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
Write as an algebraic expression: “eleven less than four times the number of text messages"
Answers
Answer:
[tex]11 < 4x[/tex]
let number of text messages be x
4x - 11
Text messages = x. So 4 multiplied by x then minus 11
Use the drop-down menus to complete the sentence:
The terminal ray of a 300° angle lies in the ______ quadrant.
This angle measures (________) Pi radians.
Answers
Answer:
fourth
5/3
Step-by-step explanation:
edge2021
Answer:
Fourth
5/3
Step-by-step explanation:
Leo has 3 8/9 ounces of sunblock. He uses one-fifth of an ounce at the beach. How much does he have left?
Answers
Step-by-step explanation:
7/9pls mark as brainliest
Answer:
Step-by-step explanation:
It's 3 31/45
Write the equation in point-slope form for the line that contains points (4,1) and (6, 8).
y - 1 = 7/2 (x - 4)
y - 8 = 7/2 (x - 6)
y - 8 = 2/7 (x - 6)
y - 4 = 7/2 (x - 1)
y - 1 = 2/7 (x - 4)
Answers
Answer:
y -1 =2/7 (x - 4)
please mark as brainliest
In a laboratory The Count of bacteria in a certain experiment was increasing at the rate of 2.5 % per hour find the bacteria at the end of 2 hours if the count wasn't really 5,06,000.
Answers
Answer:
Прости я не понямайу по англискем
The triangular faces of the peaks on a roof are congruent isosceles triangles with vertex angles U and V.
a. Which two angles are congruent to ∠WUX?
b. Find the distance between points U and V.
Answers
Answer:
(a). ∠UXV, ∠XVY ; (b). UV = 8 m .
Step-by-step explanation:
Math is genially hard
Answers
Explanation:
we need to find p
36=29+p
subtract 29 from both sides
7=p
SOMEONE PLEASE HELP ME THIS IS ALMOST DUE AND I NEED THE RIGHT ANSWER PLZ!!!
Answers
Mark brainliest
Answer: 9
Step-by-step explanation:
super easy
basically do 15-5 which is 10
thats the hypotenuse side
now apply pythegorean theorem: 5 squared + x squared= 10 squared
25+ x squared=100
x squared=75
x approxiametly equals 9
EASY WORK!! Plz look at the photo and yes it’s easy for other people but not me .
Answers
Answer: 48
Step-by-step explanation:
Answer:
b) 54 minutes ( week 6 )
Will mark brainliest!!Solve for x and round to the nearest tenth
Answers
Answer:
right triangles are 90 degrees sooooo
add 39 plus 27, that's 66
90 minus 66 issss 24
Ashley is saving money for the newest iPhone. It costs $999.75. She gets a $15 weekly allowance and babysits for 4 hours a week at $13.50 an hour. She gets paid once a week. She pays $4.50 a week for school lunch. She saves the rest of her money.
PART A Write an inequality to find the number of weeks it will take her to save enough money for the iPhone.
PART B Solve the inequality.
PART C Graph the solution to the inequality.
PART D How long will it take her to save enough money to buy the iPhone?
Answers
Answer:
A) 999.75 </= 15w + (4(13.5))w - 4.5w
B) 999.75 </= 64.5w
C) Can't Graph On Here Sorry
D) 15.5 weeks
Step-by-step explanation:
A) 999.75 </= 15w + (4(13.5))w - 4.5w
B) 999.75 </= 15w + 54w - 4.5w
999.75 </= 69w - 4.5w
999.75 </= 64.5w
C) Just graph it, Price needed being Y (Also money), Times (in weeks) being X
D) 999.75/64.5
w >/= 15.5
Find the unit price of a 4-pack of mixed fruit sells for $3.75
Answers
3.75 x
4. = 15$
what is 8÷530 TYPE FAST
Answers
Answer:
0.0150
Step-by-step explanation:
8÷530
0.0150
it is correct
What is the equation of the line of best fit for the following data ? Round the slope and y-intercept of the line to three decimal places
Answers
Answer:
y=1.164x+0.885
Step-by-step explanation:
np
Consider triangle Wes the legs each have a length of 10 units. What is the length of the hypotenuse of the triangle
Answers
5 cm
7 cm
10 cm
15 cm
8 cm
115 cm
What is the area of the object above?
OA. 60 cm2
OB. 155 cm
OC. 120 in?
OD. 225 cm2
Submit
Reset
Answers
Answer:
155
Step-by-step explanation:
calculate the areas of 2 rectangles
method A
one rectangle with lengths 8 and 10
the other 15 and 5
so 8x10 + 15x5 = 80 + 75 = 155
method B
one traingle with lenghts 5 and 7
the other 15 and 8
so 15x8 + 5x7 = 120 + 35 = 155
An air traffic controller is tracking two planes. To start, Plane A is at an altitude of 4385 feet and Plane B is at an altitude of 5000 feet. Plane A is gaining altitude at 55.5 feet per second and Plane B is gaining altitude at 45.25 feet per second.
How many seconds will pass before the planes are at the same altitude?
seconds
What will their altitude be when they're at the same altitude?
feet
Answers
Answer:
60 seconds, 7715 feet
Step-by-step explanation:
Plane A and B start out 615 feet apart, and we find this by subtracting the height of plane A from plane B, getting 5000-4385=615. Now we have to find how many more feet of altitude plane A is gaining per second over plane B.
