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2 years ago

Write the following in point-slope form using the given information: Slope: 2 points

Mathematics

1 answer:

SCORPION-xisa [38]2 years ago

8 0

Answer:

$y+5 = \frac{1}{15}(x - 3)}$

Step-by-step explanation:

Given

$m = \frac{1}{15}$ -- Slope

$(x_1,y_1) = (3,-5)$ --- Point

Required

Write an equation in point slope form

The point slope form of an equation is:

$y - y_1 = m(x - x_1)$

Substitute values for y1, x1 and m

$y-(-5) = \frac{1}{15}(x - 3)}$

$y+5 = \frac{1}{15}(x - 3)}$

Hence, the equation in point slope form is:

$y+5 = \frac{1}{15}(x - 3)}$

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A circle has a diameter with endpoints at (6, 5) and (8, 5). Write the equation for the circle.

mario62 [17]

Answer:

$(x-7)^2+(y-5)^2=1$

Step-by-step explanation:

The two things that are required to formulate the equation of the circle is the center coordinate and the radius of the circle!

Center of the circle:

The center of the circle always lies at the midpoint of the endpoints of its diameter: Let's call the endpoints A(6,5) and B(8,5).

Using the midpoint formula we'll get:

$(x_m, y_m) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$(x_m, y_m) = \left(\dfrac{6+8}{2},\dfrac{5+5}{2}\right)$

$(x_m, y_m) = (7,5)$

This is the center coordinate of our circle.

Radius:

The radius of the circle is the distance from the center of the circle to any of the endpoints of the diameter (A or B)

We can use the distance formula:

$r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$r = \sqrt{(x_1-x_m)^2+(y_1-y_m)^2}$

$r = \sqrt{(6-7)^2+(5-5)^2}$

$r = \sqrt{1^2}$

$r = 1$

Equation of the circle:

The equation is written as:

$(x-a)^2+(y-b)^2=r^2$

here, (a,b) are the center points of the circle

in our case this is $(a,b)=(x_m,y_m)=(7,5)$

and r = 1

$(x-7)^2+(y-5)^2=1^2$

$(x-7)^2+(y-5)^2=1$

This is the equation of the circle!

3 0

2 years ago

Heights for women are bell-shaped with a mean of 65 inches and standard deviation of 2.5 inches. If a random sample of 16 women

loris [4]

Answer:

μ= 65 inches; σ= 0.625 inch

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed(bell-shaped) random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .