There are 16 tablespoons in one cup. Which table correctly relates the number of cups to the number of tablespoons?
Answers
Answer:
The first table.
Step-by-step explanation:
1 cup = 1 * 16 = 16 tablespoons
2 = 2 * 16 = 32
3 = 3*16 = 48
4 = 4*16 = 64 and so on....
Related Questions
this is so confusing can anyone help?
Answers
Answer:
C.
Step-by-step explanation:
For an angle to be supplementary to another angle, they must be equal to 180. Angles 6, 10, 13, and 9 are all supplementary to angle 16. Although there are more choices in different answers it wouldn't work with question, so C is the right answer.
Angle 16 is supplementary to angle 9 by the Same Side Interior Angles Theorem, which makes it supplementary to angle 10 by the Alternate Exterior Angles Theorem, which is also congruent to angle 13 by the Vertical Angles Theorem, which is also supplementary to angle 6 by the Alternate Exterior Angles Theorem.
Help pls with answer!!!Rewrite the function in the given form.
Answers
Answer:
[tex]g(x) = \frac{-2}{x-1}+5\\\\[/tex]
The graph is shown below.
=========================================================
Explanation:
Notice that if we multiplied the denominator (x-1) by 5, then we get 5(x-1) = 5x-5.
This is close to 5x-7, except we're off by 2 units.
In other words,
5x-7 = (5x-5)-2
since -7 = -5-2
Based on that, we can then say,
[tex]g(x) = \frac{5x-7}{x-1}\\\\g(x) = \frac{5x-5-2}{x-1}\\\\g(x) = \frac{(5x-5)-2}{x-1}\\\\g(x) = \frac{5(x-1)-2}{x-1}\\\\g(x) = \frac{5(x-1)}{x-1}+\frac{-2}{x-1}\\\\g(x) = 5+\frac{-2}{x-1}\\\\g(x) = \frac{-2}{x-1}+5[/tex]
This answer can be reached through alternative methods of polynomial long division or synthetic division (two related yet slightly different methods).
-------------------------
Compare the equation [tex]g(x) = \frac{-2}{x-1}+5\\\\[/tex] to the form [tex]g(x) = \frac{a}{x-h}+k\\\\[/tex]
We can see that
a = -2h = 1k = 5The vertical asymptote is x = 1, which is directly from the h = 1 value. If we tried plugging x = 1 into g(x), then we'll get a division by zero error. So this is why the vertical asymptote is located here.
The horizontal asymptote is y = 5, which is directly tied to the k = 5 value. As x gets infinitely large, then y = g(x) slowly approaches y = 5. We never actually arrive to this exact y value. Try plugging in g(x) = 5 and solving for x. You'll find that no solution for x exists.
The point (h,k) is the intersection of the horizontal and vertical asymptote. It's effectively the "center" of the hyperbola, so to speak.
The graph is shown below. Some points of interest on the hyperbola are
(-1,6)(0,7) .... y intercept(1.4, 0) .... x intercept(2, 3)(3, 4)Another thing to notice is that this function is always increasing. This means as we move from left to right, the function curve goes uphill.
an amount of R3000, Is invested to three years at simple interest rate and it earned R905 interest. determine the simple interest rate at which the money was invested
Answers
Answer:
Step-by-step explanation:
P=R3000.00
T=3 years
SI=R905
SI=P\times R\times T\\R905=R3000\times \frac{r}{100}\times 3SI=P×R×T
R905=R3000×
100
r
×3
R905=\frac{R9000r}{100}R905=
100
R9000r
R905=\frac{R905}{R90}R905=
R90
R905
r=\frac{R905}{R90.}r=
R90.
R905
r=10.06\%r=10.06%
William invested $12,000 in a bank account that pays 9 percent simple interest. His friend invested the same amount at another bank that pays 8 percent interest compounded quarterly. These two functions, where t is time in years, represent the value of the investments: f(t) = 12(1.02)4t g(t) = 12(1.09)t The functions are graphed, and the point of intersection lies between 0.5 and 1.2. Based on the table, approximately how long will it be until both investments have the same value? Value of t f(t) = 12(1.02)4t g(t) = 12(1.09)t 0.5 12.48 6.54 0.6 12.58 7.84 0.7 12.68 9.16 0.8 12.79 10.46 0.9 12.89 11.87 1.0 12.99 13.08 1.1 13.09 14.39 1.2 13.20 15.70 A. 0.9 year B. 1.0 year C. 1.1 years D. 1.2 years
Answers
===========================================================
Explanation:
We have these two functions
f(t) = 12(1.02)^(4t)g(t) = 12(1.09)twhich represent the amounts for his friend and William in that order. Strangely your teacher mentions William first, but then swaps the order when listing the exponential function as the first. This might be slightly confusing.
