Answer:
<h3><u>Part (a)</u></h3>
<u />
<u>Equation of a circle</u>
where:
- (a, b) is the center
- r is the radius
Given equation:
Comparing the given equation with the general equation of a circle, the given equation is a <u>circle</u> with:
- center = (0, 0)
- radius =
To draw the circle, place the point of a compass on the origin. Make the width of the compass 2.5 units, then draw a circle about the origin.
<h3><u>Part (b)</u></h3>
Given equation:
Rearrange the given equation to make y the subject:
Find two points on the line:
Plot the found points and draw a straight line through them.
The <u>points of intersection</u> of the circle and the straight line are the solutions to the equation.
To solve this algebraically, substitute into the equation of the circle to create a quadratic:
Now use the quadratic formula to solve for x:
To find the coordinates of the points of intersection, substitute the found values of x into
Therefore, the two points of intersection are:
Or as decimals to 2 d.p.:
(2.35, -0.85) and (-0.85, 2.35)
Answer:
The distance would be sqrt(29) or 5.39
Step-by-step explanation:
You would use the formula sqrt(x[2]-x[1])^2+(y[2]y[1])^2)
Answer:
m∠7 = 142°
Step-by-step explanation:
Note that a straight line's degree measurement = 180°
Note that the angle directly next to (to the left of) m∠7 has a measurement of 38°. Subtract 38 from 180:
180 - 38 = 142
m∠7 = 142°
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