Can yo solve this ones, please? in adittion, can you put answers and the process. The topic are area down the curve
Answers
1) The net area between the two functions is 2.
2) The net area between the two functions is 4/3.
3) The net area between the two functions is 17/6.
4) The net area between the two functions is approximately 1.218.
5) The net area between the two functions is 1/2.
How to determine the area between two functions by definite integrals
The area between the two curves is determined by definite integrals for a interval between two values of x. A general formula for the definite integral is presented below:
[tex]A = \int\limits^{b}_{a} {[f(x) - g(x)]} \, dx[/tex] (1)
Where:
a - Lower limitb - Upper limitf(x) - "Upper" functiong(x) - "Lower" functionNow we proceed to solve each integral:
Case I - [tex]f(x) = \sqrt{x}[/tex] and [tex]g(x) = x^{2}[/tex]The lower and upper limits between the two functions are 0 and 1, respectively. The definite integral is described below:
[tex]A = \int\limits^1_0 {x^{0.5}} \, dx - \int\limits^1_0 {x^{2}} \, dx[/tex]
[tex]A = 2\cdot (1^{1.5}-0^{1.5})-\frac{1}{3}\cdot (1^{3}-0^{3})[/tex]
[tex]A = 2[/tex]
The net area between the two functions is 2. [tex]\blacksquare[/tex]
Case II - [tex]f(x) = -4\cdot x[/tex] and [tex]g(x) = x^{2}+3[/tex]The lower and upper limits between the two functions are -3 and -1, respectively. The definite integral is described below:
[tex]A = - 4 \int\limits^{-1}_{-3} {x} \, dx - \int\limits^{-1}_{-3} {x^{2}} \, dx - 3 \int\limits^{-1}_{-3}\, dx[/tex]
[tex]A = -2\cdot [(-1)^{2}-(-3)^{2}]-\frac{1}{3}\cdot [(-1)^{3}-(-3)^{3}] -3\cdot [(-1)-(-3)][/tex]
[tex]A = \frac{4}{3}[/tex]
The net area between the two functions is 4/3. [tex]\blacksquare[/tex]
Case III - [tex]f(x) = x^{2}+2[/tex] and [tex]g(x) = -x[/tex]The definite integral is described below:
[tex]A = \int\limits^{1}_{0} {x^{2}} \, dx + 2\int\limits^{1}_{0}\, dx + \int\limits^{1}_{0} {x} \, dx[/tex]
[tex]A = \frac{1}{3}\cdot (1^{3}-0^{3}) + 2\cdot (1-0) +\frac{1}{2}\cdot (1^{2}-0^{2})[/tex]
[tex]A = \frac{17}{6}[/tex]
The net area between the two functions is 17/6. [tex]\blacksquare[/tex]
Case IV - [tex]f(x) = e^{-x}[/tex] and [tex]g(x) = -x[/tex]The definite integral is described below:
[tex]A = \int\limits^{0}_{-1} {e^{-x}} \, dx+ \int\limits^{0}_{-1} {x} \, dx[/tex]
[tex]A = -(e^{0}-e^{1}) + \frac{1}{2}\cdot [0^{2}-(-1)^{2}][/tex]
[tex]A \approx 1.218[/tex]
The net area between the two functions is approximately 1.218. [tex]\blacksquare[/tex]
Case V - [tex]f(x) = \sin 2x[/tex] and [tex]g(x) = \sin x[/tex]This case requires a combination of definite integrals, as f(x) may be higher that g(x) in some subintervals. The combination of definite integrals is:
[tex]A = \int\limits^{\frac{\pi}{3} }_0 {\sin 2x} \, dx - \int\limits^{\frac{\pi}{3} }_{0} {\sin x} \, dx + \int\limits^{\frac{\pi}{2} }_{\frac{\pi}{3} } {\sin x} \, dx -\int\limits^{\frac{\pi}{2} }_{\frac{\pi}{3} } {\sin 2x} \, dx[/tex]
[tex]A = -\frac{1}{2}\cdot (\cos \frac{2\pi}{3}-\cos 0)+(\cos \frac{\pi}{3}-\cos 0 ) -(\cos \frac{\pi}{2}-\cos \frac{\pi}{3} )+\frac{1}{2}\cdot (\cos \pi-\cos \frac{2\pi}{3} )[/tex]
[tex]A = \frac{1}{2}[/tex]
The net area between the two functions is 1/2. [tex]\blacksquare[/tex]
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Related Questions
What is the f(3) for:
F (x) = 2x^2 + 5 (x-2)
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18+5
23
That should be it
could i have some quick help factoring trinomials?
