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2 years ago

14

GEOMETRY find the angle of PRQ NO LINKS!!

1 answer:

anzhelika [568]2 years ago

4 0

Answer:

55

Step-by-step explanation:

Remark

This is a really good question to know the answer to. <PRQ = 1/2 POQ (the central angle. )

The central angle for this question is 110o. So any angle that has its vertex on the circumference is 1/2 110 = 55. The central angle and the angle on the circumference must be related as they are as this question is. (Both are on the same side of PQ which is not drawn but you can draw it).

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The line l is tangent to the circle with equation x² + y2 = 169 at the point P.

timofeeve [1]

Given:

The equation of a circle is

$x^2+y^2=169$

A tangent line l to the circle touches the circle at point P(12,5).

To find:

The gradient of the line l.

Solution:

Slope formula: If a line passes through two points, then the slope of the line is

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Endpoints of the radius are O(0,0) and P(12,5). So, the slope of radius is

$m_1=\dfrac{5-0}{12-0}$

$m_1=\dfrac{5}{12}$

We know that, the radius of a circle is always perpendicular to the tangent at the point of tangency.

Product of slopes of two perpendicular lines is always -1.

Let the slope of tangent line l is m. Then, the product of slopes of line l and radius is -1.

$m\times m_1=-1$

$m\times \dfrac{5}{12}=-1$

$m=-\dfrac{12}{5}$

Therefore, the gradient or slope of the tangent line l is $-\dfrac{12}{5}$ .

6 0

2 years ago

A manufacturer of matches randomly and independently puts 24 matches in each box of matches produced. The company knows that one

DochEvi [55]

Answer:

There is a 0.36% Chance of 1 or fewer in every 24 matches being flawed.

Step-by-step explanation:

Firstly we need to know what 1/10 of 5 is. It is 0.5.

You then need to multiply 24 by 1.5 to get 36. We then need to divide that by 100 to get a percentage and we end up with 0.36%

Here is an explanation of how to get percentages: https://www.mathsisfun.com/converting-fractions-percents.html

6 0

3 years ago

Multiply 5 yards 18 inches by 3? please show work

lesya692 [45]

Answer:

5 yards = 15 feet = 180 inches

Step-by-step explanation:

180 inches plus 18 inches = 198 inches

198 x 3 = 594 inches

594 inches = 49 feet 6 inches = 16 yards 1 foot 6 inches, or 16 yards 18 inches

7 0

3 years ago

What is the complex conjugate of -3+5i

andrew-mc [135]

Answer:

-5-2i

hope this helps :)

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3 years ago

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What statement about dilation and rotation is true

sergiy2304 [10]

Rotation turns dilation shrinks

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2 years ago