The table of values is shown below. We have t represent the number of years and t starts at 0.5. It increments by 0.1
The f(t) and g(t) columns represent the outputs for those mentioned values of t. For example, if t = 0.5 years (aka 6 months) then f(t) = 12.48 and that indicates his friend has 12,480 dollars in the account.
I've added a fourth column labeled |f - g| which represents the absolute value of the difference of the f and g columns. If f = g, then f-g = 0. The goal is to see if we get 0 in this column or try to get as close as possible. This occurs when we get 0.09 when t = 1.0
So we don't exactly get f(t) and g(t) perfectly equal, but they get very close when t = 1.0
It turns out that the more accurate solution is roughly t = 0.9925 which is close enough. I used a graphing calculator to find this approximate solution.
It takes about a year for the two accounts to have the same approximate amount of money.
Answer:
B
Step-by-step explanation:
Consider the functions z = 4 e^x ln y, x = ln (u cos v), and y = u sin v.
Express dz/du and dz/dv as functions of u and y both by using the Chain Rule and by expressing z directly in terms of u and v before differentiating.
Answers
Answer:
remember the chain rule:
h(x) = f(g(x))
h'(x) = f'(g(x))*g'(x)
or:
dh/dx = (df/dg)*(dg/dx)
we know that:
z = 4*e^x*ln(y)
where:
y = u*sin(v)
x = ln(u*cos(v))
We want to find:
dz/du
because y and x are functions of u, we can write this as:
dz/du = (dz/dx)*(dx/du) + (dz/dy)*(dy/du)
where:
(dz/dx) = 4*e^x*ln(y)
(dz/dy) = 4*e^x*(1/y)
(dx/du) = 1/(u*cos(v))*cos(v) = 1/u
(dy/du) = sin(v)
Replacing all of these we get:
dz/du = (4*e^x*ln(y))*( 1/u) + 4*e^x*(1/y)*sin(v)
= 4*e^x*( ln(y)/u + sin(v)/y)
replacing x and y we get:
dz/du = 4*e^(ln (u cos v))*( ln(u sin v)/u + sin(v)/(u*sin(v))
dz/du = 4*(u*cos(v))*(ln(u*sin(v))/u + 1/u)
Now let's do the same for dz/dv
dz/dv = (dz/dx)*(dx/dv) + (dz/dy)*(dy/dv)
where:
(dz/dx) = 4*e^x*ln(y)
(dz/dy) = 4*e^x*(1/y)
(dx/dv) = 1/(cos(v))*-sin(v) = -tan(v)
(dy/dv) = u*cos(v)
then:
dz/dv = 4*e^x*[ -ln(y)*tan(v) + u*cos(v)/y]
replacing the values of x and y we get:
dz/dv = 4*e^(ln(u*cos(v)))*[ -ln(u*sin(v))*tan(v) + u*cos(v)/(u*sin(v))]
dz/dv = 4*(u*cos(v))*[ -ln(u*sin(v))*tan(v) + 1/tan(v)]
7r - 3s =26
2r - 6s =8
Answers
Answer:
r = 3 2/3
s = -0.444333
Step-by-step explanation:
Multiply the top equation by 2
14r - 6s = 52
2r - 6s = 8 Subtract the two equations
12r = 44 Divide by 12
r = 44/12
r = 3 8/12
r = 3 2/3
2r - 6s = 8
2*(2 2/3) - 6s = 8
2*2.6667 - 6s = 8
5.3334 - 6s = 8 Subtract 5.3334 from both sides.
