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2 years ago

Radius OA of circle O has a slope of 2.5. What is the slope of the line tangent to circle O to point A?

2 answers:

5 0

The tangent at A is perpendicular to OA, so has a slope that is the negative reciprocal of that of the radius: -1/2.5 = -2/5.

Mekhanik [1.2K]2 years ago

4 0

Answer: The required slope of the line tangent to the circle at point A is -0.4.

Step-by-step explanation: Given that the radius OA of a circle with center O has a slope of 2.5.

We are to find the slope of the line tangent to the circle at the point A.

We know that

The radius of a circle at a point on the circumference of a circle is perpendicular to the tangent line at the same point on the circumference of the circle.

Also, the product of the slopes of two perpendicular lines is -1.

So, if m is the slope of the tangent line at the point A, then we must have

$m\times 2.5=-1\\\\\Rightarrow m=-\dfrac{1}{2.5}\\\\\\\Rightarrow m=-\dfrac{10}{25}\\\\\Rightarrow m=-\dfrac{2}{5}\\\\\Rightarrow m=-0.4.$

Thus, the required slope of the line tangent to the circle at point A is -0.4.

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a cone with a radius of 3” has a total area of 24pie square inches. Find the volume of the cone. 12pie, 24 pie or 15 pie

Ratling [72]

Answer:

$12\pi (inches)^{2}$

Step-by-step explanation:

Given:

radius of cone = 3 inch

Total area of cone = $24\pi (inch)^{2}$

Find the volume of the cone?

We know the area of cone = $\pi r(r+s)$ -------(1)

Where r = radius

Ans s = side of the cone

Put the area value in equation 1

$24\pi=\pi r(r+s)$ -------(1)

$\frac{24\pi }{\pi r} =r+s$

$\frac{24}{ r}-r =s$

Put r value in above equation.

$s =\frac{24}{ 3}-3$

$s=8-3$

$s=5$

The side s = 5 inches

We know the side of the cone formula

$s^{2}=r^{2}+ h^{2}$

$h^{2}=s^{2}- r^{2}$

Put r and s value in above equation.

$h^{2}=5^{2}- 3^{2}$

$r^{2} = 25-9$

$r^{2} = 16$

$r = 4$

The volume of cone is

$V = \frac{1}{3} \pi r^{2} h$

Put r and h value in above equation.

$V = \frac{1}{3} \pi (3)^{2}\times 4$

$V = 12\pi (inches)^{2}$

The Volume of the cone is $12\pi (inches)^{2}$

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2 years ago

If your friend Doug is on a balcony and asks you to throw him a donut, how many stories up can he be and you would still feel co

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The building that I would imagine would be 40 stories, about 404 feet tall perhaps. If he were to throw the donut from that distance until the ground, catching it would be impossible. So no, I am not confident in catching the donut all the way there.

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daser333 [38]

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