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Studentka2010 [4]
3 years ago
14

Mathematical Literacy Assignment no 2021​

Mathematics
1 answer:
makkiz [27]3 years ago
8 0
What’s the question ??
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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
3 years ago
What is the sine of angle C?
ololo11 [35]

Answer:

4/5 or 53°

Step-by-step explanation:

soh

cah

toa

you want soh

sine=opposite/hyp

therefore sine of C is 4/5

to find the degrees you have to something a lil different.

sin^-1 (theta)= 4/5

sin^-1(4/5)=theta

53°=theta

8 0
3 years ago
6. What is the surface area of the cone? Use
Lostsunrise [7]
It would be 20ft have a great day
4 0
2 years ago
Read 2 more answers
What is n in the equation 12 + 12n = -48
Liula [17]
Hello!

To solve an algebraic equation, you must isolate the variable on one side. We’ll begin by restating the given equation:

12 + 12n = -48

Now subtract 12 from both sides of the equation:

12n = -60

Divide both sides by 12:

n = -5

We have now proven that “n” is equal to (-5).

I hope this helps!
3 0
3 years ago
Suppose f(x) = 1/4 over the range a ≤ x ≤ b, and suppose P(X > 4) = 1/2.
Anettt [7]

Answer:

a=2

b=6

Step-by-step explanation:

Assuming a uniform distribution and that a ≤ x ≤ b, if f(x) = 1/4, then:

f(x) =\frac{1}{4}=\frac{1}{b-a}\\b-a = 4

If P(X > 4) = 1/2, then:

\frac{1}{2} = 1-(\frac{x-a}{b-a})=1-(\frac{4-a}{4})\\a-4+4 =\frac{1}{2}*4\\ a=2\\b=4+a\\b=6

The values for a and b are, respectively, 2 and 6.

3 0
3 years ago
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