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sergey [27]
3 years ago
5

Consider a circle whose equation is x2 + y2 + 4x – 6y – 36 = 0. Which statements are true? Check all that apply. To begin conver

ting the equation to standard form, subtract 36 from both sides. To complete the square for the x terms, add 4 to both sides. The center of the circle is at (–2, 3). The center of the circle is at (4, –6). The radius of the circle is 6 units. The radius of the circle is 49 units.
Mathematics
1 answer:
umka21 [38]3 years ago
5 0

Answer:

1) False, to begin converting the equation to standard form, each side must be added by 36. 2) True, to complete the square for the x terms, add 4 to both sides, 3) True, the center of the circle is at (-2, 3), 4) False, the center of the circle is at (-2, 3), 5) False, the radius of the circle is 7 units, 6) False, the radius of the circle is 7 units.

Step-by-step explanation:

Let prove the validity of each choice:

1) To begin converting the equation to standard form, subtract 36 from both sides:

Let consider the following formula and perform the following algebraic operations:

(i) x^{2} + y^{2} + 4\cdot x - 6\cdot y  - 36 = 0 Given

(ii) x^{2} + 4\cdot x + y^{2} - 6\cdot y - 36 = 0 Commutative Property

(iii) (x^{2} + 4\cdot x + 4) - 4 + (y^{2} - 6\cdot y + 9) - 9 -36 = 0 Modulative/Associative Property/Additive Inverse Existence

(iv) (x+ 2)^{2} - 4 + (y - 3)^{2} - 9 - 36 = 0  Perfect Trinomial Square

(v) (x+2)^{2} +(y-3)^{2} = 4 + 9 + 36 Commutative Property/Compatibility with Addition/Additive Inverse Existence/Modulative Property

(vi) (x+2)^{2} + (y-3)^{2} = 49 Definition of Addition/Result

False, to begin converting the equation to standard form, each side must be added by 36.

2) True, step (iii) on exercise 1) indicates that both side must be added by 4.

3) The general equation for a circle centered at (h, k) is of the form:

(x-h)^{2}+ (y-k)^{2} = r^{2}

Where r is the radius of the circle.

By direct comparison, it is evident that circle is centered at (-2,3).

True, step (vi) on exercise 1) indicates that center of the circle is at (-2, 3).

4) False, step (vi) on exercise 1) indicates that the center of the circle is at (-2, 3), not in (4, -6).

5) After comparing both formulas, it is evident that radius of the circle is 7 units.

False, the radius of the circle is 7 units.

6) After comparing both formulas, it is evident that radius of the circle is 7 units.

False, the radius of the circle is 7 units.

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Answer:

The distance you are from the base of plateau = 99.97\ m\approx 100\ m

Step-by-step explanation:

Given:

Height of plateau = 70 m

Angle of elevation to the top of plateau = 35°

To find the distance you are from the base of plateau.

We will construct a triangle ABC to model the given situation. The triangle would be a right triangle for which we know an angle and its opposite side. We need to find the adjacent side of the triangle.

We will apply trigonometric ratio to find the adjacent side.

\tan\theta=\frac{Opposite\ Side}{Adjacent\ Side}

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Plugging in the values from the triangle.

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Dividing both sides by \tan 35\°

\frac{AC\times \tan 35\°}{\tan 35\°} =\frac{70}{\tan 35\°}

∴ AC=99.97\ m\approx 100\ m

The distance you are from the base of plateau = 99.97\ m\approx 100\ m

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