Answer: x² + y² - 2x - 8y + 13 = 0
Step-by-step explanation:
the equation of the circle is in the form (x - a)² + (y - b)² = r²
where (a,b) is the center of the circle and r is the radius
hence the equation is
(x - 1)² + (y - 4)² = 2²
x²-2x+1+y²-8y+16= 4
x²+ y² -2x- 8y + 17 =4
x² + y² - 2x - 8y = -13
x² + y² - 2x - 8y + 13 = 0
Answers:
1.) <span>the number 0 (for the real numbers)
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2.) a(b+c)= ab + ac or a(b -c) = ab - ac
3.) equation containing more than one variable
4.) the number 1 (for the real numbers)
5.) <span>the reciprocal of a number; if x is a number other than zero, then 1/x is the multiplicative inverse
</span>
Answer:
The answer is below
Step-by-step explanation:
We have the following information:
Number of songs you like = 2
Total number of songs = 12
a) P(you like both of them) = 2/12 x 1/11 = 0.015
This is unusual because the probability of the event is less than 0.05
b) P(you like neither of them) = 10/12 x 9/11 = 0.68
c) P(you like exactly one of them) = 2 x 2/12 x 10/11 = 0.30
d) If a song can be replayed before all 12,
P(you like both of them) = 2/12 x 2/12 =0.027
This is unusual because the probability of the event is less than 0.05
P(you like neither of them) = 9/12 x 9/12 = 0.5625
P(you like exactly one of them) = 2 x 2/12 x 9/12 = 0.25
Answer:
A) Gradient = -3
B) 3y - x = 7
Step-by-step explanation:
The curve has the equation;
y = x³ - 6x² + 9x + 1
We are given the pints it passes through as;
A(2,3) and P(3, 1)
A) to find the gradient, we will find the derivative of the given equation.
Thus;
Gradient = y' = 3x² - 12x + 9
At point A, x = 2. Thus;
Gradient = 3(2²) - 12(2) + 9
Gradient = 12 - 24 + 9
Gradient = -3
B) since the gradient of the tangent = -3, it means the gradient of the normal will be; -1/-3 = 1/3
Thus, equation of the normal to the curve at point A will be;
(y - 3) = ⅓(x - 2)
Multiply both sides by 3 to get;
3y - 9 = x - 2
3y - x = 9 - 2
3y - x = 7
