1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Gre4nikov [31]
3 years ago
10

Find the number b such that the line y = b divides the region bounded by the curves y = 36x2 and y = 25 into two regions with eq

ual area. (Round your answer to two decimal places.) b =
Mathematics
1 answer:
Gemiola [76]3 years ago
8 0

Answer:

b = 15.75

Step-by-step explanation:

Lets find the interception points of the curves

36 x² = 25

x² = 25/36 = 0.69444

|x| = √(25/36) = 5/6

thus the interception points are 5/6 and -5/6. By evaluating in 0, we can conclude that the curve y=25 is above the other curve and b should be between 0 and 25 (note that 0 is the smallest value of 36 x²).

The area of the bounded region is given by the integral

\int\limits^{5/6}_{-5/6} {(25-36 \, x^2)} \, dx = (25x - 12 \, x^3)\, |_{x=-5/6}^{x=5/6} = 25*5/6 - 12*(5/6)^3 - (25*(-5/6) - 12*(-5/6)^3) = 250/9

The whole region has an area of 250/9. We need b such as the area of the region below the curve y =b and above y=36x^2 is 125/9. The region would be bounded by the points z and -z, for certain z (this is for the symmetry). Also for the symmetry, this region can be splitted into 2 regions with equal area: between -z and 0, and between 0 and z. The area between 0 and z should be 125/18. Note that 36 z² = b, then z = √b/6.

125/18 = \int\limits^{\sqrt{b}/6}_0 {(b - 36 \, x^2)} \, dx = (bx - 12 \, x^3)\, |_{x = 0}^{x=\sqrt{b}/6} = b^{1.5}/6 - b^{1.5}/18 = b^{1.5}/9

125/18 = b^{1.5}/9

b = (62.5²)^{1/3} = 15.75

You might be interested in
Solve for equation x. <br> 3In(x)+2In(4)=In(128)
Serggg [28]

Domain:\ x > 0\\\\3\ln(x)+2\ln(4)=\ln(128)\qquad\text{use}\ \lag_ab^n=n\log_ab\\\\\ln(x^3)+\ln(4^2)=\ln(128)\qquad\text{use}\ \log_ab+\ln_ac=\ln_a(bc)\\\\\ln(16x^3)=\ln(128)\iff16x^3=128\qquad\text{divide both sides by 16}\\\\x^3=8\to x=\sqrt[3]8\\\\\boxed{x=2}\in D

3 0
3 years ago
Mark is building two separate pig-pens. The width of pig-pen A is w. The length of pig-pen A is 4 feet longer than its width. Th
Juliette [100K]

Answer:

The width of pen A is 7 feet,

The Length of Pen A is  11 feet,

The width of Pen B is 6 feet,

The Length of Pen B is 12 feet

Step-by-step explanation:

The width of pen A is 7 feet,

The Length of Pen A is 7 + 4 = 11 feet,

The width of Pen B is 7+4-5 = 6 feet,

The Length of Pen B is 2*(7+4-5) = 12 feet

w+w+w+w+4+4=(w+4-5)+(w+4-5) +2*(w+4-5)+2*(w+4-5)\\4w+8=6w-6\\14=2w\\w=7\\

8 0
3 years ago
Question in Image answer with explanation please added 20 points
Svet_ta [14]

Answer:

$117,351 JMD

Step-by-step explanation:

It is simple. 1 US dollar is 150.45 JMD, so 780 US dollars should be:

780 * 150.45 = 117,351

7 0
2 years ago
Read 2 more answers
I need some help on this, I do NOT get it lol
andrew11 [14]

Answer:

Logarithmic

Step-by-step explanation:

It's literally a logarithmic function because it includes "log" which is short for logarithmic.

3 0
3 years ago
Is 1.0277 a rational number
ch4aika [34]
<h2>Answer:</h2><h2>Its rational</h2>

<h2>Hope this helps!!</h2>

8 0
3 years ago
Read 2 more answers
Other questions:
  • How would you do 5/12 multipled by 1/5 times 8
    5·2 answers
  • What is a tenth of a decimal ?
    15·1 answer
  • Solve for r V=2π/t•r
    7·1 answer
  • Avin and andrea are two of the children in the jones family gavin has as many brothers as sister andrea has twice as many as man
    9·1 answer
  • You deposit $4300 in an account that earns 2% per year simple interest. The equation that represents this situation is: A(n) = 4
    15·1 answer
  • In the diagram below, which distance represents the distance from point D to
    12·1 answer
  • Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function,
    6·1 answer
  • In a right triangle, if the length of one leg is 4 and the length of the hypotenuse is 8, what is the length of other leg, in si
    14·1 answer
  • Learning Task 3
    8·1 answer
  • To solve the equation ‐2x + 5 = 9 for x, what operations must be performed on both sides of the equation in order to isolate the
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!