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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>
Answer:
12 centimeters
Step-by-step explanation:
96=6L+2W
6+2=8
96/8=12
Answer:
Option d is correct.
Step-by-step explanation:
The point of inflection of a function y = f(x) at a pointy c is given by f''(c) = 0.
Now, the given function is
Differentiating with respect to x on both sides we get,
Again, differentiating with respect to x on both sides we get,
So, the condition for point of inflection at point c is
k''(c) = 0 = - sin c + 2 sin c cos c
⇒ sin c(2cos c - 1) = 0
⇒ sin c = 0 or 
⇒ c = 0 or 
Therefore, option d is correct. (Answer)
Answer: We have many options:
1) 15 artists, with 2 paintings per artist.
2) 10 artists, with 3 paintings per artist.
3) 6 artists, with 5 paintings per artist.
4) 5 artists, with 6 paintings per artist.
5) 3 artists, with 10 paintings per artist.
6) 2 artists, with 15 paintings per artist.
by different artists, then the number of artists must be more than 1.
each artist shows more than 1 painting: >1 painting/artist
(30 oil paintings)/(2 paintings/artist)=15 artists
(30 oil paintings)/(3 paintings/artist)=10 artists
(30 oil paintings)/(5 paintings/artist)=6 artists
(30 oil paintings)/(6 paintings/artist)=5 artists
(30 oil paintings)/(10 paintings/artist)=3 artists
(30 oil paintings)/(15 paintings/artist)=2 artists
Answer: HCA OR ACH
Step-by-step explanation:
