All categories

3 years ago

choose the standard form of the equation of the circle with radius 5 √ 3 centered at( -6, 2) please help

Mathematics

1 answer:

Ilia_Sergeevich [38]3 years ago

8 0

Answer:

(x + 6)² + (y - 2)² = 75

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (- 6, 2) and r = 5 $\sqrt{3}$ , hence

(x - (- 6))² + (y - 2)² = (5 $\sqrt{3}$ )², that is

(x + 6)² + (y - 2)² = 75

You might be interested in

There are two exterior angles at each vertex of a triangle, and these angle measures always add to 180°.

Annette [7]

I think it has to be true

4 0

2 years ago

Ella has $115. She wants to purchase a cell phone for $53 and spend the rest on music. Each music album costs $9. Write and solv

lana [24]

53 + 9x < 115
THE LESS THAN SYMBOL SHOULD HAVE A LINE UNDER IT!

3 0

3 years ago

A garden is shaped in the form of a regular heptagon (seven-sided), MNSRQPO. A circle with center T and radius 25m circumscribes

Alenkinab [10]

The relationship between the sides MN, MS, and MQ in the given regular heptagon is $\dfrac{1}{MN} = \dfrac{1}{MS} + \dfrac{1}{MQ}$

The area to be planted with flowers is approximately <u>923.558 m²</u>

The reason the above value is correct is as follows;

The known parameters of the garden are;

The radius of the circle that circumscribes the heptagon, r = 25 m

The area left for the children playground = ΔMSQ

Required;

The area of the garden planted with flowers

Solution:

The area of an heptagon, is;

$A = \dfrac{7}{4} \cdot a^2 \cdot cot \left (\dfrac{180 ^{\circ}}{7} \right )$

The interior angle of an heptagon = 128.571°

The length of a side, S, is given as follows;

$\dfrac{s}{sin(180 - 128.571)} = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)}$

$s = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)} \times sin(180 - 128.571) \approx 21.69$

$The \ apothem \ a = 25 \times sin \left ( \dfrac{128.571}{2} \right) \approx 22.52$

The area of the heptagon MNSRQPO is therefore;

$A = \dfrac{7}{4} \times 22.52^2 \times cot \left (\dfrac{180 ^{\circ}}{7} \right ) \approx 1,842.94$

$MS = \sqrt{(21.69^2 + 21.69^2 - 2 \times 21.69 \times21.69\times cos(128.571^{\circ})) \approx 43.08$

By sine rule, we have

$\dfrac{21.69}{sin(\angle NSM)} = \dfrac{43.08}{sin(128.571 ^{\circ})}$

$sin(\angle NSM) =\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ})$

$\angle NSM = arcsin \left(\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ}) \right) \approx 23.18^{\circ}$

∠MSQ = 128.571 - 2*23.18 = 82.211

The area of triangle, MSQ, is given as follows;

$Area \ of \Delta MSQ = \dfrac{1}{2} \times 43.08^2 \times sin(82.211^{\circ}) \approx 919.382^{\circ}$

The area of the of the garden plated with flowers, $A_{req}$ , is given as follows;

$A_{req}$ = Area of heptagon MNSRQPO - Area of triangle ΔMSQ

Therefore;

$A_{req}$ = 1,842.94 - 919.382 ≈ 923.558

The area of the of the garden plated with flowers, $A_{req}$ ≈ <u>923.558 m²</u>

Learn more about figures circumscribed by a circle here:

brainly.com/question/16478185

6 0

3 years ago

Help I can’t figure it out.

polet [3.4K]

The discount price would be $21.98

The final price would be $124.56

yw, mwah

7 0

3 years ago

What is the proportionality of 4 and 1.50?

Llana [10]

Answer:

y = 0.375x

Step-by-step explanation:

Let there are two variables, one independent variable x and another dependent variable y which are in proportionality relation.

So, y ∝ x

⇒ y = kx ........... (1) {Where k is the proportionality constant}

Let us assume that the given values of 4 and 1.50 are values of x and y respectively.

Hence, from equation (1) we get, 1.5 = 4k

⇒ k = 0.375

So, the proportionality equation is y = 0.375x (Answer)

5 0

3 years ago

choose the standard form of the equation of the circle with radius 5 √ 3 centered at( -6, 2) please help ​

choose the standard form of the equation of the circle with radius 5 √ 3 centered at( -6, 2) please help