Let g(x)=Intragal from 0 to x f(t) dt, where r is the function whos graph is shown.
Picture attached with question and graphs. As well as points needed
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If
[tex]\displaystyle g(x) = \int_0^x f(t) \, dt[/tex]
then g(x) gives the signed area under f(x) over a given interval starting at 0.
In particular,
[tex]\displaystyle g(0) = \int_0^0 f(t) \, dt = 0[/tex]
since the integral of any function over a single point is zero;
[tex]\displaystyle g(4) = \int_0^4 f(t) \, dt = 8[/tex]
since the area under f(x) over the interval [0, 4] is a right triangle with length and height 4, hence area 1/2 • 4 • 4 = 8;
[tex]\displaystyle g(8) = \int_0^8 f(t) \, dt = 0[/tex]
since the area over [4, 8] is the same as the area over [0, 4], but on the opposite side of the t-axis;
[tex]\displaystyle g(12) = \int_0^{12} f(t) \, dt = -8[/tex]
since the area over [8, 12] is the same as over [4, 8], but doesn't get canceled;
[tex]\displaystyle g(16) = \int_0^{16} f(t) \, dt = 0[/tex]
since the area over [12, 16] is the same as over [0, 4], and all together these four triangle areas cancel to zero;
[tex]\displaystyle g(20) = \int_0^{20} f(t) \, dt = 24[/tex]
since the area over [16, 20] is a trapezoid with "bases" 4 and 8, and "height" 4, hence area (4 + 8)/2 • 4 = 24;
[tex]\displaystyle g(24) = \int_0^{24} f(t) \, dt = 64[/tex]
since the area over [20, 24] is yet another trapezoid, but with bases 8 and 12, and height 4, hence area (8 + 12)/2 • 4 = 40, which we add to the previous area.
Related Questions
how would is solve this?
Find the area of the shaded region. Round your answer to the nearest hundredth.
Answers
it will be 36
Step-by-step explanation:
fgdsb b zgffhxgv
Simplify 10^9 ÷ 10^7
Answers
Answer:
10^2
Step-by-step explanation:
10^9/10^7 is the same as 10^9*10^-7 if you multiply two same bases you can add there exponents. So, 9+(-7)=2. So, it’s 10^2
Answer:
100
Step-by-step explanation:
Hope it helps
If the value of a=2,y=3,find the value of x in ax/y=10
Answers
[tex]\dfrac{ax}y =10\\\\\implies \dfrac{2x}{3} = 10\\\\\implies 2x = 30\\\\\implies x = \dfrac{30}2 = 15[/tex]
Answer:
x = 15
Step-by-step explanation:
[Given] ax/y=10
[Rewrite] [tex]\frac{ax}{y} =10[/tex]
[Plug-in] [tex]\frac{(2)x}{(3)} =10[/tex]
[Simplify] [tex]\frac{2x}{3} =10[/tex]
[Multiply both sides by 3] 2x = 30
[Divide both sides by 2] x = 15
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
please help me with this last question
Answers
Answer:
Step-by-step explanation:
3t² - t
3(4²) - 4
3(16) - 4
48 - 4
44
pls help the will mean the world
Answers
Answer:
A: the area of the walls that are being painted
C: the cost per gallon of different paints
F: the number of square feet that can be painted per gallon of paint
Step-by-step explanation:
cosθ(tanθ + cotθ) =
• cscθ
• secθ
• cos^2θ
• 1
Answers
Answer:
ayo i think is ufo trying to communicate hey alien we come in peace
Step-by-step explanation:
[tex]\cos \theta(\tan \theta + \cot \theta)\\\\=\cos \theta \tan \theta + \cos \theta \cot \theta \\\\=\cos \theta \left (\dfrac{\sin \theta}{\cos \theta} \right)+ \cos \theta \left(\dfrac{\cos \theta}{\sin \theta} \right)\\\\\\=\sin \theta + \dfrac{\cos^2 \theta}{\sin \theta}\\\\=\dfrac{\sin^2 \theta + \cos^2 \theta}{\sin \theta}\\\\=\dfrac 1{\sin \theta}\\\\=\csc \theta[/tex]
is 6y +2 - y + 3 and 3 - y + 2 + 6y the same
Answers
Answer:
Step-by-step explanation:
Yes.
