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Travka [436]
3 years ago
12

Find the number b such that the line y = b divides the region bounded by the curves y = 25x2 and y = 1 into two regions with equ

al area. (Round your answer to two decimal places.)
Mathematics
1 answer:
Dennis_Churaev [7]3 years ago
4 0

Answer:

y=1/∛4 divides the area in half

Step-by-step explanation:

since the minimum value of x² is 0 (for x=0 ) and for y=1

1 = 25*x² → x= ±√(1/25) = ±1/5

then the total area between y=1  and y = 25*x²  is bounded to  x=±1/5 and y=0 . Since there is a direct relationship between x and y , we can find the value of x=a that divides the region in 2 of the same area. thus

Area below x=C = Area above x=C

Area below x=C = Total area -  Area below x=C

2*Area below x=C = Total area

Area below x=C = Total area /2

∫ 25*x² dx from x=c to x=-c =  1/2 ∫ 25*x² dx from x=1/5  to x=-1/5

25*[c³/3 - (-c)³/3] = 25/2 * [(1/5)³/3 - (-1/5)³/3]

2*c³/3 = (1/5)³/3

c = 1/(5*∛2)

thus

y=25* x²  = 25*[1/(5*∛2)]² = 1/∛4

thus the line y=1/∛4 divides the area in half

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Answer:

<h3>\boxed{ \boxed{ \bold{ {x}^{2}  + 4x - 21}}}</h3>

Step-by-step explanation:

\sf{(x - 3)(x + 7)}

Use the distributive property to multiply each term of the first binomial by each term of the second binomial.

⇒\sf{x(x  + 7) - 3(x + 7)}

⇒\sf{ {x}^{2}  + 7x - 3x  - 21}

Collect like terms

⇒\sf{ {x}^{2}  + 4x - 21}

Hope I helped!

Best regards!!

3 0
3 years ago
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B) 36 kg in the ratio 1:3:5​
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Answer:

  4 kg : 12 kg : 20 kg

Step-by-step explanation:

The total number of "ratio units" is 1+3+5 = 9, so each of them represents ...

  (36 kg)/9 = 4 kg

Multiplying the given ratio by 4 kg will show the appropriate division:

  1(4 kg) : 3(4 kg) : 5(4 kg) = 4 kg : 12 kg : 20 kg

8 0
2 years ago
analyze this situation and determine how much cookie dough is "wasted" when 3-inch cookies are cut. then have each team member c
Cerrena [4.2K]

Answer:

The result is the same.

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

Please have a look at the attached photo.  

My answer:

Given the information:

  • square 12 inches wide
  • 3-inch diameter cookies are cut => its radius is: 1.5 inches

Hence we can find some information:

  • The area of the square is: 12^{2}  = 144 square inches
  • The area of a cookies is: r^{2}π = 3.14*1.5^{2} = 7.065 square inches
  • The total number of 3-inch cookies are: 4*4 =16

=> The total area of the cookies is: 16* 7.065 = 113.04 square inches

=> how much cookie dough is "wasted" when 3-inch cookies are cut:

= The area of the square - The total area of the cookies

= 144 - 113.04 = 30.96  square inches

If the diameter is increased to 4 inches => its radius: 2 inches, we have:

  • The area of a cookies is: r^{2}π = 2^{2} *3.14 = 12.56 square inches
  • The total number of 3-inch cookies are: 3*3 =9

=> The total area of the cookies is: 9* 12.56 = 113.04 square inches

=> how much cookie dough is "wasted" when 4-inch cookies are cut:

= The area of the square - The total area of the cookies

= 144 - 113.04 = 30.96  square inches

The result is the same.

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