Andy will record 6x + 5 bacteria cells, while Samantha will record 2^x + 3 bacteria cells. These will be equal at a time when:
6x + 5 = 2^x + 3
Plotting both of these shows that they are equal when x = 5 and y = 35.
Therefore, the number of bacteria cells will be equal at 35, at t = 5 hours.
I think we can use the identity sin x/2 = sqrt [(1 - cos x) /2]
cos x - sqrt3 sqrt ( 1 - cos x) /sqrt2 = 1
cos x - sqrt(3/2) sqrt(1 - cos x) = 1
sqrt(3/2)(sqrt(1 - cos x) = cos x - 1 Squaring both sides:-
1.5 ( 1 - cos x) = cos^2 x - 2 cos x + 1
cos^2 x - 0.5 cos x - 0.5 = 0
cos x = 1 , -0.5
giving x = 0 , 2pi, 2pi/3, 4pi/3 ( for 0 =< x <= 2pi)
because of thw square roots some of these solutions may be extraneous so we should plug these into the original equations to see if they fit.
The last 2 results dont fit so the answer is x = 0 , 2pi Answer
Midpoint formula: (x1+x2/2 , y1+y2/2)
So, (-1+3/2 , 9+8/2)
-2/2 = -1 17/2 = 8.5
Answer: (-1,8.5)
You could use the substitution method. in this you’ll solve one equation for one variable. we’ll do the first one for y.
add 3x to both sides, so y = 3x + 2
then add that into the other equation for y.
7x - 8(3x +2) = 1
7x- 24x - 16 = 1
-17x - 16 = 1
-17x = 17
x= -1
now that you know what x is, you can find out y with the equation we made earlier. y = 3x+2
y = 3(-1) + 2
y = -3 + 2
y = -1
