Which is the area between the x-axis and y=x from x=1 to x=5
Answers
Answer:
[tex]\displaystyle A = 12[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
FunctionsFunction NotationGraphingCalculus
Integrals
Definite IntegralsArea under the curveIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
y = x
Interval: x = 1 to x = 5
Step 2: Sort
Graph the function. See Attachment.
Bounds of Integration: [1, 5]
Step 3: Find Area
Substitute in variables [Area of a Region Formula]: [tex]\displaystyle A = \int\limits^5_1 {x} \, dx[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle A = \frac{x^2}{2} \bigg| \limits^5_1[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle A = 12[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
Related Questions
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answers
Answer:
x =48.6
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp side / hypotenuse
sin x = 54 /72
Taking the inverse sin of each side
sin ^ -1( sin x) =sin ^-1 ( 54/72)
x = 48.59037789
To the nearest tenth
x =48.6
Answer:36.9
Step-by-step explanation:
Use slope to determine if lines AB and CD are parallel, perpendicular, or neither. A(0,2), B(5,4), C(1,8), and D(3,3). What is the slope of line CD? Enter as a ratio in its lowest terms.
Answers
Answer:
Perpendicular, CD has a slope of -5/2
Step-by-step explanation:
Parallel lines have the same slope, perpendicular have slopes that are negative reciprocals, or in other words if one slope is m then the other's slope is -1/m and if it is neither fo those then it is neither parallel or perpendicular. Also, if two lines have the same slope you have to make sure they are not the same line.
Now, to find the slope when you have two points you use the formula (y2 - y1)/(x2 - x1), where the points are (x1, y1) and (x2, y2). You can make either point point 1 or point 2. Just make sure x1 and y1 are from one point and x2 and y2 are from the other point.
So the two lines are AB and CD. Since the question asks I will start with CD. The points are (1,8) and (3,3) So I will call C point 1 and D point 2.
(y2 - y1)/(x2 - x1)
(3 - 8)/(3 - 1)
-5/2
Thankfully this is lowest terms.
Now for AB. A will be point 1 and B will be point 2
(y2 - y1)/(x2 - x1)
(4-2)/(5-0)
2/5
So they are not the same, so what if you take negative 1 over one of the slopes.
well. -1/(2/5) = -5/2
So these are perpendicular.
If you would like an explanation for how to find the full equation of a line I can explain that.
Does the point (7, 2) satisfy the equation y = x - 5? yes no
Answers
Yes
Replace x in the equation with the x in the solution and see if t equals the y in the solution:
Y = 7-5 = 2
The answer is yes.
HELPP!
The functions f(x) and g(x) are described using the following equation and table:
f(x)=-4(1.09)x
Answers
Given:
The function is:
[tex]f(x)=-4(1.09)^x[/tex]
The table of values for the function g(x).
To find:
The equation that best compares the y-intercepts of f(x) and g(x).
Solution:
We have,
[tex]f(x)=-4(1.09)^x[/tex]
Putting [tex]x=0[/tex], we get
[tex]f(x)=-4(1.09)^0[/tex]
[tex]f(x)=-4(1)[/tex]
[tex]f(x)=-4[/tex]
So, the y-intercept of the function f(x) is -4.
From the given table of values, it is clear that the function f(x) passes through the point (0,-4). So, the y-intercept of the function g(x) is -4.
The y-intercept of f(x) is equal to the y-intercept of g(x).
Therefore, the correct option is A.
Answer:
A) The y-intercept of f(x) is equal to the y-intercept of g(x).
What is the answer for this equation
Answers
Answer:
the answer is -5,-7,-10,-14,-19
Take -4 + 3a 2 from 7a - a 2.
Answers
Answer:
Refer to the attachment!~
cho hàm số f(x), đồ thị hàm số y=f'(x) là đường cong trong hình bên: xét g(x)=F(2x)-4x. mệnh đề nào dưới đây đúng
Answers
Answer:
khgygygiugug
Step-by-step explanation:
A pair of linear equations is shown
y=-3x5
y=x+2
Which of the following statements best explains the steps to solve the pair of equations graphically?
on a graph, find the point of intersection stwo lines; the first line has y-intercept - 5 and slope - -3, and the second line has y-intercept = 2 and slope - 1.
