Answer:
y = 2x − 1
Step-by-step explanation:
By eliminating the parameter, first solve for t:
x = 4 + ln(t)
x − 4 = ln(t)
e^(x − 4) = t
Substitute:
y = t² + 6
y = (e^(x − 4))² + 6
y = e^(2x − 8) + 6
Taking derivative using chain rule:
dy/dx = e^(2x − 8) (2)
dy/dx = 2 e^(2x − 8)
Evaluating at x = 4:
dy/dx = 2 e^(8 − 8)
dy/dx = 2
Writing equation of line using point-slope form:
y − 7 = 2 (x − 4)
y = 2x − 1
Now, without eliminating the parameter, take derivative with respect to t:
x = 4 + ln(t)
dx/dt = 1/t
y = t² + 6
dy/dt = 2t
Finding dy/dx:
dy/dx = (dy/dt) / (dx/dt)
dy/dx = (2t) / (1/t)
dy/dx = 2t²
At the point (4, 7), t = 1. Evaluating the derivative:
dy/dx = 2(1)²
dy/dx = 2
Writing equation of line using point-slope form:
y − 7 = 2 (x − 4)
y = 2x − 1
Changing g(x) to this form: a(x-h) + k, we have:
g(x) = 4 (x+3)^2 - 6
Comparing this to the original equation, f(x) = x^2, we have the following transformations:
The graph is widened.
The graph is shifted left 3 units.
Answer:
14
Step-by-step explanation:
73 - 59=14
Answer:
D. 62.8 in.
Step-by-step explanation:
<u>Given:</u>
C=?
D=r*2=10*2=20<u><em>(r=radius which in this case is 10. Multiply by 2 to get diameter)</em></u>
π=3.14
<u>Explanation:</u>
C=(3.14)(20)
C=62.8