The line y = x + 3 has slope 1, so we look for points on the curve where the tangent line, whose slope is dy/dx, is equal to 1.
y² = x
Take the derivative of both sides with respect to x, assuming y = y(x) :
2y dy/dx = 1
dy/dx = 1/(2y)
Solve for y when dy/dx = 1 :
1 = 1/(2y)
2y = 1
y = 1/2
When y = 1/2, we have x = y² = (1/2)² = 1/4. However, for the given line, when y = 1/2, we have x = y - 3 = 1/2 - 3 = -5/2.
This means the line y = x + 3 is not a tangent to the curve y² = x. In fact, the line never even touches y² = x :
x = y² ⇒ y = y² + 3 ⇒ y² - y + 3 = 0
has no real solution for y.
Answer:
117600
Step-by-step explanation:
50 x 49 x 48 = 117,600 ways
You have 50 possible for 1st, 49 for 2nd, 48 for 3rd
or
Permutations 50P3 = 117,600
X is the amount of weeks.
Equation: 425+25x=875-15x
Solve for x:
25x+15x=875-425
40x=450
x=11.25
The answer is 11.25 weeks.
8=12-8x
-4=8x
-4÷8=8x÷8
-0.5=x
