Answer:
y = 1x - 3
Step-by-step explanation:
Note that the given line has slope +1.
Any line parallel to this line must also have slope +1.
Apply the slope-intercept form y = mx + b:
Inserting -3 for y, 0 for x and 1 for m, we get the y-intercept
-3 = 1(0) + b, which tells us that b = -3 and that the desired equation is
y = 1x - 3
Hope this helps you. Thank you....
<h3>
Answer:</h3>
- x-intercept: 82.75
- y-intercept: -2.15
<h3>
Step-by-step explanation:</h3>
To find the x-intercept, set y=0 and solve.
... 0 = log(12x +7) -3
... 3 = log(12x +7) . . . . add 3
... 1000 = 12x +7 . . . . take the antilog. (10^3 = 1000)
... 993 = 12x . . . . . . . .subtract 7
... 82.75 = x . . . . . . . . divide by 12
To find the y-intercept, set x=0 and solve.
... y = log(12·0 +7) -3
... y = log(7) -3 . . . . . . simplify
... y ≈ 0.85 -3 = -2.15 . . . . use a calculator for the log function
Lim[x.sin(4π/x)] when x →∞. To apply the Hospital rule we need a fraction:
lim[x.sin(4π/x)] could be written:
lim [sin(4π/x)] / (1/x) . Now let's find the derivative of the numerator and the denominator:
Numerator = sin(4π/x) → (Numerator)' = cos(4π/x).(-4π/x²) [Chaine rule
(sinu)' = cosu. u'] So derivative of Numerator = cos(4π/x).(-4π/x²)
Denominator = 1/x → Numerator derivative = -1/x²
Now : (numerator)'/(denominator)' = cos(4π/x).(-4π/x²) / -1/x²
Simplify by x² : → cos(4π/x).(-4π) / -1
OR cos(4π/x).(4π) . When x→∞ , 4π/x → 0 and cos(0) = 1, then:
lim[x.sin(4π/x)] when x →∞. is 4π