Calculus Problem shown in the attached image. I understand the concept of integrals but this particular question has me perplexed. I doubt its all that complex I just don't fully understand what its asking.
Answers
(a) For some given x, A(x) gives the signed area under f(t) on the interval [a, x]. Since f(t) is simple to integrate, and with a = 2, you can compute it exactly:
A(x) = ∫₂ˣ f(t) dt
A(x) = ∫₂ˣ (3t + 2) dt
A(x) = (3/2 t ² + 2t ) |₂ˣ
A(x) = 3/2 x ² + 2x - 10
which is parabolic and easy to graph.
(b) Differentiating A(x) is also easy if you use the "closed" form above:
A'(x) = (3/2 x ² + 2x - 10)'
A'(x) = 3x + 2
and this function tells you how the area under f(t) changes as you adjust the size of the integration interval.
You can get the same result using the fundamental theorem of calculus:
A'(x) = d/dx ∫₂ˣ f(t) dt = f(x) = 3x + 2
Related Questions
I will mark you Brainly-est pls! I need this done by tomorrow :) it’s 55 points btw
Answers
Answer:
Step-by-step explanation:
9. 1.6f + 0.4j - 13
11. -6y + 13
13. -1/2j + 15
can anyone please help with this???
Answers
Answer:
car is decelerating
Step-by-step explanation:
Is 3/2 less than greater than equal than 1
Answers
Answer:
greater than
Step-by-step explanation:
2/2 = 1
3/2 = 1 1/2
Four sisters are all 2 years apart in age. The
total of their ages is equal to 36 years. How
old is the youngest sister
Answers
The equation that represents the age of the youngest sister is 4x + 12 = 36. Then the age of youngest sister will be 6 years old.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The four sisters are all 2 years apart in age. The total of their ages is equal to 36 years.
Let x be the age of the youngest sister. Then the age of other sister will be x + 2, x + 4, and x + 6. Then the equation is given as,
x + x + 2 + x + 4 + x + 6 = 36
4x + 12 = 36
4x = 36 - 12
4x = 24
x = 24 / 4
x = 6
The equation that represents the age of the youngest sister is 4x + 12 = 36. Then the age of youngest sister will be 6 years old.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ5
The test scores of students in a math class are 56, 42, 50, 63, 58, 41, 50, 48, 68, and 48. What is the mean of this set of data?
A. 55.6
B. 50
C. 52.4
D. 48.6
Answers
(1) 56 + (2) 42 + (3) 50 + (4) 63 + (5) 58+ (6) 41 + (7) 50 + (8) 48 + (9) 68 + (10) 48 = 524
524/10 = 52.4
Answer:
C. 52.4
Step-by-step explanation:
solve for x x−6/9=−5
x=
Answers
Answer:
4 4/9
Step-by-step explanation:
Move all terms not containing x
to the right side of the equation.
Exact Form:
x=−409
Decimal Form:x=−4.¯4
Mixed Number Form:
4 4/9
Answer:
-39
Step-by-step explanation:
x-6/9 = -5
then multiply both sides by 9
9 ° (x-6) / 9 = 9 ° -5
simplify
x-6= -45
add 6 to both sides
x-6+6=-45+6
simplify
x= -39
Total of three numbers is 45.5 two of them are equal the third one is half of other two what are the three numbers
Answers
Answer:
im taking a nap
Step-by-step explanation:
Work out volume of this sphere leave your answer in terms of pi
Answers
Answer:
36pi
Step-by-step explanation:
Volume formula = 4/3 × pi × r^3
Simplify the following expression (2x^2y^5)^3
Answers
Answer:
The correct answer is,
[tex] {8x}^{6y {}^{5} } [/tex]
Can someone please explain how I apply SOHCAHTOA properly to this?
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Answer:
e
Step-by-step explanation:
Y-4x=9 in standard form please show your work
Answers
Answer:
y = x + 9/4 or y = x + 2 1/4
Step-by-step explanation:
y - 4x = 9
y - x = 9/4 (divide both sides by 4)
y = x + 9/4 (Add x to both sides)
Consider this quadratic expression.
x² – 10x + c + 11 – c
What value of c is needed to complete the square for this expression?
A. 10
B. 20
C. 25
D. 100
Answers
Answer:
c = 25Step-by-step explanation:
Given this quadratic expression.
x² – 10x + c = 0
We are to find the value c that will make the expression a perfect square'
Using the completing the square method
Add the square of the half of coefficient of x
Coefficient of x = -10
Half of -10 = 1/2(-10) = -5
Square of -5 = (-5)^2 = 25
Hence the value of c to complete the expression is 25
PLEASE HELP ME i rly need an a
what is how much sales tax will Larry pay for his $939 doorbell in Las Vegas, where the sales tax is 8.38%? Use appropriate units and round your answer to the nearest cent if necessary. * plez i beg
Answers
Answer:
939/x 8.38/100
x8.38 93900
x= 11205.25
Step-by-step explanation:
Find the value of x.
