Represent any point on the curve by (x, 1-x^2). The distance between (0, 0) and (x, 1-x^2) is
To make this easier, let's minimize the SQUARE of this quantity because when the square root is minimal, its square will be minimal.
So minimize
Find the derivative of L and set it equal to zero.
This gives you
or
You can use the Second Derivative Test to figure out which value(s) produce the MINIMUM distance.
When x = 0, the second derivative is negative, indicating a relative maximum. When
, the second derivative is positive, indicating a relative MINIMUM.
The two points on the curve closest to the origin are
<h3>Answer:</h3>
y = 17x - 4.5x²
height = 16m at 2 sec
total time = 3.77 sec
<h3>Step-by-step explanation:</h3>
Given the initial velocity of rocket = 56ft/sec
We use newton formula
<h3 /><h3>s = ut + 1/2at²</h3><h3>where s = distance</h3>
u = initial velocity
t= time
a = acceleration due to gravity = 9.8m/s²
since the rocket is launched upward, it is against the gravity so a = -9.81.
56 feet = 17.0688 = 17
suppose s = height = y and time = x
y = 17x - 1/2(9.81)x²
or
y = 17x - 4.5x²
b)
as x can not be negative so domain will be from 0 to 3.78
put value of x to find value of y and then plot these on graph
This graphs will be a parabola which opens downward.
c)
at 2 sec, y value is greatest = 16 meters
time for which rocket was in the air = 3.77sec
The diagonal of any square always occurs in a ratio of
relative to the square's sides. That means if
is the side length, then
gives the length of the diagonal. It follows that
.
Then the area of the square is
square inches
Answer:
x <
Step-by-step explanation:
Given
- 4x + 35 > 2 ( subtract 35 from both sides )
- 4x > - 33
Divide both sides by - 4, reversing the symbol as a result of dividing by a negative quantity.
x <
1819 because it makes more sense than the other ones