All you have done is changed the order. They are exactly the same.
You can sort of verify this by using
-4 + 6 - 8 + 2 = - 4
2 + 6 - 4 - 8 =
8 - 12 = - 4
You invest AED 5000 in a saving account that earns 4% interest each year. If you do not use the account for a year, how much money will you have in your account after a year?
Answers
9514 1404 393
Answer:
AED 5200
Step-by-step explanation:
The interest in the first year will be ...
I = Prt . . . . principal P invested at rate r for t years
I = 5000×0.04×1 = 200
The account will have AED 5200 in it after a year.
The list of ordered pairs below represents a function.
{(-12, –8), (-2,7), (0,4), (-4,3)}
Find the range of the function. Write your answer' as a comma separated list.
Answers
Answer:
{-8, 3, 4, 7}
Step-by-step explanation:
range is y values in the ordered pairs
{-8, 3, 4, 7}
Translate 9 times the sum of n and 12 to symbols
Answers
to simplify, use the distributive property
9 • 12 = 108
9 • n = 9n
9n • 108
y>= -5x + 8 what is m?
Answers
Answer:
The slope = -5
Step-by-step explanation:
y ≥ -5x + 8
Look at the problem as y = -5x + 8 and compare to the slope intercept form. The slope = -5
idrk uuhm ...........................................................
Answers
Answer:
huh
Step-by-step explanation:
Answer: Im sorry what is the question?
Step-by-step explanation:
In a Parallelogram CARS , <C = 5x-20 and <A = 3x+20. Find the value of x ?
Answers
Given that
In a Parallelogram CARS ,∠C = (5x-20)°
∠A = (3x+20)°
angle C and angle A are adjacent angles
We know that
In a Parallelogram the adjacent angles are supplementary.
⇛∠C + ∠A = 180°
⇛ (5x-20)°+(3x+20)° = 180°
⇛5x°-20°+3x°+20° = 180°
⇛(5x°+3x°)+(20°-20°) = 180°
⇛8x°+0 = 180°
⇛8x° = 180°
⇛ x° = 180°/8
⇛ x° = 22.5°
Answer:-The value of x = 22.5°
also read similar questions: In parallelogram MATH, m= (3x+ 20) and t= (5x-4) find A
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find the value of x (5x+12) (3x+8) a 10 b 15 c 20 d 25
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What is .7899 rounded 4 decimal places
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Hope this helped. :)
I need help please I don't understand this
Answers
Answer:
So
12 would round to 12
0.49 would round to 0
or could possibly round to 0.50
Step-by-step explanation:
So, 12 x 0.49
would be about
12-13
#Nova
Have a good day
Work out
47% of £900
Answers
Answer:
47 percent *900 =
(47:100)*900 =
(47*900):100 =
42300:100 = 423
Now we have: 47 percent of 900 = 423
Question: What is 47 percent of 900?
Percentage solution with steps:
Step 1: Our output value is 900.
Step 2: We represent the unknown value with $x$.
Step 3: From step 1 above,$900=100\%$.
Step 4: Similarly, $x=47\%$.
Step 5: This results in a pair of simple equations:
$900=100\%(1)$.
$x=47\%(2)$.
Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both
equations have the same unit (%); we have
$\frac{900}{x}=\frac{100\%}{47\%}$
Step 7: Again, the reciprocal of both sides gives
$\frac{x}{900}=\frac{47}{100}$
$\Rightarrow x=423$
Therefore, $47\%$ of $900$ is $423$
PLS HELP NOW! WILL GIVE BRAINLIEST TO WHO EVER ANSWERS FIRST
Answers
Answer:
y = 1.6x −5
Step-by-step explanation:
We start with two points, let’s say (0,-5) and (4,1.4).
