Is 5/8 a real number?

Find the center and the radius of the circle with the equation:

nekit [7.7K]

Answer:

$(x+1)^2 + (y-1)^2 = 16$

And the general formula for a circle is given by this expression:

$(x-h)^2 +(y-k)^2 = r^2$

With the center (h,k) and the radius r. If we compare this general expression with the formula that we obtain in (1) we see that :

$h = -1, k =1 , r =4$

So then the best solution for this cae would be:

b. center: (-1,1)

radius =4

Step-by-step explanation:

For this case we have the following equation given:

$x^2 +2x + y^2 -2y -14=0$

And we can complete the squares for this case like this:

$x^2 +2x +(2/2)^2 +y^2 -2y +(2/2)^2 =14 +1+1$

$(x^2 +2x +1) +(y^2 -2y +1) =16$

Now we can rewrite the last expression like this:

$(x+1)^2 + (y-1)^2 = 16$

And the general formula for a circle is given by this expression:

$(x-h)^2 +(y-k)^2 = r^2$

With the center (h,k) and the radius r. If we compare this general expression with the formula that we obtain in (1) we see that :

$h = -1, k =1 , r =4$

So then the best solution for this cae would be:

b. center: (-1,1)

radius =4

5 0

3 years ago

The breaking strengths of cables produced by a certain manufacturer have a mean, , of pounds, and a standard deviation of pounds

olchik [2.2K]

The question is incomplete. The complete question is :

The breaking strengths of cables produced by a certain manufacturer have a mean of 1900 pounds, and a standard deviation of 65 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 150 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1902 pounds. Assume that the population is normally distributed. Can we support, at the 0.01 level of significance, the claim that the mean breaking strength has increased?

Solution :

Given data :

Mean, μ = 1900

Standard deviation, σ = 65

Sample size, n = 150

Sample mean, $\overline x$ = 1902