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2 years ago

What is the ratio of the area of sector ABC to the area of sector DBE?

Mathematics

2 answers:

Alex73 [517]2 years ago

8 0

The area of sector ABC is = x. The area of sector DBE is = y. The ratio of the area ABC to the area of DBE = x/y (x over y OR x divided by y)

shusha [124]2 years ago

7 0

We have to find the" ratio of the area of sector ABC to the area of sector DBE".

Now,

the general formula for the area of sector is

Area of sector= 1/2 r²θ

where r is the radius and θ is the central angle in radian.

180°= π rad

1° = π/180 rad

For sector ABC, area= 1/2 (2r)²(β°)

= 1/2 *4r²*(π/180 β)

= 2r²(π/180 β)

For sector DBE, area= 1/2 (r)²(3β°)

= 1/2 *r²*3(π/180 β)

= 3/2 r²(π/180 β)

Now ratio,

Area of sector ABC/Area of sector DBE = $\frac{2r^{2}*\ \frac{\pi}{180} beta}{3/2 r^{2}*\ \frac{\pi}{180}beta}$

= 4/3

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In a film, an actor played an elderly uncle character is criticized for marrying a woman when he is 3 times her age. He wittily

yanalaym [24]

Answer:the uncle is 54 years old.

The woman is 18 years old

Step-by-step explanation:

Let x represent the age of the uncle.

Let y represent the age of the woman that he married.

In the film, an actor played an elderly uncle character is criticized for marrying a woman when he is 3 times her age. This means that

x = 3y

He wittily replies, "Ah, but in 18 years time I shall only be twice her age. It means that

x + 18 = 2(y + 18)

x + 18 = 2y + 36 - - - - - - - - - - 1

Substituting x = 3y into equation 1, it becomes

3y + 18 = 2y + 36

3y - 2y = 36 - 18

y = 18

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2 years ago

Can you simplify before multiplying 14×25/27

castortr0y [4]

Answer:

No.

Step-by-step explanation:

You can not simplify this expression before multiplying it, because no whole numbers go into both 14 and 27, and also no whole numbers go into both, 25 and 27. This is the correct answer to this question.

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2 years ago

Korey starts a small carwash business to save up some cash. He decides to offer two different price packages to his clients. Pac

rosijanka [135]

Answer:

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Step-by-step explanation:

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2 years ago

Find the average value of the function f(x, y, z) = 5x2z 5y2z over the region enclosed by the paraboloid z = 4 − x2 − y2 and the

S_A_V [24]

The paraboloid meets the x-y plane when x²+y²=9. A circle of radius 3, centre origin.

Use cylindrical coordinates (r,θ,z) so paraboloid becomes z = 9−r² and f = 5r²z. 

If F is the mean of f over the region R then F ∫ (R)dV = ∫ (R)fdV 

∫ (R)dV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] rdrdθdz 

= ∫∫ [θ=0,2π, r=0,3] r(9−r²)drdθ = ∫ [θ=0,2π] { (9/2)3² − (1/4)3⁴} dθ = 81π/2 

∫ (R)fdV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] 5r²z.rdrdθdz 

= 5∫∫ [θ=0,2π, r=0,3] ½r³{ (9−r²)² − 0 } drdθ 

= (5/2)∫∫ [θ=0,2π, r=0,3] { 81r³ − 18r⁵ + r⁷} drdθ 

= (5/2)∫ [θ=0,2π] { (81/4)3⁴− (3)3⁶+ (1/8)3⁸} dθ = 10935π/8 

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3 0

2 years ago

Two processes are used to produce forgings used in an aircraft wing assembly. Of 200 forgings selected from process 1, 10 do not

tangare [24]

Answer:

$\bar p_1=0.05\\\bar p_2=0.067$

b-Check illustration below

c.(-0.0517,0.0177

Step-by-step explanation:

a.let $p_1 \& p_2$ denote processes 1 & 2.

For $p_1$ : T1=10,n1=200

For $p_2$ :T2=20,n2=300

Therefore

$\bar p_1=\frac{t_1}{N_1}=\frac{10}{200}=0.05\\\bar p_2=\frac{t_2}{N_2}=\frac{20}{300}=0.067$

b. To test for hypothesis:-

$H_0:p_1=p_2\\H_A=p_1\neq p_2\\\alpha=0.05$

ii.For a two sample Proportion test

$Z=\frac{\bar p_1-\bar p_2}{\sqrt(\bar p(1-\bar p)(\frac{1}{n_1}+\frac{1}{n_2})}\\$

iii. for $\frac{\alpha}{2}=(-1.96,+1.96)$ (0.5 alpha IS 0.025),

reject $H_o$ if $|Z|>1.96$

iv. Do not reject $H_o$ . The noncomforting proportions are not significantly different as calculated below:

$z=\frac{0.050-0.067}{\sqrt {(0.06\times0.94)\times \frac{1}{500}}}$

z=-0.78

c. $(1-\alpha).100\%$ for the p1-p2 is given as:

$(\bar p_1-\bar p_2)\pm Z_0_._5_\alpha \times \sqrt \frac{ \bar p_1(1-\bar p_1)}{n_1}+\frac{\bar p_2(1-\bar p_2)}{n_2}\\\\=(0.05-0.067)\pm 1.645 \times \sqrt \ \frac{0.05+0.95}{200}+\frac{0.067+0.933}{300}\\$

=(-0.0517,+0.0177)

*CI contains o, which implies that proportions are NOT significantly different.

4 0

2 years ago