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3 years ago

12

Find the arc length and area of a sector with radius R =60 inches and central angle equals 30° round your answer to the nearest

hundredth

2 answers:

Sergeu [11.5K]3 years ago

8 0

Answer:

(a)31.42 inches

(b)942.48 Square Inches

Step-by-step explanation:

Black_prince [1.1K]3 years ago

3 0

Answer:

(a)31.42 inches

(b)942.48 Square Inches

Step-by-step explanation:

Given a sector of a circle with the following dimensions:

Radius of the circle =60 inches

Central Angle of the sector =30°

(a)Arc Length

Arc Length $=\dfrac{\theta}{360^\circ}X2\pi r$

$=\dfrac{30}{360^\circ}X2*60*\pi\\\\=10\pi\\\\=31.42$ Inches (correct to the nearest hundredth)$

(b)Area of the sector

Area of the sector $=\dfrac{\theta}{360^\circ}X\pi r^2$

$=\dfrac{30}{360^\circ}X\pi*60^2\\\\=300\pi\\\\=942.48$ Square Inches (correct to the nearest hundredth)$

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Which of the following sets are subspaces of R3 ?

Ratling [72]

Answer:

The following are the solution to the given points:

Step-by-step explanation:

for point A:

$\to A={(x,y,z)|3x+8y-5z=2} \\\\\to for(x_1, y_1, z_1),(x_2, y_2, z_2) \varepsilon A\\\\ a(x_1, y_1, z_1)+b(x_2, y_2, z_2) = (ax_1+bx_2,ay_1+by_2,az_1+bz_2)$

$=3(aX_l +bX_2) + 8(ay_1 + by_2) — 5(az_1+bz_2)\\\\=a(3X_l+8y_1- 5z_1)+b (3X_2+8y_2—5z_2)\\\\=2(a+b)$

The set A is not part of the subspace $R^3$

for point B:

$\to B={(x,y,z)|-4x-9y+7z=0}\\\\\to for(x_1,y_1,z_1),(x_2, y_2, z_2) \varepsilon B \\\\\to a(x_1, y_1, z_1)+b(x_2, y_2, z_2) = (ax_1+bx_2,ay_1+by_2,az_1+bz_2)$

$=-4(aX_l +bX_2) -9(ay_1 + by_2) +7(az_1+bz_2)\\\\=a(-4X_l-9y_1+7z_1)+b (-4X_2-9y_2+7z_2)\\\\=0$

$\to a(x_1,y_1,z_1)+b(x_2, y_2, z_2) \varepsilon B$

The set B is part of the subspace $R^3$

for point C: $\to C={(x,y,z)|x$

In this, the scalar multiplication can't behold

$\to for (-2,-1,2) \varepsilon C$

$\to -1(-2,-1,2)= (2,1,-1)$ ∉ C

this inequality is not hold

The set C is not a part of the subspace $R^3$

for point D:

$\to D={(-4,y,z)|\ y,\ z \ arbitrary \ numbers)$

The scalar multiplication s is not to hold

$\to for (-4, 1,2)\varepsilon D\\\\\to -1(-4,1,2) = (4,-1,-2)$ ∉ D

this is an inequality, which is not hold

The set D is not part of the subspace $R^3$

For point E:

$\to E= {(x,0,0)}|x \ is \ arbitrary) \\\\\to for (x_1,0 ,0) ,(x_{2},0 ,0) \varepsilon E \\\\\to a(x_1,0,0) +b(x_{2},0,0)= (ax_1+bx_2,0,0)\\$

The $x_1, x_2$ is the arbitrary, in which $ax_1+bx_2$ is arbitrary

$\to a(x_1,0,0)+b(x_2,0,0) \varepsilon E$

The set E is the part of the subspace $R^3$

For point F:

$\to F= {(-2x,-3x,-8x)}|x \ is \ arbitrary) \\\\\to for (-2x_1,-3x_1,-8x_1),(-2x_2,-3x_2,-8x_2)\varepsilon F \\\\\to a(-2x_1,-3x_1,-8x_1) +b(-2x_1,-3x_1,-8x_1)= (-2(ax_1+bx_2),-3(ax_1+bx_2),-8(ax_1+bx_2))$

The $x_1, x_2$ arbitrary so, they have $ax_1+bx_2$ as the arbitrary $\to a(-2x_1,-3x_1,-8x_1)+b(-2x_2,-3x_2,-8x_2) \varepsilon F$

The set F is the subspace of $R^3$

5 0

3 years ago

In your pattern which shape covers more of the plane blue rhombus red trapezoid or green triangles? Explain how you know.

mixas84 [53]

Answer:

Which shapes cover more of the plane" means that we are comparing the areas covered by the different types of shapes. In these patterns, two triangles match up to one rhombus, and three triangles match up to one trapezoid.

In both Pattern A and Pattern B, the first hexagonal part is made up of 7 triangles, 4 rhombuses, and 3 trapezoids.

The first hexagonal part is repeated across the pattern, so whichever type of shape covers the most area of this first part also covers the most area in the whole pattern.

<em>hope it helps</em>

3 0

3 years ago

If Owen and Eliza had a combined taxable income of $68,200 and filed their federal income tax return with the Married Filing Joi

tangare [24]

Answer:

9425

D

Step-by-step explanation:

They are in the third tax bracket down. That means that their joint income is over 67900 but less than 137050.

The base rate is 9350. But they are 68200 - 67900 = 300 over the minimum.

So 25% of that 300 is also to be paid to the government 25/100 * 300 = 75 dollars

Now they must pay 9350 + 75 = 9425

Answer D

7 0

3 years ago

Read 2 more answers

Does 6(3−5w)=5(4−2w)−20w have one solution, no solution, or infinitely many solutions? <br><br> plzz

Vikki [24]

Answer:

No solutions

Step-by-step explanation:

18-30w=20-10w-20w

18-30w=20-30w

18-20=30w-30w

-2 does not equal to 0

No solutions

6 0

3 years ago

0.5% of 490 is what number show work please

Genrish500 [490]

You would set it up: .5/100 = x/490 and then cross multiply .5 time 490 and 100 times x, and end up with: 245=100x. divide by 100, and get 2.45

6 0

3 years ago