To find this we subtract 45.25 from 55.5 and get 10.25 feet per second. Now to find out how many seconds until they'll be at the same altitude we simply divide 615 by 10.25, getting 60 seconds.
For the second part, to find the altitude at this point, we simply multiply the altitude gain of one of the planes per second by the time of 60 seconds to get how much altitude they gained over that time, and add it to the starting altitude. Doing this with plane B we get 45.25*60=2715, and we add that to 5000 to get the final answer of 7715.
Find the x- and y- intercepts of the line with the given equation
-6x+8y=-36
Answers
Answer:
Y int at
(
0
,
3
2
)
X int at
(
3
,
0
)
Step-by-step explanation:
The line is easier to visualize when the equation is in slope-intercept form:
4
x
+
8
y
=
12
Divide each side by 4:
x
+
2
y
=
3
2
y
=
−
x
+
3
y
=
−
1
2
x
+
3
2
Y-intercept (plug in 0 for x):
y
=
−
1
2
(
0
)
+
3
2
y
=
3
2
X-intercept (plug in 0 for y):
0
=
−
1
2
x
+
3
2
−
3
2
=
−
1
2
x
x
=
3
Answer:
x-intercept (6,0)
y-intercept (0,-4.5)
Step-by-step explanation:
the x-intercept will be when y=0
and the y-intercept will be when x=0
so
[tex]y=0\\\\-6x+8(0)=-36\\\\-6x=-36\\\\x=6[/tex]
so the x intercept will be at (6,0)
[tex]x=0\\\\-6(0)+8y=-36\\\\8y=-36\\\\y=-\frac{9}{2}\\\\y=-4.5[/tex]
so the y intercept will be at (0,-4.5)
Simplify -14x^3/x^3-5x^4
A. -14/5x-1; where x=1/5,0
B.-14x/1-5x;where x=1/5
C.1-5x/-14x; where x=0
D.-14/1-5x; where x=1/5,0
Answers
Answer:
The answer is D
Step-by-step explanation:
A diagram of a new competition swimming pool is shown. If the width of the
pool is 25 meters, find the length of the actual pool. (Round to the nearest
tenth)
Answers
47m at least I think it is
(-3,1) (4,2) slope
Show work pls
Answers
Answer:
The slope is:
[tex] \frac{1}{7} [/tex]
Step-by-step explanation:
⁕ Remember that slope formula is:
[tex]m = \frac{y_2 - y_1 }{x_2 - x_1}[/tex]
⁕ Let's plug in and solve.
[tex]m = \frac{ 2 - 1}{4 - ( - 3)} = \frac{ 1}{ 7}[/tex]
Therefore, the slope is:
[tex] \frac{1}{7} [/tex]
Kevin reads 8 pages in 15 minutes. If he reads at a constant rate, how long will it take him to read 20 pages? 65PTS!!
Answers
Answer:
37.5 minutesStep-by-step explanation:
Use page/min ratio to solve:
8/15 = 20/xx = 20*15/8x = 37.5 minutesAnswer:
37.5 minutes I think
Step-by-step explanation:
In the 1900s, the life expectancy of a human in the United States was 50 years. The life expectancy of a human now is 78 years. What is the percentage change in the life expectancy of a human in the United States?
Answers
Answer:
There would be a 56% increase
Step-by-step explanation:
We need to find the amount of change before we can find the percent of change. We'll take the greater value, 78, and subtract the lesser value, 50. 78 - 50 = 28. We then take this amount of change and put it over the original amount, Percent of change = Amount of change/ original amount or for this problem, 28/50. We then use that as a division equation for 28 divided by 50. 28 divided by 50 = 0.56. Finally we move the decimal to the right two times and we can then find the percentage increase.
If the cornerstone represents when a building was built and it reads MDCCLXXV, when was the building built?
Answers
Step-by-step eAnswer:
1775
xplanation:
In the figure below, what are the lengths of “a”, “b”, and “c”? Round answers to nearest tenth.
Answers
Answer:
use a ruler to answer the question
Can i Have some help
Answers
Answer:
a= .293
b= .924
c= 9.455
d= 1.975
The answer is B luv !
Im serious this time is it appropriate to use a old notebook for a new class in highschool?
Specifically math cuz they made us get big five subject notebooks and we haven't even filled half of it and the years almost over I thought about reusing it for next year's math class
Answers
Answer:
Of course it is!
Step-by-step explanation:
You might want to have a separator, so you know what page your new year textbook starts. I hope this is a food tip to save money!
Can anyone please help me please
Answers
Answer:
this isnt spanish
Step-by-step explanation:
Under 4 is 15
Under 9 is 20
4.Figure ABCD is similar to figure RSTU.
What is the length of side RU?
a.3cm
b.3.2cm
c.3.5cm
d.4cm
Answers
HOPE THIS HELPS
Given f(x) = x^3 + kx + 2, and x + 1 is a factor of f(x), then what is the value of
k?
Answers
Answer:
k = 1
Step-by-step explanation:
Given that,
[tex]f(x) = x^3 +kx + 2[/tex]
If (x+1) is a factor of (x), we need to find the value of k.
Using remainder theorem to find it.
Put (x+1) = 0
x = -1
Put x = -1 in equation below.
[tex]x^3 + kx + 2=0\\\\(-1)^3+k(-1)+2=0\\\\-1-k+2=0\\\\1-k=0\\\\k=1[/tex]
So, the value of k is 1.