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Solution 1
6x² + 34x -126x² + 36x -2x -126x(x+6)-2(x+6)(6x-2)(x+6)Solution 2
48c²-160c+10012c² - 40c + 2512c² - 30c -10c + 256c(2c-5) -5(2c-5)(6c-5)(2c-5)Solution 3
-6x-51xy+27xy²3x(-2-17y+9y²)3x(-2-18y+y+9y²)3x(-2(1+9y)+y(1+9y))3x(9y+1)(y-2)#1
6x²+34x-126x²+36x-2x-126x(x+6)-2(x+6)(x+6)(6x-2)#2
48c²-160c+100Cancel by 4
12c²-40c+2512c²-30c-10c+25(2c-5)(6c-5)#3
-6x-51xy+27xy²3x(-2x-17y+9y²)Write an equation of the line in slope-intercept form.
y =
Answers
Therefore the equation is
y = - 4x / 3
PLEASE HELP ASAP DUE TOMORROW
Answers
The area of the shaded part of the given figure is 60 square inches'
How to calculate the area of a composite shape.The given figure is made up of a rectangle and 2 similar triangles
Area of the shaded part = Area of rectangle + area of 2 triangles
From the figure
Area of rectangle = 12 * 4 = 48 square in
Area of one triangle = 0.5(6)(4) = 12 square in
Area of the figure = 48 + 12
Area of the figure = 60 square inches'
Hence the area of the shaded part is 60 square inches.
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ents
Suppose a furniture builder has two models of a bookcase: standard and artisan. The standard
model requires 4 hours to assemble and 2 hours for finishing touches. The artisan model requires 2
hours to assemble and 2 hours for finishing touches. Based on their current staffing, they can
manage a maximum number of assembly hours available is 48 per day, and the maximum number
of finishing hours available is 44 per day.
Let x = the number of standard model bookcases produced per day and y = the number of artisan
model bookcases produced per day.
Write the system of inequalities that represents the maximum number of bookcases that can be
produced in one day.
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Answer:
48 ≥ 4x + 2y
44 ≥ 2x + 2y
First, we will look at assembling hours.
"The standard model requires 4 hours to assemble [and] the artisan model requires 2 hours to assemble"
We also know they have 48 hours per day for assembly, x is standard model and y is artisan model.
48 = 4x + 2y
Lastly, they do not need to make that many, but they can so we will use greater than or equal to.
48 ≥ 4x + 2y
Now let us look at finishing hours.
"The standard model requires ... 2 hours for finishing touches. The artisan model requires ... 2 hours for finishing touches."
We also know they have 44 hours per day for assembly, x is standard model and y is artisan model.
44 = 2x + 2y
Again, they do not need to make that many, but they can so we will use greater than or equal to.
44 ≥ 2x + 2y
5x-2y=42
-3x+2y=-26
which of the following shows the results of the two equation added together?
Answers
Answer:
Step-by-step explanation:
When we add the two equaions, y will be cancelled becaue -2y + 2y = 0.
Thus we can find the value of x.
5x - 2y = 42 -----------(I)
-3x + 2y = -26 {Now add}
2x = 16
x = 16/2
x = 8
Solve this system of equations. -2x-4y=-12
Answers
Answer:
x = 6 and y = 3
Step-by-step explanation:
Your equation: -2x-4y=-12
__________________________________________________
First, we'll solve for x.
You need to divide -2x on both sides.
**We'll exclude/forget the -4y since we're not dealing with it right now.
-2x = -12
x = 6
When dividing with negatives, if both of the numbers are negatives they shall cancel and become positive.
-12 divided by -2 is 6 positive.
Therefore, x = 6
_______________________________________________________
Next, we'll solve for y
The same thing as last, we'll exclude our -2x since we're not dealing with it anymore.
-4y = -12
-12 divided by -4 is a positive answer since the two negatives cancel out.
-12/ -4 = 3
Therefore, y = 3
________________________________________________________
The proper vocabulary of the "x" and the "y" are x-intercept and y-intercept.
We just solved for both.
A bycycling club has 18 members,of which 11 are males and the rest females. What is the ratio of males to all club members
Answers
Answer:
11 : 18
Step-by-step explanation:
to figure out number of female members (not neccessary to solve this problem)
18 members = male + female members
18 members = 11 members + female members
-11 -11
---------------------------------------------------------------------
7 members = female members
ratio of males to all club members
11 : 18
Compare using inequalities <>, or
During February in Du Bois, Pennsylvania the temperature was -23 degrees at 11 am. The temperature was -6 degrees
at 7 pm.
-0)
A)
-23 >-6
B)
-23<-6
O
-6<-23
D)
-6=-23
Answers
Answer:
B. - 23 < -6
Step-by-step explanation:
Arderi Air Conditioning sells one primary model of air conditioner. Each unit of this model costs them $61.25 to produce, but it sells for $142.50 apiece. Arderi Air Conditioning employs three salespeople, each of whom earns a different commission per unit sold, as shown on the following table. Salesperson Commission/Sale Mary $36.25 Jay $28.50 Abby $25.75 Last month, Arderi Air Conditioning had a total fixed overhead cost of $7,622.25. It is known that one salesperson sold 51 units, one salesperson sold 43 units, and one salesperson sold 54 units. Which arrangement of sales would cause Arderi Air Conditioning to break even? a. Mary sells 54 units; Jay sells 51 units; Abby sells 43 units b. Mary sells 54 units; Jay sells 43 units; Abby sells 51 units c. Mary sells 43 units; Jay sells 51 units; Abby sells 54 units d. Mary sells 43 units; Jay sells 54 units; Abby sells 51 units Please select the best answer from the choices provided
Answers
The arrangement of sales which would cause Arderi Air Conditioning to break even is Mary sells 54 units; Jay sells 51 units; Abby sells 43 units.
What is a break even point?The break even point is the point at which the cost of production of an item to produce is equal to the revenue generated after selling it.
Arderi Air Conditioning sells one primary model of air conditioner. Each unit of this model costs them $61.25 to produce, but it sells for $142.50 apiece. Thus,
Cost price C=$61.25Sells price S=$142.50Arderi Air Conditioning employs three salespeople, each of whom earns a different commission per unit sold, as shown in the following table.
Salesperson Commission/Sale Mary $36.25 Jay $28.50 Abby $25.75It is known that one salesperson sold 51 units, one salesperson sold 43 units, and one salesperson sold 54 units. Thus, the total AC sold is,
[tex]n=51+43+54\\n=148[/tex]
Now, the selling price is $142.50. Thus, the revenue after selling 148 units is,
[tex]R=148\times142.50\\R=21090[/tex]
The cost price is $61.25. Thus, the cost of production of 148 units is,
[tex]R=148\times61.25\\R=9065[/tex]
Last month, Arderi Air Conditioning had a total fixed overhead cost of $7,622.25. Suppose, Mary sells 43 units; Jay sells units; Abby sells 54 units. Thus, the total cost,
[tex]C_t=7622.25++9065+43\times36.25 +51\times28.50 +54\times25.75\\ C_t=21090[/tex]
The total cost is equal to the total revenue. This point is break even point.
Thus, the arrangement of sales which would cause Arderi Air Conditioning to break even is Mary sells 54 units; Jay sells 51 units; Abby sells 43 units.
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Answer:
c.
Mary sells 43 units; Jay sells 51 units; Abby sells 54 units
mollie wants to measure the capacity of the kitchen sink she has a 1 L container and a 10 mL container which should she use
Answers
Answer:
1 L
Step-by-step explanation:
Kitchen sinks are pretty large in terms of volume in Liters
use the 1 L container
Simplify the expression.