On a graph, find the point of intersection of two lines, the first line has y-intercept -3 and slope - 5, and the second line has y-intercept - 1 and slope - 2.
On a graph, find the point of intersection of two lines, the first line has y-intercept -- and slope - 3, and the second line has y-intercept = -2 and slope --1
On a graph, find the point of intersection of two lines; the first line has y-intercept = 3 and slope -5, and the second line has y-intercept -1 and slope --2.
Answers
Answer:
y=-3×5
so'n
y=-15ans
another has no number only one number 2 alphabets
f(x) = x5 – 9x3 Choose all of the zeroes of f(x)
Answers
Answer:
[tex]x^{3} (x^{2} -9)[/tex]
[tex]x^{3} (x+3)(x-3)[/tex]
zeros at : 0,3,-3
Step-by-step explanation:
I do not understand any of this
Answers
Answer:
to get the slope. take the change of y axis value divide by the change of x axis value
The difference of twice a number and five is three.Find the number.Translate the world problem to an equation.Which steps describe how to solve the equation?
Answers
Answer:
Step-by-step explanation:
let the number=x
2x-5=3
2x=3+5
2x=8
x=8/2=4
Need help on this question asap pleasee :)
Answers
Answer:
1/4
Step-by-step explanation:
What are the solutions to X2 + 8X + 7 = 0?
Answers
Answer:
x = - 7, x = - 1
Step-by-step explanation:
Given
x² + 8x + 7 = 0
Consider the factors of the constant term (+ 7) which sum to give the coefficient of the x- term (+ 8)
The factors are + 7 and + 1 , since
7 × 1 = 7 and 7 + 1 = 8 , then
(x + 7)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 7 = 0 ⇒ x = - 7
x + 1 = 0 ⇒ x = - 1
Answer:
[tex]x=-1,-7[/tex]
Step-by-step explanation:
[tex]x^2+8x+7=0[/tex] where a [tex]\neq[/tex] 0 so a = 1 b = 8 c = 7
Quadratic Formula: [tex]x=-b\frac{\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=-8\frac{\sqrt{8^2-4(1)(7)} }{2(1)}[/tex]
[tex]x=-8\frac{\sqrt{64-28} }{2}[/tex] Evaluate the exponent and multiply 4ac
[tex]x=-8\frac{\sqrt{36} }{2}[/tex] Subtract b^2 - 4ac and multiply 2a
[tex]x=-8\frac{\sqrt{6} }{2}[/tex] Solve for the sqrt root of 35
x = - 8 ± 6/2 =
x = - 8 + 6/2 = -1
x = - 8 - 6/2 = -7
Four graphs are shown below:
Scatter plot A shown with data points that move in an upward direction and are located at 1 and 0.3, 2 and 1, 3 and 2, 4.1 and 4, 5.2 and 6.1, 5.9 and 9.5. Additional points are located at 4.6 and 5, 5.8 and 7.4, 5.2 and 7.1. Scatter plot B is shown with data points that move in an upward direction and are located at 1 and 3, 2 and 4, 3 and 5, 4 and 6, 5 and 6, 6, and 7, 7 and 8, 8 and 9. Scatter plot C is shown with data points that move in a downward direction and are located at 1 and 8.7, 4 and 5.6, 5 and 4.3, and 6 and 0.5. Additional points are located at 5.9 and 1.5, 5.5 and 3.5. Scatter plot D is shown with data points that move in a downward direction and are located at 0 and 7, 1 and 6, 2, and 5, 3 and 4, 4 and 3, 5 and 4, 6, and 5.
Which graph represents a negative linear association between x and y?
Graph A
Graph B
Graph C
Graph D
Answers
Answer:
graph D
Step-by-step explanation:
because d it at 0 then moves
Answer:
a
Step-by-step explanation:
Question 3 of 5
Select the correct answer.
Which of these tables represents a function?
Х
х
у
Х
у
Х
у
১| u
0
2
2.
-3
1
1
3
-3
9
0
3
2.
1
1
0
3
0
2
3
0
1
1
-3
2.
-3
1
3
1
1
2
-3
w.
X.
Y.
z.
w
Х
Answers
Answer:
only Y
Step-by-step explanation:
all the others have for at least 1 value of x more than one different y values defined.
but a function must be clear about the association between an x unit value and the corresponding result.
many different input values can have the same functional result. but there can be only one defined result per input value. otherwise it is not a function.
you cannot say 1+1 = 2 or 3. it is either 2 or 3, but you need to define what. you can't leave it open.
The function is given by the table Y
x = { -3 , 2 , 0 , 3 } and y = { 1 , 1 , 1 , 1 }
What is a function rule?The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
Given data ,
Let the function be represented as A
Now , the value of A is
Let the x values of the function be represented as
x = { -3 , 2 , 0 , 3 }
Now , the y values of the function is
y = { 1 , 1 , 1 , 1 }
From the table , we can see that for every different values of x there are range of values of y
No two same values of ranges have the same domain
Therefore , it is a function
Hence , the function is table Y
To learn more about function rule click :
https://brainly.com/question/3760195
#SPJ7
Question 1 of 10 An equation allows you to find the x- and y-coordinates of any point on the xy- plane. A. True B. False
Answers
Answer:
True
Step-by-step explanation:
The requried, an equation allows you to find the x- and y-coordinates of any point on the xy- plane. The given statment is true.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
An equation in two variables (such as y = mx + b, where m and b are constants) allows you to find the x- and y-coordinates of any point on the xy-plane that satisfies the equation.
To find the x-coordinate of a point, you can plug in a value for y and solve for x. To find the y-coordinate of a point, you can plug in a value for x and solve for y.
Learn more about equations here:
brainly.com/question/10413253
#SPJ7
Where do the light-dependent reactions of photosynthesis occur in a plant cell? Choose 1 answer:
A) Chloroplast; stroma
B) Mitochondrion: thylakoid membrane
C) Chloroplast; thylakoid membrane
D) Chloroplast: outer membrane
Answers
Answer:
C) Chloroplast; thylakoid membrane
Step-by-step explanation:
The question is a biological science question
The light-dependent reactions also known as the light reactions take place at the location site of the chlorophyll of the plant cell, within the chloroplast thylakoid membrane, and involves the energizing of the electrons within the pigment molecules, the electrons are then transferred through a transport chain within the thylakoid membrane
The dark reactions take place inside the stroma
Therefore, the correct option is chloroplast; thylakoid membrane
Drag numbers to the table so it shows a proportional relationship between x and y.
Answers
Answer:
7.5 30
45 180
Step-by-step explanation:
The given line has x = 1.25 and y = 5.
y/x = 5/1.25 = 4
x is multiplied by 4 to get y since 1.25 * 4 = 5.
That means the equation is
y = 4x
For a proportional function, every value of x must be multiplied by 4 to get y.
x = 7.5
y = 4x = 4(7.5) = 30
7.5 30
We need to find the values for the last line.
11 * 4 = 44
There is no 44
13.75 * 4 = 55
There is no 55.
17.5 * 4 = 70
There is no 70
30 * 4 = 120
There is no 120.
45 * 4 = 180
There is a 180.
45 180
Answer:
7.5 30
45 180
What do you know about the hypotenuse of triangle abc
Answers
Step-by-step explanation:
it is the longest side of the triangle and to find it we must appy a formula c square =a square + b square..thats all i know hehe
please help
thank you!
have a nice day!
