Does this graph represent a function?
1 answer:
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Answer:
a). Center of the circle = (-2, 5)
b). Equation of the line ⇒ y =
Step-by-step explanation:
Equation of the circle is,
x² + 4x + y²- 10y + 20 = 30
a). [x² + 2(2)x + 4 - 4] + [y²- 2(5)y + 25] - 25 + 20 = 30
[x² + 2(2)x + 4] - 4 + [y² - 2(5)y + 25] - 25 + 20 = 30
(x + 2)² + (y - 5)²- 29 + 20 = 30
(x + 2)² + (y - 5)²- 9 = 30
(x + 2)² + (y - 5)² = 39
By comparing this equation with the standard equation of a circle,
Center of the circle is (-2, 5).
b). A point (2, 10) lies on this circle.
Slope of the line joining this point to the center (-2, 5),
=
=
Let the slope of the tangent which is perpendicular to this line is ''
Then by the property of perpendicular lines,
Now the equation of the line passing though (2, 10) having slope
y - y' =
y - 10 =
y - 10 =
y =
y =
Therefore, equation of the line will be, y =
Given:
Kelly purchased 5 containers of ice cream for a party.
Each container holds 8 cups of ice cream.
Her brother ate 2 cups of ice cream.
One serving of ice cream = 2/3 of a cup.
To find:
Number of servings of ice cream will be left for the party?
Solution:
We have,
1 container = 8 cups of ice cream
5 containers = 5×8 = 40 cups of ice cream
Her brother ate 2 cups of ice cream. So, remaining cups of ice cream is
cups
Now,
of a cup = 1 serving
1 cup = serving
38 cup = serving
= serving
= 57 serving
Therefore, 57 servings of ice cream will be left for the party.