2^t =38
take the log of each side
log ( 2^t) = log (38)
the exponent gets multiplies
t log (2) = log (38)
divide by log 2
t = log(38)/log (2)
t≈5.2479
Consider two pairs of coordinates (x₁, y₁) and (x₂, y₂), the mid-point of these coordinates are
![( \frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )](https://tex.z-dn.net/?f=%28%20%5Cfrac%7Bx_1%2Bx_2%7D%7B2%7D%20%2C%20%5Cfrac%7By_1%2By_2%7D%7B2%7D%20%29%20)
We have midpoint (-1, 7i) and one pair of coordinate (3, 8i)
The other pair of coordinate would be given by
![( \frac{x_1+3}{2}= -1, \frac{y_1+8}{2} =7)](https://tex.z-dn.net/?f=%28%20%5Cfrac%7Bx_1%2B3%7D%7B2%7D%3D%20-1%2C%20%5Cfrac%7By_1%2B8%7D%7B2%7D%20%3D7%29)
The value of x is (2 × -1) - 3 = -2 - 3 = -5
The value of y is (2 × 7) - 8 = 14 - 8 = 6
The value of x represents the real part
The value of y represents the imaginary part
The other coordinate is (-5, 6i)
Y α x²
y = kx²
64 = k*4²
64 = k*4*4
64 = 16k
64/16 = k
4 = k
k = 4
y = kx²
y = 4*6²
y = 4*6*6
y = 144
Answer:
The graph of the system in the attached figure
Step-by-step explanation:
we have
isolate the variable y
----> equation A
This is the equation of a vertical parabola open down (because the leading coefficient is negative)
The vertex represent a maximum
the vertex is the point (0,2)
---> equation B
This is the equation of a circle centered at (0,0) with radius 3 units
The solution of the system of equations is the intersection points both graphs
using a graphing tool
The solutions are the points (-2.05,-2.19) and (2.05,-2.19)
see the attached figure
Answer:
a
Step-by-step explanation:
something are very complex