- 6s = 2 2/3 Divide by - 6
s = - 0.4443333
Dada la función f(x)=1+6Sen(2x+π/3) . Halle: Período, amplitud y desfase (1.5 puntos) Dominio y rango de la función (1.5 puntos) Grafique la función trigonométrica (2 puntos)
Answers
Dada una ecuación de la forma
y = A sin(B(x + C)) + DTenemos que:
la amplitud es Ael periodo es 2π/Bel desfase es C (a la izquierda es positivo)el desplazamiento vertical es DSabemos que:
f(x)=1+6Sen(2x+π/3)
Y podemos reescribirla como:
f(x)=6Sen(2(x+π/6))+1
Siendo:
A = 6 → AmplitudT = 2π/B = 2π/2 = π → PeríodoC = π/6 → DesfaseEl dominio de un a función trigonométrica es todo el conjunto de los números reales (x ∈ R ).La imagen de una función trigonométrica de esta forma es:
y ∈ [-A+D,A+D]
y ∈ [-6+1, 6+1]
y ∈ [-5,7]
La gráfica se adjunta.
Two systems of equations are given below. For each system, choose the best description of its solution.
x - 5y = 5
-x + 5y = -5
a. The system has no solution.
b. The system has a unique solution:
(x,y) = _______
c. The system has infinitely many solutions. They must satisfy the following equation:
y = ________
Answers
Answer:
Infinitely many solutions.
They must satisfy [tex]y = \frac{1}{5}(x - 5)[/tex]
Step-by-step explanation:
Given
[tex]x - 5y = 5[/tex]
[tex]-x + 5y = -5[/tex]
Required
The best description
Add both equations
[tex]x - x - 5y + 5y = 5 - 5[/tex]
[tex]0+0 =0[/tex]
[tex]0 = 0[/tex] ---- this means that the system has infinitely many solutions.
Make y the subject in: [tex]-x + 5y = -5[/tex]
Add x to both sides
[tex]5y = x - 5[/tex]
Divide through by 5
[tex]y = \frac{1}{5}(x - 5)[/tex]
Hence, they must satisfy: [tex]y = \frac{1}{5}(x - 5)[/tex]
Find out the quotient
-72 ÷ (-2) = ?
-72 ÷ 2 = ?
72 ÷ (-2) = ?
(Thank you to whoever helps me out )
Answers
Answer/Step-by-step explanation:
✔️-72 ÷ (-2)
The division of two negative numbers will give us a positive number. i.e. - ÷ - = +
Therefore:
-72 ÷ (-2) = 36
✔️-72 ÷ 2
The division of a negative number and a positive number will give us a negative number. i.e. - ÷ + = -
Therefore:
-72 ÷ 2 = -36
✔️72 ÷ (-2)
The division of a positive number and a negative number will give us a negative number. i.e. + ÷ - = -
Therefore:
72 ÷ (-2) = -36
Select the correct answer. Which function is continuous across Its domain
Answers
Answer:
D is the answer
Step-by-step explanation:
plug the -2's in line 1 & 2 then 4 in 2 and 3
the 1&2 , and the 2 and 3 numbers have to match
Using the conditions for continuity, we find that the function D.) is continuous.
How to check if a function is continuous?A function f(x) is said to be continuous at a point x = a, in its domain if the following three conditions are satisfied:
f(a) exists (i.e. the value of f(a) is finite)the right-hand limit = left-hand limit, and both are finite.right-hand limit = left-hand limit = f(a)Since for -4 <= x < -2, -2 <= x < 4 and 4 <= x <= 8, the function f(x) is defined by straight lines , the function will be continuous for all x ≠ -2 and 4. Now for x = -2, 4, let us check all the three conditions:
A.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 + 6 = 4
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit, the function is not continuous at x = -2. No need to check further.
B.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 -2 = -4
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit, the function is not continuous at x = -2. No need to check further.
C.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 + 4 = 2
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit is equal to f(-2), the function is continuous at x = -2.
f(4) = 25 - 3*4 = 13
left hand limit = 0.5 * (4)² = 8
right hand limit = 25 - 3*4 = 13
Since, left hand limit is not equal to right hand limit, the function is not continuous at x = 4.
D.
f(-2) = 0.5 * (-2)² = 2
left hand limit = -2 + 4 = 2
right hand limit = 0.5 * (-2)² = 2
Since, left hand limit is not equal to right hand limit is equal to f(-2), the function is continuous at x = -2.
f(4) = 20 - 3*4 = 8
left hand limit = 0.5 * (4)² = 8
right hand limit = 20 - 3*4 = 8
Since, left hand limit is not equal to right hand limit is equal to f(-2), the function is continuous at x = 4.
