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2 years ago

Eliminate the parameter. X=t^2+1, y=t^2-1

Mathematics

1 answer:

Kaylis [27]2 years ago

6 0

Solve for t

by taking the square root of both sides of the equation.

y=)(√ x-1,-√ x-1)2-1

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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 923.558 m²

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, $A_{req}$ ≈ 923.558 m²

Learn more about figures circumscribed by a circle here:

brainly.com/question/16478185

6 0

2 years ago

Is this right, be fr please

larisa86 [58]

Answer:

1. yes

2.yes

Step-by-step explanation: you did the math right good

8 0

3 years ago

Read 2 more answers

Convert Зcis 180° to rectangular form. А. -3 в. -3i с. з D. Зі.

Sunny_sXe [5.5K]

Answer:

-3

Step-by-step explanation:

$3 cis(180^\circ)$ means $3(\cos(180^\circ)+i \sin(180^\circ))$

What is the $x$ -coordinate value that corresponds to $\theta=180^\circ$ . That value is -1.

What is the $y$ -coordinate value that corresponds to $\theta=180^\circ$ . That value is 0.

So this implies $\cos(180^\circ)=-1 \text{ and } \sin(180^\circ)=0$ .

$3 cis(180^\circ)$

$3(\cos(180^\circ)+i \sin(180^\circ))$

$3(-1+i (0))$

$3(-1+0)$

$3(-1)$

$-3$

5 0

3 years ago

Graph the linear equation. Find the three points that solve the equation then plot on the graph. -y=-x+1

Vinil7 [7]

Answer:

Step-by-step explanation:

The first step will be to make y the subject of the formula, by multiplying both sides of the equation by -1.

y = x - 1

This is simply the equation of a line with a slope of 1 and y-intercept (0,-1)

To determine the three points that solve the equation, we can let x be;

0, 1, 2

When x =0, y = 0-1 = -1

When x = 1, y = 1-1 = 0

When x = 2, y = 2 - 1 = 1

Therefore, we have the following three sets of points that can be used to graph the given linear equation;

(0, -1)

(1, 0)

(2, 1)

Find the attached for the graph

3 0

3 years ago

How do you write 6.0 as a percentage?

FrozenT [24]

Im pretty sure that it would be 600%. If it was 600% that would be 600 over 100 which would be 6

6 0

3 years ago