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3 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]3 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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The area of a circle is 80.86cm2. Find the length of the radius rounded to 2 DP.

weeeeeb [17]

Answer:

Solution given:

The area of a circle =80.86cm²

we have:

The area of a circle =πr²

substituting value of area of circle we get

80.86cm=3.14*r²

dividing both side by 3.14

80.86/3.14=3.14*r²/3.14

25.75=r²

doing square root on both side

$\sqrt{25.75}=\sqrt{r²}$

r=5.07cm

The length of radius is 5.07cm

5 0

2 years ago

A team of scientists is traveling by boat to study a pod, or group, of dolphins. The equation y = 0.2x can be used to find the d

Alenkinab [10]

Answer:

42 minutes.

Step-by-step explanation:

We know that:

y = 0.2*x

is the equation that that defines the distance, in miles, that the boat travels in x minutes.

We know that the dolphins are at 8.4 miles from the boat.

Then when we have y = 8.4, this will mean that the boat reached the dolphins.

Then we need to solve the equation:

y = 8.4 = 0.2*x

for x

To do that, we just need to isolate x in one side of the equation, so we can just divide both sides by 0.2 to get:

8.4/0.2 = (0.2*x)/0.2

42 = x

And x is time in minutes, thus, the boat needs to travel for 42 minutes to reach the dolphins.

6 0

3 years ago

A(3,4) and B(-3,2) are pointd on a coordinate plane. find the coordinate of a points C on the x axis such that AC=BC

mr Goodwill [35]

Answer:

Step-by-step explanation:

Here's the game plan. In order to find a point on the x-axis that makes AC = BC, we need to find the midpoint of AB and the slope of AB. From there, we can find the equation of the line that is perpendicular to AB so we can then fit a 0 in for y and solve for x. This final coordinate will be the answer you're looking for. First and foremost, the midpoint of AB:

and

Now for the slope of AB:

and

So if the slope of AB is 1/3, then the slope of a line perpendicular to that line is -3. What we are finding now is the equation of the line perpendicular to AB and going through (0, 3):

and filling in:

y - 3 = -3(x - 0) and

y - 3 = -3x + 0 and

y - 3 = -3x so

y = -3x + 3. Filling in a 0 for y will give us the coordinate we want for the x-intercept (the point where this line goes through the x-axis):

0 = -3x + 3 and

-3 = -3x so

x = 1

The coordinate on the x-axis such that AC = BC is (1, 0)

7 0

2 years ago

If 24 apples represents 30% of her apple supply. How many total apples does Jasmine have?

Colt1911 [192]

Answer:

She has 80 apples in all.

Step-by-step explanation:

24=30%

(24÷3)=(30÷3)%

8=10%

(8×10)=(10×10)%

80=100%

7 0

3 years ago

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What is the 99 times x=4

Musya8 [376]

The answer i x=4/99 (fraction form )

4 0

3 years ago

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