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4 years ago

If a circle has a Diameter of 4m and a Radius of 4 units. Then what is Circumference and Area of the circle?

Mathematics

1 answer:

Fiesta28 [93]4 years ago

3 0

Answer & Step-by-step explanation:

$Circumference=d\pi \\Area=r^2\pi$

The diameter of the circle is 8 m and the radius of the circle is 4 units. So, now we have to plug in the numbers so we can find the circumference and the area of the circle.

$Circumference=(8)\pi$

$Circumference=25.12$

So, the circumference of the circle is 25.12 m.

$Area=(4)^2\pi$

$Area=16\pi$

$Area=50.24$

So, the area of the circle is 50.24 units².

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Rewrite with only sin x and cos x.

Annette [7]

Option A

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

Solution:

Given that we have to rewrite with only sin x and cos x

Given is cos 3x

$cos 3x = cos(x + 2x)$

We know that,

$\cos (a+b)=\cos a \cos b-\sin a \sin b$

Therefore,

$\cos (x+2 x)=\cos x \cos 2 x-\sin x \sin 2 x$ ---- eqn 1

We know that,

$\sin 2 x=2 \sin x \cos x$

$\cos 2 x=\cos ^{2} x-\sin ^{2} x$

Substituting these values in eqn 1

$\cos (x+2 x)=\cos x\left(\cos ^{2} x-\sin ^{2} x\right)-\sin x(2 \sin x \cos x)$ -------- eqn 2

We know that,

$\cos ^{2} x-\sin ^{2} x=1-2 \sin ^{2} x$

Applying this in above eqn 2, we get

$\cos (x+2 x)=\cos x\left(1-2 \sin ^{2} x\right)-\sin x(2 \sin x \cos x)$

$\begin{aligned}&\cos (x+2 x)=\cos x-2 \sin ^{2} x \cos x-2 \sin ^{2} x \cos x\\\\&\cos (x+2 x)=\cos x-4 \sin ^{2} x \cos x\end{aligned}$

$\cos (x+2 x)=\cos x-4 \cos x \sin ^{2} x$

Therefore,

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

Option A is correct

7 0

3 years ago

To determine how a city's residents feel about building a new youth center, a group considers surveying 50 random children at a

Novay_Z [31]

Answer:

This would most probably result in biased sample since only a specific part of the community is being surveyed that does not represent all of the community.

Step-by-step explanation:

A survey is being conducted to determine how a city's residents feel about building a new youth center.

They are considering to survey 50 random children at a local elementary school.

This would most probably result in biased sample since only a specific part of the community is being surveyed that does not represent all of the community.

Moreover, it is likely that the students of elementary school might not even have any interest in youth center so results would be biased.

Therefore, it is suggested to include a variety of samples that is surveying different age groups that covers all of the community.

8 0

3 years ago

Read 2 more answers

2(15+3m)-7 Plz explain and answer

Alekssandra [29.7K]

6m+23

You have to use distributive property, so 15x2=30 and 2x3m= 6m. You then subtract 30 from 7 and get 23.

4 0

3 years ago

Read 2 more answers

Bucket A has 5 1/2 gallons of water, but is draining at a rate of 3/4 gallons per hour. Bucket B has 2 1/4 gallons of water, but

Ivenika [448]

Answer:

9/0

Step-by-step explanation:

6 0

3 years ago

Squandering Sam has $1,050 in his bank account. Every week he withdraws $40 to buy scratch off tickets. Saving Sally doesn’t hav

shtirl [24]

Answer:

15 weeks

Step-by-step explanation:

Week 1: 1,050 ≠ 0

Week 2: 1,010 ≠ 35

Week 3: 970 ≠ 70

Week 4: 930 ≠ 105

Week 5: 890 ≠ 140

Week 6: 850 ≠ 175

Week 7: 810 ≠ 210

Week 8: 770 ≠ 245

Week 9: 730 ≠ 280

Week 10: 690 ≠ 315

Week 11: 650 ≠ 350

Week 12: 610 ≠ 385

Week 13: 570 ≠ 420

Week 14: 530 ≠ 455

Week 15: 490 = 490

4 0

3 years ago