Monique sells lemonade at a lemonade stand. The model she uses to predict future
1 answer:
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Answer: <em>the length of each edge is 0.5 ft.</em>
Step-by-step explanation:
Answer:
The equation is that of ellipse withe angle of rotation 30° ⇒ answer (d)
Step-by-step explanation:
* Lets talk about the general form of the conic equations
- Ax² + Bxy + Cy² +D = 0 (center is the origin)
- A is the coefficient of x² , B is the coefficient of xy
C is the coefficient of y² , D is the numerical term
* Now we will study how to know the type of the graph of this equation
- If A and C have different signs (different values)
∴ The equation is that of an ellipse
- If A and C have different signs (different values)
∴ The equation is on a hyperbola
* Now look at the equation:
13x² + 6√3 xy + 7y² - 16 = 0
∵ A = 13 , B = 6√3 , C = 7 , D = -16
∵ A and C have same sign
∴ The equation is that of an ellipse
* Now lets find the angle of rotation by using the Rule:
- tan(2Ф) = B/(A - C) ⇒ Ф is the angle of rotation
- By using the value of A , B and C
∴ tan(2Ф) = 6√3/(13 - 7) = 6√3/6 = √3
∴ 2Ф =
∴ 2Ф = 60° ⇒ divide both sides by 2
∴ Ф = 30°
∴ The angle of rotation is 30°
∴ The equation is that of ellipse withe angle of rotation 30°
* The graph represent the ellipse
- The purple line represents the angle of rotation
Answer:
Part 1)
Part 2)
Part 3)
Step-by-step explanation:
Part 1) Find the measure of angle ECF
we know that
CF is tangent at point C
so
the radius EC is perpendicular to the tangent CF
therefore
Part 2) Find the measure of angle AKB
we know that
The measure of the interior angle is the semi-sum of the arcs comprising it and its opposite
substitute the values
Part 3) Find the measure of angle ACF
we know that
The inscribed angle is half that of the arc it comprises
substitute the values