Resolver con proceso 3√256−3√16+3√54

Find area of the shaded region.

Monica [59]

Answer:

The area of the shaded region is about 38.1 square centimeters.

Step-by-step explanation:

We want to find the area of the shaded region.

To do so, we can first find the area of the sector and then subtract the area of the triangle from the sector.

The given circle has a radius of 6 cm.

And the given sector has a central angle of 150°.

The area for a sector is given by the formula:

$\displaystyle A=\pi r^2\cdot \frac{\theta}{360^\circ}$

In this case, r = 6 and θ = 150°. Hence, the area of the sector is:

$\displaystyle \begin{aligned}A&=\pi(6)^2\cdot \frac{150}{360}\\ &=36\pi\cdot \frac{5}{12}\\&=3\pi \cdot 5\\&=15\pi \text{ cm}^2\end{aligned}$

Now, we can find the area of the triangle. We can use an alternative formula:

$\displaystyle A=\frac{1}{2}ab\sin(C)$

Where a and b are the side lengths, and C is the angle between them.

Both side lengths of the triangle are the radii of the circle. So, both side lengths are 6.

And the angle C is 150°. Hence, the area of the triangle is:

$\displaystyle A=\frac{1}{2}(6)(6)\sin(150)=18\sin(150)$

The area of the shaded region is equivalent to the sector minus the triangle:

$A_{\text{shaded}}=A_{\text{sector}}-A_{\text{triangle}}$

Therefore:

$A_{\text{shaded}}=15\pi -18\sin(150)$

Use a calculator:

$A_{\text{shaded}}=38.1238...\approx 38.1\text{ cm}^2$

The area of the shaded region is about 38.1 square centimeters.

6 0

2 years ago

PLEASE HELP ME.....

Virty [35]

Answer:

They would meet each other at $01 : 24$ PM.

Step-by-step explanation:

Erik took a trip to see his friend Mike who lives 308 miles away.

He left his place at 10 AM driving at 70 mph.

In 2 hours, his friend Mike left his place driving towards Erik at an average speed of 50 mph.

As Erik left his house at 10 AM driving at 70 mph and in 2 hours, his friend Mike left his place driving towards Erik at an average speed of 50 mph. It means

Erik left his place at 12:00 PM noon.

so, at 12:00 PM Erik had already traveled:

$2\times 70=140\:\:miles$

Miles left $=308-140=168\:\:miles$

Let 't' be the time when they meet

so

$70t\:+\:50t\:=168$

$120t=168$

$\mathrm{Divide\:both\:sides\:by\:}120$

$\frac{120t}{120}=\frac{168}{120}$

$t=\frac{7}{5}$

so

$t=\frac{7}{5}=1.4\:\:hours$

or $1$ hour and $24$ minutes after $12:00$ noon

i.e.

$12\:+\:1.4\:=1\:O'clock\:+\:24\:minutes$

Therefore, they would meet each other at $01 : 24$ PM.

7 0

3 years ago

2 Describe the solution set of y=8

Vedmedyk [2.9K]

Answer:

what is your question there is no equation

7 0

2 years ago

Tell whether this statement is sometimes, always, or never true. Identify the answer with a sketch. If B is a point between A an

Ksivusya [100]

The statement is always true

7 0

2 years ago

5x5=25 i did the quiz and got it right

Sedaia [141]

Congratsss good jobbb

5 0

2 years ago

Read 2 more answers

Resolver con proceso 3√256−3√16+3√54​

Resolver con proceso 3√256−3√16+3√54