Thus, the function is continuous.
Learn more about continuity here
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A charter school did a local beach cleanup. They collected a total of 55 pounds of plastic bottles and aluminum cans. The California refund value for plastic is $1.60 per pound and $1.28 per pound for aluminum. The school recycled a total of $77.60 worth of plastic and aluminum. How many pounds of each, plastic and aluminum, did the class collect?
Answers
Answer:
Plastic is 22.5 pounds and aluminum is 32.5 pounds.
Step-by-step explanation:
total junk = 55 pounds
Value of plastic = $ 1.60 per pound
Value of aluminum = $ 1.28 per pound
Total value= $ 77.60
Let the plastic is p and the aluminum is 55 - p.
Total cost
77.60 = 1.6 p + (55 - p) x 1.28
77.60 = 1.6 p + 70.4 - 1.28 p
7.2 = 0.32 p
p = 22.5 pounds
So, plastic is 22.5 pounds and aluminum is 32.5 pounds.
Jose bought a piece of fabric that was 5.6 meters long. From that, he cut 0.4
meter. How much fabric is left?
Answers
Answer:
Jose has 5.2 meters of fabric left.
Step-by-step explanation:
5.6 - 0.4 = 5.2
Help please. I'm stuck
Answers
Answer:
The numbers are 65, 67, and 69
Step-by-step explanation:
Hi there!
We need to find 3 consecutive odd integers.
Consecutive numbers are numbers that follow each other (ex. 1, 2, 3, 4)
We're given that 5 times the first number + 4 times the second + 3 times the third = 800
Let's make the first number x
Since the second number is consecutive to the first and odd, it will be x+2 (Why? Well, let's say x is 5. In that case, x+1=6, which is even. However, x+2=7)
Therefore, the third number is x+4 (once again, if x is 5, x+3=8, but x+4=9)
5 times the first number is 5x
4 times the second is 4(x+2)
3 times the third is 3(x+4)
And of course, that equals 800
As an equation, it'll be:
5x+4(x+2)+3(x+4)=800
open the parenthesis
5x+4x+8+3x+12=800
combine like terms
12x+20=800
Subtract 20 from both sides
12x=780
Divide by 12 on both sides
x=65
The first number is x, so the first number is 65
The second number is x+2, or 65+2=67
The third number is x+4, or 65+4=69
Hope this helps!
What is the least possible degree of a polynomial that has roots -5,1 + 4i, and -4i?
3
2
5
4
Answers
Without any extra conditions, the answer could be 3, and the simplest polynomial with the given roots would be
(x + 5) (x - (1 + 4i )) (x + 4i )
= x ³ + 4x ² + (11 - 4i ) x + 80 - 2i
If the polynomial is supposed to have only real coefficients, then any complex roots must occur along with their complex conjugates:
(x + 5) (x - (1 + 4i )) (x - (1 - 4i )) (x + 4i ) (x - 4i )
= x ⁵ + 3x ⁴ + 23x ³ + 133x ² + 112x + 1360
and then the degree would be 5.
Plz help. Last one today. 20 points. Thx!
Answers
the line that is negative is dashed meaning the symbol isn’t less then or equal to the symbol is just less than! that’s why it’s not a! because the other line isn’t dotted, which means the equation for the line is y is less than or equal to something
* Insert a digit to make numbers that are divisible by 6 if it is possible:
234_6
Answers
Answer:
i put in 3 to make 23436 because 36 is divisible by 6
What is the sum of 4th squared number and the 2nd cube number
Answers
Answer:
mark me as brinalist if answers are correct
3. A)Find the next number in the sequence.
$1,27, 9, 3, _1_
B) Is the sequence arithmetic, geometric, or neither?
Help me find this answer please
Answers
9514 1404 393
Answer:
1/3; geometric
Step-by-step explanation:
Apparently, your sequence is ...
81, 27, 9, 3, 1, ...
The differences between these numbers vary, but the ratio of each to the one before is a constant:
27/81 = 9/27 = 3/9 = 1/3
The sequence is geometric with a common ratio of 1/3. The next number in the sequence is (1)(1/3) = 1/3.
What is the value of x in the diagram below? If necessary, round your answer
to the nearest tenth of a unit.
Answers
9514 1404 393
Answer:
A. 7.2
Step-by-step explanation:
In this geometry, all of the right triangles are similar. This means corresponding sides have the same ratio.
short side/hypotenuse = x/12 = 12/20
Multiplying by 12 gives ...
x = 12(12/20) = 144/20
x = 7.2
anyone please lol ?
Answers
Answer:
The circumference and diameter of a circle
Step-by-step explanation:
Proportional relationships can be written as [tex]y=kx[/tex], where [tex]k[/tex] is some constant of proportionality. The formula for a circumference of a circle can be written as [tex]C=d\pi[/tex], where [tex]d[/tex] is the diameter of the circle. Therefore, the constant of proportionality is [tex]\pi[/tex] and the circumference and diameter of a circle are in a proportional relationship.
express the ratio 60cm to 20m in the form 1:n
Answers
Answer:
1:1/3
Step-by-step explanation:
60:20
6:2
1:1/3
n=1/3
Brainliest please~
The value of n=100/3
As per given the value of 1m 100cm
then the ratio of value be 60/2000 is equal to the 1/(2000/60) 1/(100/3) on compare with 1:n then the Value be
n=100/3
What does it mean to express it as a ratio?
In mathematics, a ratio indicates how often one number contains another. For example, if you have 8 oranges and 6 lemons in a fruit bowl, the ratio of oranges to lemons will be 8: 6 (that is, 8: 6, or 4: 3).
For example, if you have one boy and three girls, you can write the ratio as follows: 1: 3 (every boy has 3 girls) 1/4 is a boy and 3/4 is a girl. 0.25 is a boy (by dividing 1 by 4)
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2. Commission: A car saleswoman earns a
commission of 7% on each car she sells. How
much did she earn on the sale of a car for
$12,500?
Answers
Answer:
Step-by-step explanation:
commission = 0.7% of $12,500
= 0.007×$12,500
= $87.5
the volume of pyramid a is the volume of pyramid b. if the heigh of pyramid b increases to twice that of pyramid a the new volume of pyramid b the volume of pyramid a
Answers
Answer:
12.259-12.25 890654321
The function f is defined by f(x)=2x+5/x+4 find f (3x)
Answers
Answer:
[tex]\displaystyle f(3x) = \frac{6x + 5}{3x + 4}[/tex]
General Formulas and Concepts:
Algebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = \frac{2x + 5}{x + 4}[/tex]
Step 2: Find
Substitute in x [Function f(x)]: [tex]\displaystyle f(3x) = \frac{2(3x) + 5}{3x + 4}[/tex]Simplify: [tex]\displaystyle f(3x) = \frac{6x + 5}{3x + 4}[/tex]What is equal to 30- 6v - 13w
Answers
Hope this helps !!!!!
class 7th chapter: Simple Equation
The solution of the equation p-1 =20 is -------- *
a) 19
b) 20
c) 21
Answers
Answer:
C
Step-by-step explanation:
p=20+1
The diagram shows triangle ABC.
С
Work out the sizes of angles x, y and z.
40°
110°
х
Z
A
В
Answers
Answer:
x=70
y=30
z=20
Step-by-step explanation:
x=180-110 (angles on a straight line)
y=180-110-40 (angle sum of triangle)
z= 180-90-70 (angle sum of triangle)
Answer:
x=70°
y=30°
z=20°
Step-by-step explanation:
x=180°-110°(anlges on a straight line)
x=70°
y+110°+40°=180°(sum of angles of triangle)
y+150°=180°
y=180°-150°
y=30°
z+x+90°=180°(sum of angles of triangle)
z+70°+90°=180°
z+160°=180°
z=180°-160°
z=20°
A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 310.
(a) Find an expression for the number of bacteria after
hours.
(b) Find the number of bacteria after 3 hours.
(c) Find the rate of growth after 3 hours.
(d) When will the population reach 10,000?
Answers
Answer:
a) The expression for the number of bacteria is [tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex].
b) There are 2975 bacteria after 3 hours.
c) The rate of growth after 3 hours is about 3365.3 bacteria per hour.
d) A population of 10,000 will be reached after 4.072 hours.
Step-by-step explanation:
a) The population growth of the bacteria culture is described by this ordinary differential equation:
[tex]\frac{dP}{dt} = k\cdot P[/tex] (1)
Where:
[tex]k[/tex] - Rate of proportionality, in [tex]\frac{1}{h}[/tex].
[tex]P[/tex] - Population of the bacteria culture, no unit.
[tex]t[/tex] - Time, in hours.
The solution of this differential equation is:
[tex]P(t) = P_{o}\cdot e^{k\cdot t}[/tex] (2)
Where:
[tex]P_{o}[/tex] - Initial population, no unit.
[tex]P(t)[/tex] - Current population, no unit.
If we know that [tex]P_{o} = 100[/tex], [tex]t = 1\,h[/tex] and [tex]P(t) = 310[/tex], then the rate of proportionality is:
[tex]P(t) = P_{o}\cdot e^{k\cdot t}[/tex]
[tex]\frac{P(t)}{P_{o}} = e^{k\cdot t}[/tex]
[tex]k\cdot t = \ln \frac{P(t)}{P_{o}}[/tex]
[tex]k = \frac{1}{t}\cdot \ln \frac{P(t)}{P_{o}}[/tex]
[tex]k = \frac{1}{1}\cdot \ln \frac{310}{100}[/tex]
[tex]k\approx 1.131\,\frac{1}{h}[/tex]
Hence, the expression for the number of bacteria is [tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex].
b) If we know that [tex]t = 3\,h[/tex], then the number of bacteria is:
[tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex]
[tex]P(3) = 100\cdot e^{1.131\cdot (3)}[/tex]
[tex]P(3) \approx 2975.508[/tex]
There are 2975 bacteria after 3 hours.
c) The rate of growth of the population is represented by (1):
[tex]\frac{dP}{dt} = k\cdot P[/tex]
If we know that [tex]k\approx 1.131\,\frac{1}{h}[/tex] and [tex]P \approx 2975.508[/tex], then the rate of growth after 3 hours:
[tex]\frac{dP}{dt} = \left(1.131\,\frac{1}{h} \right)\cdot (2975.508)[/tex]
[tex]\frac{dP}{dt} = 3365.3\,\frac{1}{h}[/tex]
The rate of growth after 3 hours is about 3365.3 bacteria per hour.
d) If we know that [tex]P(t) = 10000[/tex], then the time associated with the size of the bacteria culture is:
[tex]P(t) = 100\cdot e^{1.131\cdot t}[/tex]
[tex]10000 = 100\cdot e^{1.131\cdot t}[/tex]
[tex]100 = e^{1.131\cdot t}[/tex]
[tex]\ln 100 = 1.131\cdot t[/tex]
[tex]t = \frac{\ln 100}{1.131}[/tex]
[tex]t \approx 4.072\,h[/tex]
A population of 10,000 will be reached after 4.072 hours.
Joyce paid $60.00 for an item at the store that was 50 percent off the original price. What was the original price?
$
Give your answer to the nearest cent.
Answers
%50 equals half so multiply 60x2=120
Find the area enclosed by y1 = (x - 1)3 and y2 = x -1.
I wanted to double check the answer. The professor got something completely different.
Find area between two curves
Answers
9514 1404 393
Answer:
0.5
Step-by-step explanation:
The "enclosed area" can be taken to mean different things. Here, we consider it to mean the finite area bounded between the two curves, regardless of which curve is higher value than the other.
The area is bounded on the interval [0, 2]. On half that interval y1 > y2; on the other half, y2 > y1. This means the integral of the area between the curves will be different for one part of the interval than for the other. (The curves are symmetric about the point (1, 0).)
The area on the interval [0, 1] is given by the integral ...
[tex]\displaystyle\int_0^1{(y_1-y_2)}\,dx=\int_0^1{((x-1)^3-(x-1))}\,dx\\\\=\int^1_0{(x(x-1)(x -2))}\,dx=\left.(\frac{x^4}{4}-x^3+x^2)\right|^1_0=\boxed{\frac{1}{4}}[/tex]
The area on the interval [1, 2] is the integral of the opposite integrand, but has the same value.
The positive area over the whole interval from 0 to 2 is 1/4+1/4 = 1/2.
If you simply integrate y2-y1 or y1-y2 over that interval, the result is 0.
