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
kifflom [539]
3 years ago
15

There is a line through the origin that divides the region bounded by the parabola y=2x-4x^2 and the x-axis into two regions wit

h equal area. What is the slope of that line? ...?
Mathematics
1 answer:
shtirl [24]3 years ago
7 0
Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions here.

y = 7x - 4x² 

<span>7x - 4x² = 0 </span>

<span>x(7 - 4x) = 0 </span>

<span>x = 0, 7/4 </span>

<span>Find the area of the bounded region... </span>

<span>A = ∫ 7x - 4x² dx |(0 to 7/4) </span>

<span>A = 7/2 x² - 4/3 x³ |(0 to 7/4) </span>

<span>A = 7/2(7/4)² - 4/3(7/4)³ - 0 = 3.573 </span>

<span>Half of this area is 1.786, now set up an integral that is equal to this area but bounded by the parabola and the line going through the origin... </span>

<span>y = mx + c </span>

<span>c = 0 since it goes through the origin </span>

<span>The point where the line intersects the parabola we shall call (a, b) </span>

<span>y = mx ===> b = m(a) </span>

<span>Slope = m = b/a </span>

<span>Now we need to integrate from 0 to a to find the area bounded by the parabola and the line... </span>

<span>1.786 = ∫ 7x - 4x² - (b/a)x dx |(0 to a) </span>

<span>1.786 = (7/2)x² - (4/3)x³ - (b/2a)x² |(0 to a) </span>

<span>1.786 = (7/2)a² - (4/3)a³ - (b/2a)a² - 0 </span>

<span>1.786 = (7/2)a² - (4/3)a³ - b(a/2) </span>

<span>Remember that (a, b) is also a point on the parabola so y = 7x - 4x² ==> b = 7a - 4a² </span>
<span>Substitute... </span>

<span>1.786 = (7/2)a² - (4/3)a³ - (7a - 4a²)(a/2) </span>

<span>1.786 = (7/2)a² - (4/3)a³ - (7/2)a² + 2a³ </span>

<span>(2/3)a³ = 1.786 </span>

<span>a = ∛[(3/2)(1.786)] </span>

<span>a = 1.39 </span>

<span>b = 7(1.39) - 4(1.39)² = 2.00 </span>

<span>Slope = m = b/a = 2.00 / 1.39 = 1.44</span>

You might be interested in
A man and a woman agree to meet at a certain location about 12:30 p.m. if the man arrives at a time uniformly distributed betwee
Svetllana [295]
We define the spaces of the man and the woman's independent arrivals.
In this case, 
f(man) = 1 (45-15) = 1/30
f(woman)=1/(60-0)= 1/60
f(man)*f(woman) = 1/1800

Probability = P 
P (man-woman)< 5 = 1/1800* integral of (y ) with limits of (x+5) and (x-5) from 45 to 15. 
P (man-woman) <5 = 1/6
8 0
3 years ago
Help please thank you and also show the work please
ziro4ka [17]

Answer:

y= -1.4x-6.6

Step-by-step explanation:

(1,-8)

7x+5y=-7

Make the equation into standard form

Subtract 7x from both sides

5y=-7x-7

Divide all by 5

y=-1.4x-1.4

Since they are parrallel, we know the slope is -1.4x

y=-1.4x+b

(1,-8) is one of the points it goes through

Replace the x and y in the equation for the x and y in the incomplete equation

-8=-1.4+b

Add 1.4 to both sides

-6.6=b

Thus the equation is

y=-1.4x-6.6

3 0
3 years ago
The volume of a cylinder is 54π cubic inches and the height is 6 inches. Find the radius.
Anika [276]

Answer:

The radius of the cylinder is 3 inches.

Step-by-step explanation:

For any given cylinder, the volume can be expressed as:

volume = \pir^{2}h

where r is the radius of its circular surface, and h is its height.

Given that: volume = 54π cubic inches, and the height = 6 inches.

then,

54\pi = \pi x r^{2} x 6

54\pi  = 6\pir^{2}

r^{2} = \frac{54\pi }{6\pi }

   = 9

r = \sqrt{9}

r = 3

The radius of the cylinder is 3 inches.

8 0
3 years ago
Write an equation that represents the relationship between the distance the car has traveled in miles, , and the amount of gas l
harina [27]

Answer: y= Y/x = ?

Step-by-step explanation: write the equation like said, and use the numbers you get to fill in. So say you traveled 500 miles , and you had 540 miles till empty yku would have 40 miles left , so you traveled 500 miles per gallon of gas :) hope this helps

6 0
3 years ago
Judi's father is 6feet tall the minimum height to ride a rollercoster is given in inches. How many inches tall is judi's father
iogann1982 [59]
Judi's father is 72 inches tall
5 0
4 years ago
Read 2 more answers
Other questions:
  • Show that (2xy3 + cos x)dx + (3x2 y2 − sin y)dy = 0 is exact, and find the solution. Find c if y(0) = π
    14·1 answer
  • A clock tower has a circular clock face with an circumference of 144 pi ft
    10·2 answers
  • rogers father knows that dial it up sells data plans at $16 for 2 gigabytes and ring sells data plans at $9 for 1 gigabytes
    13·1 answer
  • What is the area of a rectangle with vertices at ​ (−4, 0) ​, ​ (−3, 1) ​ , (0, −2) , and (−1, −3) ?
    5·1 answer
  • Please help with this question I will give points and brainliest thank you!
    13·1 answer
  • 3a. The distance around a circular track.<br> Circumference<br> Area<br> HELP ASAP
    8·1 answer
  • HELP PLESEEEEEEEEEE
    7·2 answers
  • 20 points, please help I really bloody need it
    7·1 answer
  • Josh And ash order 2 whole pizzas to eat.Josh ate 5/8 slices of pizza and ash ate 6/8 slices of pizza.Who much pizza is still le
    13·1 answer
  • Can you identify the like terms in this expression: 4x+9+3y+x
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!