What is the quotient of the following rational expression? x^3+3x^2-4x+5/x^2-2
1 answer:
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Answer:
(a) f'(1)=-4
(b) y+4x-4=0
Step-by-step explanation:
<u>Tangent Line of a Function</u>
Given f(x) a real differentiable function in x=a, the slope of the tangent line of the function in x=a is given by f'(x=a). Where f' is the first derivative of f.
We are given
The derivative is
(a) The slope of the tangent line at (1,0) is
(b) The equation of the tangent line can be found with the general formula of the line:
Where m is the slope and the point (xo,yo) belongs to the line. We have m=-4, xo=1, yo=0, thus
Or, equivalently
Answer:
The height of the ball after 3 secs of dropping is 16 feet.
Step-by-step explanation:
Given:
height from which the ball is dropped = 160 foot
Time = t seconds
Function h(t)=160-16t^2.
To Find:
High will the ball be after 3 seconds = ?
Solution:
Here the time ‘t’ is already given to us as 3 secs.
We also have the relationship between the height and time given to us in the question.
So, to find the height at which the ball will be 3 secs after dropping we have to insert 3 secs in palce of ‘t’ as follows:
h(3)=160-144
h(3)=16
Therefore, the height of the ball after 3 secs of dropping is 16 feet.
Answer:
It takes <em>10 minutes</em> to the park.
Step-by-step explanation:
Given that:
Time taken = 6 minutes
Distance left to be traveled = 40%
To find:
The equation to represent the distance , that still needs to be traveled after
minutes.
Solution:
As per given statement, distance traveled in 6 minutes = 60%
We can say that:
Distance traveled each minute = = 10%
After 1 minute, distance traveled = 10%
Distance left = 100 - 10 = 90%
After 2 minutes, distance traveled = 20%
Distance left = 100 - 20 = 80%
After minutes, distance traveled = 10
%
Distance left, = (100 - 10
)%
Therefore, the equation is:
Time taken by the bike to reach to the park can be found by putting = 0 (i.e. distance left to be traveled = 0)