(m^-1 m^5/m^-2)^-3
a)- 3m^4/m^2
b)-m^216
c)m^18
d)1/m^18
Answers
Explanation:
(m^-2/m-1m5)^3
m^-6/m^-3m^15
1/m^6 / m^15/m^3
1/m^6 / m^12
1/m^6 (1/m^12)
1/m^18
let me know if you want clarification
Answer:
[tex]D)\frac{1}{m^{18} }[/tex]
Step-by-step explanation:
Multiply [tex]m^{-1}[/tex] by [tex]m^{5}[/tex] by adding the exponents.
Use the power rule [tex]a^{m} a^{n} =a^{m+n}[/tex] to combine exponents.
[tex](\frac{m^{-1+5} }{m^{-2} } )^{-3} \\[/tex]
Add -1 and 5.
[tex](\frac{m^{4} }{m^{-2} } )^{-3}[/tex]
Move [tex]m^{-2}[/tex] to the numerator using the negative exponent rule [tex]\frac{1}{b^{-n} } =b^{n}[/tex].
[tex](m^{4} m^{2} )[/tex]
Multiply [tex]m^{4}[/tex] by [tex]m^{2}[/tex] by adding the exponents.
Use the power rule [tex]a^{m} a^{n} =a^{m+n}[/tex] to combine exponents.
[tex](m^{4+2} )^{-3}[/tex]
Add 4 and 2.
[tex](m^{6} )^{-3}[/tex]
Multiply the exponents in [tex](m^6)^{-3}[/tex]
Apply the rule and multiply exponents, [tex](a^m)^n=a^{mn}[/tex].
[tex]m^{6*-3}[/tex]
Multiply 6 by -3.
[tex]m^{-18}[/tex]
Rewrite the expression using the negative exponent rule [tex]b^{-n} =\frac{1}{b^{n} }[/tex].
[tex]\frac{1}{m^{18} }[/tex]
Can somebody help me I’m confused on how solving the equation
Answers
Answer:
You answer is.
(d)YesA = -9Step-by-step explanation:
Example Problem.
y = 2^ (x - h) + k
y = 8^(x-0) - 9
The h = 0 so there no transition left/right.
There is a k = -9 which means transition down/up but it is a negative so down.
Domain: all real number ( -inf , +inf)
Range: (k, inf) -> (-9, +inf)
k = -9 is also y=-9 that the graph can't pass.
The percentage error in measuring a clothe is 40% if the error committed is 10cm what is the original Value of the measurement??
Answers
cross multiply:
40% - 10
100% - x
so 40x = 1000
x=25
Eight pounds of peanuts cost $24.00. Six pounds of walnuts cost half as much.
Answers
Answer:
1 pound of peanuts cost 3 dollars
1 pound of wallnuts costs 2 dollars
Step-by-step explanation:
24/6=4
12/6=2
Simplify this fraction to the lowest terms 14/12
Answers
Answer:
1 1/6 or 7/6
Step-by-step explanation:
Divide both 14 and 12 by 2
What is the vertex of this quadratic function? y=6(x+1)2-9 Please Help!
Answers
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ y = 6(x+1)^2-9\implies y = 6[x-(\stackrel{h}{-1})]^2\stackrel{k}{-9}\qquad \qquad \stackrel{vertex}{(-1~~,~~-9)}[/tex]
Identify a set of parallel lines
Answers
Answer:
D
Step-by-step explanation:
Since EF is perpendicular to both AB and CD, that makes AB and CD parallel.
Answer: D
help me help me help me
Answers
Answer:
read step by step
Step-by-step explanation:
6 is +4.
19, 23, 27, 31
7 is all perfect square numbers
25, 36, 49, 64
8 is x2.
32, 64, 128, 256
9 is each number multiplied by the next. ex: 1x2=2, 2x3+6, 3x4=12
so the next few would be 30, 42, 56, 72
Find the quotient of 3/5 and 2/3
Give your answer as a fraction in its simplest form.
Answers
I’m confused can someone help?
Answers
Answer:
(a) check the first one, and the second one
(b) check the last one
Step-by-step explanation:
This is quite easy actually.
(A)3x+24 = 3 * x + 3 * 8
3(x+8) using distribute property.
