Answer:
k = 11.
Step-by-step explanation:
y = x^2 - 5x + k
dy/dx = 2x - 5 = the slope of the tangent to the curve
The slope of the normal = -1/(2x - 5)
The line 3y + x =25 is normal to the curve so finding its slope:
3y = 25 - x
y = -1/3 x + 25/3 <------- Slope is -1/3
So at the point of intersection with the curve, if the line is normal to the curve:
-1/3 = -1 / (2x - 5)
2x - 5 = 3 giving x = 4.
Substituting for x in y = x^2 - 5x + k:
When x = 4, y = (4)^2 - 5*4 + k
y = 16 - 20 + k
so y = k - 4.
From the equation y = -1/3 x + 25/3, at x = 4
y = (-1/3)*4 + 25/3 = 21/3 = 7.
So y = k - 4 = 7
k = 7 + 4 = 11.
Answer:
-34.5≥ x
Step-by-step explanation:
- Simply because the values start from -34.5 and then decrease
For this on you need to set up two equations
x + y = 155 total number of packages
3x+8y=815 total weight
Then multiply both sides of the first equation by 3: 3x +3y = 465
Then combine the two equations by subtracting the first one from the second one which gets you 5y=350 so y = 70 so we have 70 packages weighting 8 pounds.
