Step-by-step explanation:
The volume of a pyramid or cone is:
V = ⅓ Ah
where A is the area of the base and h is the height.
The pyramid has a square base, so:
A = s²
A = (7 cm)²
A = 49 cm²
The height is 14 cm, so the volume is:
V = ⅓ (49 cm²) (14 cm)
V = 686/3 cm³
V ≈ 228.67 cm³
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.
Hello,
Answer D:
the roots are -5,1+4i,1-4i,-4i,4i.
Answer:
x⁴+3x³ -5x +1
Step-by-step explanation:
To multiply this we are going to <u>multiply each term of the binomial by each term of the polynomial.</u>
Now we are going to <u>combine like terms (this means we are going to sum up terms with the same exponent)</u>
Thus, the answer is x⁴+3x³ -5x +1
9,000 or (9×1,000) either one can be the answer