The equation is:
y=mx+b
m is the slope and b the y-intercept.
We can find the slope by:
[tex]\frac{y_2-y_1}{x_2-x_1} = \frac{-5-1.4}{0-4} = 1.6[/tex]
Then solve the equation for b:
y = 1.6x + b ->
−5 = 1.6(0) + b ->
b = -5.
So the final equation is:
y = 1.6x −5.
Hope that helps! :)
Can someone please help me
Answers
Answer:
The linear ones
options 1 and 3
Step-by-step explanation:
4 and 5 are parabolic with maxima at y = -4 and minima at y = -3.25 respectively
2 is asymptotic to the negative x axis on the positive side
which of the following is the inverse of F(x) = 2 x + 3?
Answers
Answer:
[tex]\frac{x-3}{2}[/tex]
Step-by-step explanation:
Please Help! it's simple!
Answers
Answer:
28.27
circumference of finding a circle divided by two.
[tex](2\pi \:r {}^{2} ) \div 2[/tex]
(2×3.14×9)/2
56.55/2
28.27
Which is the quotient for 0.9 divide by 0.75
Answers
Answer:
1.2!
Step-by-step explanation:
The value of the numerical expression 0.90 ÷ 0.75 in the decimal form will be 1.20.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The numbers are given below.
0.90 and 0.75
Then the division between the numbers 0.90 and 0.75 will be given by putting a division sign between them. Then we have
⇒ 0.90 ÷ 0.75
⇒ 0.90 / 0.75
⇒ 1.20
The worth of the mathematical articulation 0.90 ÷ 0.75 in the decimal structure will be 1.20.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ2
hhhhhhhhhhhhhhhhhhhhhheeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeellllllllllllllllllllllllllllllllllllpppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answers
Answer:
E
Step-by-step explanation:
Like and give 5 star rating
Factor this completely thank you
Answers
4(2x raise to power 2-4-7x)
plz help me find this answer
Answers
Answer:
C
You have to check which of numbers is the lowest.
Cheers :D
Can anyone answer this?
Answers
Answer:
∠AMB = 103°
Step-by-step explanation:
The sum of angles in ∆AMB is ...
(∠A)/2 +(∠B)/2 + ∠AMB = 180°
∠AMB = 180° -(∠A +∠B)/2 = 180° -(58° +96°)/2
∠AMB = 103°
help help help help!
Answers
Answer:
Is a give number 4 5 is a reflexive property
Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate).
4 sin(2θ) − 2 sin(θ) = 0
Answers
Answer:
θ = πk, 1.318+2πk, 4.965+2πk
Step-by-step explanation:
4sin(2θ) − 2sin(θ) = 0
8sin(θ)cos(θ) - 2sin(θ) = 0
2sin(θ)[4cos(θ)-1] = 0
2sin(θ) = 0
sin(θ) = 0
θ = πk
4cos(θ)-1 = 0
4cos(θ) = 1
cos(θ) = 1/4
θ ≈ 1.318+2πk, 4.965+2πk
Therefore, θ = πk, 1.318+2πk, 4.965+2πk
Rewrite without parentheses and simplify.
(check my page and answer my other questions if u can please it would mean alot)
Answers
Answer:
x² +14x +49
Step-by-step explanation:
Use the distributive property and collect terms.
(x +7)² = (x +7)(x +7)
= x(x +7) +7(x +7)
= x² +7x +7x +49
= x² +14x +49
Find x for brainiest 3
Answers
Answer:
115
Step-by-step explanation:
[tex]65 + x = 180 \\ x = 180 - 65 \\ x = 115[/tex]Find an equation for the perpendicular bisector of the line segment whose endpoints
are (2, -1) and (6, -9).
Answers
Answer:
x-2=y+1
Step-by-step explanation:
here is ur answer