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4 years ago

HELP WITH THIS QUESTION ASAP!!

Mathematics

1 answer:

vitfil [10]4 years ago

6 0

Answer:

The answer to your question is: the second option

a) f(0) = 4

b) f(1/2) = 17/4

c) f(-1) = 5

Step-by-step explanation:

f(x) = x² + 4

a) f(0)

f(0) = (0)² + 4 = 0 + 4 = 4

b) f(1/2)

f(1/2) = (1/2)² + 4

f(1/2) = 1/4 + 4

f (1/2) = (1 + 16) / 4 = 17/4

c) f(-1) = (-1)² + 4

f(-1) = 1 + 4

f(-1) = 5

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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 <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

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Citrus2011 [14]

The answer is -15 yayaya

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3 years ago

in the actual room, the distance between the front and back walls is 8 feet. what is the actual length of the front wall, in fee

Bogdan [553]

Answer:

8 feet

Step-by-step explanation:

it actually will be 8 feet

3 0

3 years ago

Which statements are correct interpretations of this graph?

kupik [55]

Answer:

B. 3 pages are edited every five minutes

D. 6/10 of a page is edited per minute

Step by step:

Three pages are done at an interval of five minutes.

Six tenths of a page is done every minute

0.6 * 5 = 3 per five minutes

The other statements are false.

12/3 = 4, four done every minute, really?

5 pages are edited every three minutes.

This would disprove statement B.

And does not align with the graph.

Hope this helps.

7 0

3 years ago

S=n(a1+an)/2 gives the partial sum of an arithmetic sequence. What is the formula solved for an?

Veseljchak [2.6K]

S = n(a1 + an)/2
2S = n(a1 + an)
2S = na1 + nan
nan = 2S - na1
an = (2S - n a1)/n

6 0

3 years ago

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