Answer:
(x - 3)² + (y - 5)² = 16
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r the radius
given (h, k ) = (3, 5 ) we require to find r
r is the distance from the centre to a point on the circle
given x = - 1 is a tangent the r is the distance between the x- coordinates
r = | 3 - (- 1) | = | 3 + 1 | = | 4 | = 4
then equation of circle is
(x - 3)² + (y - 5)² = 4² , that is
(x - 3)² + (y - 5)² = 16
A notation for representing an interval as a pair of numbers. The numbers are the endpoints of the interval. Parentheses and/or brackets are used to show whether the endpoints are excluded or included.
For example, [3, 8) is the interval of real numbers between 3 and 8, including 3 and excluding 8.
Answer:
x=1
Explain:
y=2x^2−4x+1
dy/dx=4x-4
The line of symmetry will be where the curve turns (due to the nature of the
x^2 graph.
This is also when the gradient of the curve is 0.
Therefore, let
dy/dx=0
This forms an equation such that:
4x−4=0
solve for x,
x=1
and line of symmetry falls on the line
x=1
Answer:
The null and alternative hypotheses are:
Under the null hypothesis, the test statistic is:
Where:
is the sample mean
is the sample standard deviation
is the sample size
Now, the right tailed t critical value at 0.05 significance level for df = n-1 = 10-1 = 9 is:
Since the t statistic is less than the t critical value at 0.05 significance level, therefore,we fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim that the average phone bill has increased.
