Word Problem?

Question

Television sets. What does it mean to refer to a 20 inch t.v. set or a 25 inch tv set? such units refer to the diagonal of the screen. A 25 inch t.v. set also has a with of 20 inches. Whats the height? What is the height of a 25 inch t.v.?


If a pro basketball player has a verticle leap of about 20 inches, what is his hang time? Use the hang time fraction v=48T^2
his hang time is? seconds.


solve.
(x+6)(x-9)(x+3)>0
the solution set is{xI }

Answer 1

Based on your description, the height of a 25 inch t.v. is 15 inch.
x^2 = 25^2 - 20^2
x^2 = 625 - 400
x = 15

v=48T^2
20 = 48* T^2
T^2 = 20/48
T = sqrt(5/12)
T = 0.65 seconds

(x+6)(x-9)(x+3) > 0
(x+6)>0
(x+3)>0
(x-9) > 0
so: x > 9
or (x+6) > 0 and (x+3)<0 and (x-9) < 0
so: -6 < x < -3
answer so: x > 9
or (x+6) > 0 and (x+3)<0 and (x-9) < 0
so: -6 < x < -3 or x>9

Answer 2

The first is a 3-4-5 triangle...you have 5x5 for the diagonal, 5x4 for the width... 5x3 is the height.

The second one is just plugging in the values y=20, I'd divide 20/48 and take the square root of it.

Those have been done...

The third one is not solved by setting x+6>0 and solving...
You have four intervals and 3 points to consider
x+6=0, x-9=0, and x+3=0
x=-6. x=9, or x=-3.... you don't have to consider the points because they make the function 0≯0

So the intervals you have to consider are
x<-6, -69
Pick one point in each interval and plug it into (x+6)(x-9)(x+3).
If the point satisfies the condition, i.e., makes the product >0, then the whole interval is in your solution set.

Example. testing -3 (0+6)(0-9)(0+3)= -162 ≯ 0 so that interval IS NOT in your solution set... see how it works?

Answer 3

The Dimension given for a TV is usually the Diagonal distance from corner to corner. Use Pythagoras with the given hypotenuse and width to determine the height.

V=48t^2 V=20
20=48t^2
20/48=t^2
5/12=t^2
t=sqrt(5/12)

a*b*c>0 implies a,b,c are all positive or two are negative and one is positive
for a,b&c to all be positive, x>9
for 1 Positive and 2 negatives, -6 :. solution set is {-69}

Answer 4

From Pythagorus, this is a right-angled triangle with sides 15, 20 and 25.

not sure

-3 > x > -6

or

x > 9

Answer 5

1. Use Phythag thm. width^2+height^2=25^2