = height / x

x tan (20.25) = height

And on the other side [ 30' = .5 degrees ]

tan ( 62.5°) = height / (4 - x)

(4 - x) tan (62.5) = height

Set the heighs equal

(4 - x) tan (62.5) = xt an(20.25)

4tan(62.5)  - x tan(62.5) = x tan (20.25)

4tan(62.5) =  x [ tan (20.25  + tan (62.5) ]

x =   4tan (62.5)  [ tan(20.25) + tan (62.5) ]   ≈ 3.36 miles

So...the height is

(3.36)tan(20.25) = height ≈  1.24 miles

g(x)=(2/3)x(x+8)

In this form the x intercepts are easy to find...these are just the roots

So (2/3) x (x - 8 ) = 0      multiply through by 3/2

x ( x - 8) = 0

x = 0     is a root = x intercept

And

x - 8 = 0

x = 8     is a root = x intercept

This is a parabola....The axis of symmetry is vertical..this is  just the average of the roots 

So...the axis of symmetry  is

x = (0 + 8) / 2  

x = 8 /2

x = 4  =  axis of symmetry

Second part

The total displacement, s,  is the green area

Notice that the total  shaded area of the bottom  rectangle is   u* t

And the area of the top rectange  is (v - u)* t

But only half of this rectangle is shaded...so....the shaded area in the top rectangle is  (1/2)(v - u) * t

So.....the displacement is

u * t + (1/2) ( v - u) *t  =

u * t +  (1/2)v*t  - (1/2)u*t =

1/2 v* t   + 1/2 u*t =

(1/2) ( u + v) * t    =   s

The slope of the line passing through  (0, 5)  and (-4, 8) is given by

[ 8 -  5 ] / [ -4 - 0 ]  =   3/-4  = -3/4

A line parallel to this has the same slope so we have

y = (-3/4) ( x - 1) + 2       simplify

y = (-3/4)x + 3/4 + 2

y = (-3/4)x + 3/4 + 8/4

y = (-3/4)x + 11/4

The line that passes through (0,5) and (-4,8) has the slope (y_2-y₁)/(x_2-x₁) = (8-5)/(-4-0) = 3/-4 = -3/4

y = mx + b, plug in the point (1,2):

2 = (-3/4)(1) + b

2 = -3/4 + b

b = 2.75

y = (-3/4)x + 2.75

Again....the hard part is selecting the correct graph

f(x) is a parabla.....it is the same on both graphs

g(x) = 2^x

When x = 0, 2^0 = 1

So....the point (0, 1) is on g(x)

So....the top graph is correct

Note that the intersection points (solutions) are

x = 0     and x  = 2

The ladder forms the hypotenuse of a right triangle

We know an angle and we are looking for the adjacent side to this angle

So....the cosine =  adjacent / hypotenuse

So we have

cos (72°) =  adj / 20      multiply both sides by 20

20 cos (72°) = adj   ≈ 6.18 ft  = 6.2 ft     from the building base

The hard part here is selecting the correct graph

f(x) is the parabola  ....it is the same in both graphs

g(x)   =    sqrt (x) - 1

Note that when x = 0, y = -1

So.... (0, -1) is on the graph of g(x)

So.... the bottom graph is correct

The intersection  occurs at x = 4....so....this is the solution

Just look at the columns where  f(x) = g(x)

Notice these are      

3      3        and 

6     6

This means that  when x = 1,  f(x) = g(x)   

And when x = 11,  f(x) = g(x)

So.....the x values that make these functions equal  are  the solutions  =

1  and 11

thank you

I believe this is correct

P(x > 15 )  =  

0

P ( 2 < x < 5 )

Thanks Tertre but you put the powers for the first brackets in the wrong place.

It is just a careless error but it could be confusing to the asker.

59 miles /1 hour  x    5280 ft / 1 mile   x     1 hour /60 min    x   1m / 60 sec  =  

[ 59 * 5280 ] / [ 60 * 60 ]   =  86.5 ft/ sec  = 87 ft / sec

BTW....here's an easier formula to use to convert to ft /sec

88 ft /sec = 60 mph

So

59  x   88 /60  =   86.5 ft/sec

y= 8 cot(nΘ)

Using the chain rule

y '  =   -8csc^2(nΘ) * n    =   -8n csc^2(nΘ)