3x + 24
You cannot simplify 3x+24 any further
And 3(8x+1) just doesn't work
since it's multiplying
The "*" is an X sign
(B)The first, second, and third are not correct
But the last one is.
1) Zero helps mark directions in value Choose ALL contexts that correctly describes zero.
A) elevation:0 feet is called the ground floor
B bank account below 5D is a
negative balance
C)electricity an object that has 0 charge is neutral
D) buildings on an elevator, o represents the sea level
temperature temperature above is a negative temperature
E) temperature : temperature above 0 is a negative temperature
Answers
Answer: A,C,D
Step-by-step explanation:
Answer:
bank account and electricity
Step-by-step explanation:i tried the other one and it was all incorrect
Help plssssssssssssssssssss I NEED THIS TODAY!! PLS
Answers
Answer:
The first 1 is the answer (a)
Step-by-step explanation:
2. Find the probability of throwing a 10 with a pair of dice and choosing a red from a standard deck of cards.
Answers
Answer:
Step-by-step explanation:
You can get 10 with a pair of dice with:
4 + 6, 6 + 4, 5 + 5
out of a possibile 36 results
There are 52 cards in a standard deck of cards. Reds make up half of them (hearts and diamonds) , meaning theres a 50/50 chance of pulling red
10/36 * 1/2 = 5/36 chance of throwing 10 + pulling red
Laurence earned scores of 87, 80, 75, and 85 on four biology tests. What score must he earn on his next test to have an 85 average?
A. 95
B. 98
C. 80
D. 85
Answer: 98
Answers
To get an 85 average, Laurence needs a score of 25 on his upcoming biology exam.
What is math average?
The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics.
When calculating the average for a set of data, we first sum up all the values and divide the result by the total number of values.
Average = (sum of values) / (number of values)
The total of Laurence's marks on the first four biology exams can be calculated using the following formula
Sum of scores = 87 + 80 + 75 + 85
= 327
We need the total of all five scores to be 85 x 5 = 425 in order to obtain an average of 85 for five tests.
Therefore, We need the total of all five scores to be 85 x 5 = 425 in order to obtain an average of 85 for five tests.
Next score = (sum of all five scores) - (sum of first four scores)
= (85 x 5) - 327
= 25
Therefore, To get an 85 average, Laurence needs a score of 25 on his upcoming biology exam.
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the circumference of the hub cap of a tire is 79.38 cm. Find the area of this hub cap. use 3.14 for pi
Answers
Answer:
ans 19785.719
Step-by-step explanation:
formula πr^2
In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 53.3 inches, and standard deviation of 1 inches. What is the probability that the height of a randomly chosen child is between 53.3 and 55.3 inches
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Answer:
a) We need to find p(x<68.15)
Standardize x to z, we have, z = (68.15-μ)/σ
=(68.15-57)/8.1
=1.38
Reading from standard normal tables,
p(z<1.38) =0.9162.
b) We need to find p(x>54.4)
Standardize x to z, we have, z = (54.4-μ)/σ
=(54.4-57)/8.1
=-0.32
Reading from standard normal tables,
p(z>-0.32) = 0.6255
Please somebody help me. I’m begging.
Answers
Answer:
d=1
Step-by-step explanation:
d=2*r
r=(1/2)
d=2*(1/2)=1
What is the Area of the circle
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Area of circle :
[tex]\qquad \sf \dashrightarrow \:\pi r {}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: \pi\times (3.5) {}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:12.25 \: \pi[/tex]
[tex]\qquad \sf \dashrightarrow \:38.465 \: \: unit {}^{2} [/tex]
Answer:
38.465 units²
Step-by-step explanation:
The formula to find the area of a circle is πr². Simply substitute the radius in the formula to find the area.
Substituting the radius in the formula:
⇒ πr²
⇒ π(3.5)² [Radius (r) = 3.5 units]
Evaluating the area:
⇒ π x 12.25
⇒ 3.14 x 12.25
⇒ 38.465 units²
ANSWER QUICK FOR A. AND B. !
Answers
Answer: a=4
b=1600x
Step-by-step explanation: