<span>The standard dice has opposite sides which sum is always 7. So, if you see the side of a dice with one point (number 1), then the opposite side is with 6 points on it (7-1=6).
If if you see the side of a dice with 2 points (number 2), then the opposite side is with 5 points on it (7-2=5).
if you see the side of a dice with three points (number 3), then the opposite side is with 4 points on it (7-3=4).
if you see the side of a dice with four points (number 4), then the opposite side is with 3 points on it (7-4=3)...and so on. </span>
From the given function modeling the height of the ball:
f(x)=-0.2x^2+1.4x+7
A] The maximum height of the ball will be given by:
At max height f'(x)=0
from f(x),
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
thus the maximum height would be:
f(3.5)=-0.2(3.5)^2+1.4(3.5)+7
f(3.5)=9.45 ft
b]
How far from where the ball was thrown did this occur:
from (a), we see that at maximum height f'(x)=0
f'(x)=-0.4x+1.4
solving for x we get:
-0.4x=-1.4
x=3.5ft
This implies that it occurred 3.5 ft from where the ball was thrown.
c] How far does the ball travel horizontally?
f(x)=-0.2x^2+1.4x+7
evaluationg the expression when f(x)=0 we get:
0=-0.2x^2+1.4x+7
Using quadratic equation formula:
x=-3.37386 or x=10.3739
We leave out the negative and take the positive answer. Hence the answer 10.3739 ft horizontally.
Before budget change :
Maintenance = 1 - 1/3 - 1/3 - 1/4 = 1/12
After budget change :
Maintenance = 1 - 1/3 - 1/8 - 1/4 = 7/24
Difference in budget for maintenance = 7/24 - 1/12 = 5/12
Well, if 1 mile = 1.6 kilometers and he's traveling at 18mph, then do 18 x 1.6 which = 28.8.
So, this is his current speed in kph
3 x 28.8 = 86.4
They will have traveled 86.4 kilometers
(I haven't worked with this kind of math in a while so correct me if I'm wrong!)
First, you must distribute the negative sign(otherwise considered a negative one). This gives you x - 4x + 7 = 5x - x - 21.
Then, simplify any like terms you can: -3x + 7 = 4x - 21.
Simplify this even further: 28 = 7x
The final answer is x = 4
