60 = a * (-30)^2
a = 1/15
So y = (1/15)x^2
abc)
The derivative of this function is 2x/15. This is the slope of a tangent at that point.
If Linda lets go at some point along the parabola with coordinates (t, t^2 / 15), then she will travel along a line that was TANGENT to the parabola at that point.
Since that line has slope 2t/15, we can determine equation of line using point-slope formula:
y = m(x-x0) + y0
y = 2t/15 * (x - t) + (1/15)t^2
Plug in the x-coordinate "t" that was given for any point.
d)
We are looking for some x-coordinate "t" of a point on the parabola that holds the tangent line that passes through the dock at point (30, 30).
So, use our equation for a general tangent picked at point (t, t^2 / 15):
y = 2t/15 * (x - t) + (1/15)t^2
And plug in the condition that it must satisfy x=30, y=30.
30 = 2t/15 * (30 - t) + (1/15)t^2
t = 30 ± 2√15 = 8.79 or 51.21
The larger solution does in fact work for a tangent that passes through the dock, but it's not important for us because she would have to travel in reverse to get to the dock from that point.
So the only solution is she needs to let go x = 8.79 m east and y = 5.15 m north of the vertex.
5700 is 5731 rounded to the nearest hundred
Answer:
is equivalent to 
and 
is equivalent to 
and 
.
The expressions which are equivalent to neither:
and 
Step-by-step explanation:
Given the expressions:
1)
2)
To find:
The expressions equivalent to the given expressions.
or the expressions which are not equivalent to any of the given expressions.
Solution:
First of all, let us solve the brackets from the given expressions.
can be written as (because when we multiply a negative sign with negative, it becomes positive.)
Similarly can be written as (because when we multiply a positive sign with negative, it becomes negative.)
Therefore, the answer is:
is equivalent to and
is equivalent to and .
The expressions which are equivalent to neither:
and
Answer:
Step-by-step explanation: if you are doing subtitution then
Let's solve your system by substitution.
y=4x+14 and y=6x+8
Rewrite equations:
y=4x+14;y=6x+8
Step: Solvey=4x+14for y:
y=4x+14
Step: Substitute4x+14foryiny=6x+8:
y=6x+8
4x+14=6x+8
4x+14+−6x=6x+8+−6x(Add -6x to both sides)
−2x+14=8
−2x+14+−14=8+−14(Add -14 to both sides)
−2x=−6−2x−2=−6−2
(Divide both sides by -2)
x=3
Step: Substitute3forxiny=4x+14:
y=4x+14
y=(4)(3)+14
y=26(Simplify both sides of the equation)
Answer:
x=3 and y=26
Answer:
9^24. and in feet is 19683 ft
Step-by-step explanation:
