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
katrin [286]
3 years ago
14

Find the number b such that the line y = b divides the region bounded by the curves y = 25x2 and y = 4 into two regions with equ

al area. (round your answer to two decimal places.
Mathematics
1 answer:
umka2103 [35]3 years ago
4 0
y=25x^2\implies x=\pm5\sqrt y

The area between the parabola and the line is

\displaystyle\int_0^4(5\sqrt y-(-5\sqrt y))\,\mathrm dy=10\int_0^4\sqrt y\,\mathrm dy=\dfrac{10}{\frac32}y^{3/2}\bigg|_{y=0}^{y=4}=\dfrac{20}3\times8=\frac{160}3

But you're looking for the line y=b such that the areas of each subdivision are equal. This means you want b to satisfy

\displaystyle10\int_0^b\sqrt y\,\mathrm dy=\dfrac{80}3

You have

\displaystyle\int_0^b\sqrt y\,\mathrm dy=\dfrac83
\dfrac23y^{3/2}\bigg|_{y=0}^{y=b}=\dfrac83
\dfrac23b^{3/2}=\dfrac83
b^{3/2}=4
b=4^{2/3}=2\sqrt[3]2\approx2.52
You might be interested in
Which graph represents f(x)=4⋅5x ?
vovangra [49]

Answer:

5

Step-by-step explanation:

5

8 0
3 years ago
Read 2 more answers
Please help me with this problem!): (#5)
astra-53 [7]

5a.

18/9 = 12/x

18x = 12(9)...cross multiply

18x = 108

x=108/18

x=6



6 0
3 years ago
Let f(x) = x2 and g(x) = x - 3.<br> Evaluate (gºf)(-2).<br> A. -20<br> B. 20<br> C. 7<br> D. 1
7nadin3 [17]

Answer:

D. 1

Step-by-step explanation:

Step 1: Find g of f(x)

g(f(x)) = (x²) - 3

Step 2: Plug in -2 as <em>x</em>

g(f(x))(-2) = (-2)² - 3

g(f(x))(-2) = 4 - 3

g(f(x))(-2) = 1

7 0
3 years ago
What time is it when the small hand is in between the 8 and 9 and when the big hand is at the 6?
Finger [1]
The time would be 8:30
3 0
3 years ago
The box plots show the average gas mileage, in miles per gallon, of cars and minivans tested by a certain company.
mr_godi [17]

Answer:

b.The interquartile range for cars is about 7 mpg, and the interquartile range for minivans is about 3 mpg.

Step-by-step explanation:

i got it right

4 0
3 years ago
Read 2 more answers
Other questions:
  • PLEASE HELP!!!
    15·1 answer
  • The delivery times for all food orders at a fast-food restaurant during the lunch hour are normally distributed with a mean of m
    10·1 answer
  • 2 ( 3x - 1) = -6x -2​
    14·2 answers
  • The measure of the angles of a pentagon are (x - 5), (x - 6), (2x - 7), x° and (2x - 2). Find the
    13·1 answer
  • Suppose the sides of a pendant are 18 mm long. what is the height of the pendant to the nearest tenth of a millimeter?
    9·1 answer
  • Think y=mx+b
    5·1 answer
  • The dots in the diagram are 1 unit apart. What is the longest segment that can be drawn between two of the dots without
    9·1 answer
  • A car uses 8 gallons of gasoline to travel 290 miles.Juanita wants to take a trip that is 400 miles. What equation will she need
    12·1 answer
  • A rectangular bedroom is 2 ft longer than it is wide. Its area is 99 ft^2. What is the width of the room?
    8·1 answer
  • Beginning with the graph of f(x)= x², what transformations are needed to form g(x)=3(x+2)^2-1 ?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!