92°
36°
Answers
Answer: the answer is 7°
Step-by-step explanation:
Plz help due tomorrow
Answers
Answer:
Step-by-step explanation:
1/6 x 1/5 + 1/30
= 1/30 + 1/30
= 2/30
=1/15
It is asking us to plug in 1/5 so let’s plug it in
1/6(1/5) + 1/30 = 1/30 + 1/30 = 2/30
So we reduce the fraction and the answer is 1/15
Help plz:)))I’ll mark u Brainliest
Answers
Answer:
Scale factor = 1.5
Step-by-step explanation:
Formula for the scale factor,
Scale factor = [tex]\frac{\text{Measure of one side of the Image}}{\text{Measure of one side of the preimage}}[/tex]
In this question, image is triangle Y and preimage is triangle X.
Scale factor of X to Y = [tex]\frac{15}{10}[/tex]
= 1.5
Therefore, scale factor = 1.5 is the answer.
If three pounds of bananas cost $4.50 find the cost of 10 pounds of bananas
Answers
Answer:
45
Step-by-step explanation:
4.50 × 10 =45!
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.
.
.
.
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Answer:
$15
Step-by-step explanation:
$4.50 time 3 = $13.50 (9 lbs)
$4.50 divided by 3 = $1.50 (1 lb)
$1.50 plus $13.50 = $15
The sum of four times a number and fifteen is forty-seven. Find the number.
Answers
Answer:
8 is the number
Step-by-step explanation:
I don't know why it took me so long to figure it out, 4 x 8 = 32 32 + 15 = 47
It probably took me a really long time because I am tired, and I am not using a calculator.
HELP !!!! find the measurements of each angle
Answers
Given that P(B|A)=0.75 and P(A)=0.47, what is P(B AND A)? Round to three decimal places.
Answers
Answer:
0.627
Step-by-step explanation:
i need help with finding area whats the area of a 3m an 7m regtangle
Answers
Answer:
34
Step-by-step explanation:
Answer:
Area of rectangle =LXB
L=7m
B=3m
so 7m multiply by 3m gives 21 so the area is 21
Dean purchased a box of cereal Which of these measurements BEST describes the volume of the box?
1.)154 cubic feet
2.)154 cubic inches
3.)154 cubic meters
4.)154 cubic millimeters
Answers
Answer:
2
Step-by-step explanation:
You don't measure cereal in the others because feet, meters and millimeters are too big. Hope this helps.
How many proper subsets does the set T= {x,y,z} have?
Answers
Answer:
Total Proper Subsets = 2ⁿ - 1 = 2³ -1 =8-1 =7
Step-by-step explanation:
Basically the formula for,
No of subsets = 2ⁿ
Where n is number of elements in a set. As one subset is improper which is equal to the set itself so we have to find proper subsets which are = 2ⁿ - 1.
Someone help me quick
Answers
Answer: x > - 18
Step-by-step explanation:
first multiply both sides
then multiply reduce
then arrange and thats the answer
hope this helps <3
Express the reoccurring decimal 0.56 as a fraction
Please see screenshot
Answers
Answer:
I have made it in pic hope it helps
If 1 foot of chain costs 17¢, then 4 yards of this chain would cost
A. $0.68
B. $1.53
C. $2.04
D. $2.75
Answers
Answer:
a
Step-by-step explanation:
17x4+68
Answer: C. $2.04
Step-by-step explanation: 4 yards = 12 feet. 17 x 12 = 204 cents which equals to $2.04
Simplify
6(-5n + 7 thank you
Answers
Answer:
-30n + 42
Step-by-step explanation:
6( -5n + 7)
-30n + 42
Hope this helps!
What is 9876÷448+892-24????
Answers
Answer:
99685/ 112
or
890 5/112
Step-by-step explanation:
Please solve using dimensional analysis
Answers
Answer:
34^23 (that is 34 to the 23 power)
Step-by-step explanation:
Do 3.4x10^23=34^23
Daniel's age is 15% of
Sarah's. Luke's age is 75% of
Sarah's and 300% of Daniel's.
When they added their ages,
the total was 141. How old is
Rachel?
Answers
Answer:
27 years oldStep-by-step explanation:
Full question isDaniel's age is 15% of Sara's. Luke's age is 75% of Sara's and Rachel's is 300% of Daniel's. When they added their ages, the total was 141. How old is Rachel? SolutionDaniel = d, Sara = s, Luke = l, Rachel = r
We get below relations:
d = 0.15sl = 0.75sr = 3d ⇒ r = 3*0.15s ⇒ r = 0.45sSum of ages:
d + s + l + r = 141Substitute and solve for s:
0.15s + s + 0.75s + 0.45s = 1412.35s = 141s = 141/2.35s = 60Rachel's age is:
r = 0.45*60 = 27