Answers
Answer:
From left to right:
The first one is 2
The second one is 1/2
The third one is 2
The fourth one is 1
Step-by-step explanation:
In parallelogram BCDE if m
C
B
70
50°
E
Answers
Answer:
[tex]x=130[/tex]
Step-by-step explanation:
Opposite angles of a parallelogram are equal
EBC = 50° while, CDE = 50° too
Area of a parallelogram is 360°
Suppose, BCD to be x too, & form an equation:
[tex]50+50+x+x=360[/tex]
[tex]100+2x=360[/tex]
[tex]2x=360-100[/tex]
[tex]2x=260[/tex]
[tex]x=260/2[/tex]
[tex]x=130[/tex]
{CHECK: [tex]130+130+50+50=360^{o}[/tex]}
Answer:
m∠DEB = 130°
Step-by-step explanation:
Key: Only two angles are congruent because of the parallelogram
Since m∠EBC = 50° m∠CDE = 50°
Then we are missing m∠BCD and m∠DEB
50 + 50 + m∠BCD + m∠DEB = 360°
100 + m∠BCD + m∠DEB = 360°
m∠BCD + m∠DEB = 360 - 100
m∠BCD + m∠DEB = 260
m∠BCD + m∠DEB = 260/2
m∠BCD + m∠DEB = 130°
m∠BCD and m∠DEB = 130°
Prove:tan^3x/sin^2x-1/sinx.cosx+cot^3x/cos^2x=tan^3x+cot^3x
Answers
Answer:
picture above my answer is the answer you asked
Henri bought a swim suit at a cost of $8. Which statements are true regarding the cost of the suit?
Answers
Answer:
What are the statements?
Step-by-step explanation:
No trolling please. I will mark brainlist
Answers
Quan= 15
4/5 (3x-10) = 15
12/5x-8 = 15
12x- 40= 75
12x= 40+ 75
12x = 115
x= 115/12
x= 9.583
Answer:
A) $35.80
B) $28.64
Step-by-step explanation:
I'm not sure tho it might be wrong
PLS PLS PLS PLS PLS PLS PLS HELP I DON'T GET IT!!! Write missing monomials to make an identity:
A) (.....+2a)^2=.....+12ab+4*....
B) (3x+.....)^2=....*x^2+.....+49y^2
Answers
Answer:
I only have the answer for B
Step-by-step explanation:
This is the answer: 1st blank: 7y
2nd blank: 9
3rd blank: 42xy
PLS HELP ASAP¡!!!
solve for f(3) if
f(x)=x^3+2x^2-x-1
Answers
= 41
Please help me... I stink at math
Answers
Answer:
142 [tex]cm^3\\[/tex]
Step-by-step explanation:
You have to do [tex](7*5)+(5*3)+(7*3)+(7*3)+(5*7)+(3*5)[/tex].
This equals 142 [tex]cm^3\\[/tex].
Answer:
The answer is 142cm
Step-by-step explanation:
PLEASE HELP!!
Wesley initially filled a measuring cup with 5/6 of a cup of syrup from a large jug. Then he poured 1/2 of a cup back into the jug. How much syrup remains in the measuring cup?
Answers
Answer:
2/6 or 1/3
Step-by-step explanation:
We start off with 5/6 of a cup of syrup in a measuring cup.
Then Wesley pours out 1/2 of the syrup in the measuring cup.
Our equation looks like this:
5/6 - 1/2 = ?
However, we can't use this equation because the denominators (6 & 2) aren't the same. So we will find the LCD (least common denominator).
Mulitiples of 6: 6, 12, 18, 24
Multiples of 2: 2, 4, 6, 8
6 is the LCD for the both of them.
Multiply 3 to the numerator and denominator of 1/2 (because to get from 2 to 6 using multiplication, you mulitiply 3)
1/2 x 3/3 = 3/6
Now we can substitue 3/6 into our original equation and solve it:
5/6 - 3/6 = 2/6
It's better to use the simplified answer, 1/3.
Hope it helps and good luck (●'◡'●)
Match each angle pair with their relationship
Answers
Answer:
oh I thought you were talk about love well dang :(
Step-by-step explanation:
____ more than 3455 is two hundred seventy -eight thousand five hundred eighty three
Answers
Answer:
275,128
Step-by-step explanation:
"___ more than 3455" is the same as saying "___ added to 3455"
So it will look something like this:
___ + 3,455 = 278,583
Then rearrange the equation to use subtraction to solve it:
278,583 - 3,455 = ____
Plug it in the calculator or solve it by hand, and you have your answer!
(To double check, add 3,455 and 275,128, and you get 278,583)
Hope it helps (●'◡'●)
