Answer:
Step-by-step explanation:
In order to find the equation of the line tangent to that circle, we have to find the derivative by implicit differentiation which will give us the slope formula of that tangent line. Let's begin by expanding through the parenthesis to get the standard form of the circle:
Moving the 9 to the other side since the derivative of a constant is 0 gives us
By implicit differentation, the derivative of that function is
To find the derivative, we have to solve for dy/dx:
Factor out the dy/dx to get:
Now divide to get your slope formula (first derivative):
Now we can sub in the x and y values from the coodinate to get the slope of that tangent line:
So now that have the slope, we can use the point-slope form of a line to write the equation of the tangent line. The point-slop form of a line is:
y-y₁ = m(x-x₁)
Filling in we get:
y - 0 = 5/3(x - 5) so the equation of the tangent line is:
Good luck in your calculus class!
√-16
Step-by-step explanation:
C. 4i
I hope it will be help you...
Answer:
imaginary number and a real number
Answer:
x + 14 = 2(x + 6)
x = 2
Step-by-step explanation:
Let
Algebra book age = x
Chemistry book age = x + 8
In 6 years time
Chemistry book age = x + 8 + 6
= x + 14
Algebra book age = x + 6
the chemistry book will be twice as old as the Algebra book.
x + 14 = 2(x+6)
x + 14 = 2x + 12
x - 2x = 12 - 14
- x = - 2
Divide both sides by -1
x = 2
Check:
Chemistry book age = x + 14
= 2 + 14
= 16
Algebra book age = x + 6
= 2 + 6
= 8
Answer:
At least 68% of observations lie between 22 and 26 months.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 24
Standard deviation = 2
22 = 24 - 2
22 is one standard deviation below the mean
26 = 24 + 2
26 is one standard deviation above the mean.
So, by the empirical rule, at least 68% of observations lie between 22 and 26 months.