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4 years ago

Find the area lying outside r=6cos(theta) and inside r=3+3cos(theta)

1 answer:

7 0

The area bounded by the 2 parabolas is A(θ) = 1/2∫(r₂²- r₁²).dθ between limits θ = a,b...

the limits are solution to 3cosθ = 1+cosθ the points of intersection of curves. 
2cosθ = 1 => θ = ±π/3 

A(θ) = 1/2∫(r₂²- r₁²).dθ = 1/2∫(3cosθ)² - (1+cosθ)².dθ 
= 1/2∫(3cosθ)².dθ - 1/2∫(1+cosθ)².dθ 
= 9/8[2θ + sin(2θ)] - 1/8[6θ + 8sinθ +sin(2θ)] .. 
.............where I have used ∫(cosθ)².dθ=1/4[2θ + sin(2θ)] 
= 3θ/2 +sin(2θ) - sin(θ) 

Area = A(π/3) - A(-π/3) 
= 3π/6 + sin(2π/3) -sin(π/3) - (-3π/6) - sin(-2π/3) + sin(-π/3) 
= π.

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Is it possible to construct a triangle with side lengths of 15 inches, 17 inches, and 32 inches? Why or why not? (PLEASE HELP ME

dem82 [27]

B because the sum of 2 sides must be GREATER than the 3rd side

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4 years ago

Somebody help me lol

vladimir2022 [97]

Answer: $1.03*10^{-1}>3.1*10^{-2}>2.01*10^{-3}>2.32*10^{-4}>4.2*10^{-5}$

Step-by-step explanation:

1. A number written in scientific notation has the following form:

$a10^{b}$

Where is $a$ is a number between 1 and 10 but not including 10, and b is an integer.

2. The negative exponent indicates the number of places the decimal point must be moved to the left to obtain the number as a decimal number.

3. Keeping this on mind, you can know that: if the exponent of a number written in scientific notation indicates that the decimal point must be moved 5 places to the left and another number written in scientific notation indicates that the decimal point must be moved 2 places to the left, then the first number is smaller than the second one.

4. Therefore, you can arrange the numbers given in the problem as following:

$1.03*10^{-1}>3.1*10^{-2}>2.01*10^{-3}>2.32*10^{-4}>4.2*10^{-5}$

3 0

3 years ago

What is 27 divided by 1,581

quester [9]

Answer:

0.01707779886

Step-by-step explanation:

Just do 27/1581

6 0

3 years ago

For an outdoor concert by the city orchestra, concert organizers estimate that 16 comma 000 people will attend if it is not rai

Sladkaya [172]

Answer: 13300

========================================

Work Shown:

A = event that it rains

B = event that it does not rain

P(A) = 0.30

P(B) = 1-P(A) = 1-0.30 = 0.70

Multiply the attendance figures with their corresponding probabilities

if it rains, then 7000*P(A) = 7000*0.30 = 2100
if it doesn't rain, then 16000*P(B) = 16000*0.70 = 11200

Add up the results: 2100+11200 = 13300

This is the expected value. This is basically the average based on the probabilities. The average is more tilted toward the higher end of the spectrum (closer to 16000 than it is to 7000) because there is a higher chance that it does not rain.

3 0

3 years ago

A square pyramid is sliced parallel to the base and halfway up the pyramid.

Anna [14]

Answer:

A square smaller than the base

Explanation:

A square pyramid is a 3 Dimensional image. When you slice a 3 Dimensional image you form is a 2 Dimensional image for example a rectangle, a square, a triangle e.t.c.

The shape of the cross sections formed after slicing a 3 Dimensional image is dependent on the way it was sliced.

This means it can be sliced horizontally or vertically and this would result in different shapes.

If square pyramid is sliced parallel to the base and halfway up the pyramid, the shape of the cross section formed is a square smaller than the base.

6 0

3 years ago