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Answer with explanation:</h2>
We are given a semi-ellipse gate whose dimensions are as follows:
Height of 20 feet and a width of 15 feet.
Now, if a truck is loaded then:
Height of truck is: 12 feet and a width of truck is: 16 feet
The truck won't pass through the gate since the width of truck is more than that of the gate.
When the truck is not loaded then:
Height of truck is: 12 feet and a width of truck is: 10 feet
The truck would easily pass through the gate since, the dimensions of truck are less than that of the gate.
The slope:
m = ( y2 - y1 ) / ( x2 - x1 ) = ( 8 2 ) / ( 3 - 2 ) = 6 / 1
m = 6 ( we have the same slope for AB and A`B` )
AB = √[( 3 - 2 )² + ( 8 - 2 )²] = √37
A`B` = 3.5 √37 = 21.29
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.
Answer:
A correlation coefficient of 0.02 indicates that the data are not correlated.
Step-by-step explanation:
0.02 is very close to zero and tells you that there is no linear relationship between the two variables.
By definition, the density is given by:
Where,
m: mass
V: volume
Clearing the mass we have:
The volume is given by:
Then, we have the following conversion:
Applying the conversion we have:
On the other hand we have the following conversions:
Applying the conversions for the density we have:
Then, the mass of the water is:
Answer:
1190 kilgrams of water are required to fill the waterbed
