The derivative of the function y = ∫0^(3sin(4t)) ex dt with respect to t is y'(t) = (3/4) (ex cos(4t)).
To use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function y = ∫0^(3sin(4t)) ex dt, we need to first understand what the theorem states.
Part 1 of the Fundamental Theorem of Calculus states that if a function f(x) is continuous on the closed interval [a, b], and if F(x) is any antiderivative of f(x), then the definite integral of f(x) from a to b is equal to F(b) - F(a), or ∫[a,b] f(x) dx = F(b) - F(a).
In other words, the theorem provides a way to calculate the definite integral of a function by evaluating the difference between two antiderivatives of the function.
Now, let's apply this theorem to the function y = ∫0^(3sin(4t)) ex dt. To do this, we need to first find an antiderivative of the integrand ex.
The antiderivative of ex is simply ex itself, so we have:
∫ ex dt = ex + C, where C is the constant of integration.
Now, we can use this antiderivative to find an antiderivative of the integrand in our original function y. Let u = 4t, so that du/dt = 4 and dt = du/4. Then, we have:
y = ∫0^(3sin(4t)) ex dt = ∫0^(3sin(u)) ex (du/4) = (1/4) ∫0^(3sin(u)) ex du
Let F(u) = ∫ ex du = ex + C, where C is a constant of integration. Then, we have:
y = (1/4) F(3sin(u)) - (1/4) F(0) = (1/4) (ex)|_0^(3sin(u)) = (1/4) (ex - 1)
Using the chain rule again, we have:
d/dt (3sin(u)) = 3cos(u) (du/dt) = 3cos(4t)
Substituting this expression back into the previous equation, we get:
y'(t) = (1/4) (ex) (3cos(4t)) = (3/4) (ex cos(4t))
Therefore, the derivative of the function y = ∫0^(3sin(4t)) ex dt with respect to t is y'(t) = (3/4) (ex cos(4t)).
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Pleas help if possible :)
Answer: i don’t know but good luck, you got this!Have a nice day!
Step-by-step explanation:
Help am i correct please Ehejahrs
25 POINTS!!!!! HELP NEEDED
(05.01 MC)
The graph shows the prices of different numbers of bushels of corn at a store in the
current year. The table shows the prices of different numbers of bushels of corn at
the same store in the previous year.
Current Year
98
70
Price of
Com
56
(dollars) 42
28
14
0 2 4 6 8 10 12 14
Number of Bushels
Previous Year
Number of Bushels Price of Corn (dollars)
2
10
4.
20
6
30
8
40
PART A:
To find the rate of change, put change in y over change in x. In order to first find the changes, you must subtract two y values from each other and two x values from each other, like this:
Change in y = 20-10
Change in x = 4-2
Then you can put these over each other:
20-10/4-2
Then simplify
20-10/4-2 = 10/2 = 5/1 = 5
So, this means the rate of change is 5. $5 per bushel.
If you also need part B it would be helpful to see the other chart because it's hard to understand in the writing you included. :) Comment and let me know if you post it so I can help you out!
Part A: 7 dollars
- The graph shows that 2 bushels is 14 dollars, because the graph has a straight line, the rate remains constant you must divide the sides by two to find the amount for one bushel which would be 7 dollars.
- And to double check you would divide 28 by 4, 42 by 6, 56 by 8, 70 by 10, 84 by 11, and 98 by 12. they all equals 7 dollars So, the equation would be y = 7x.
- 7 can be known as the slope and rate of change.
Part B:2 dollars
- The years before show 2 bushes was 10 dollars
-so you would divide 10 by two you would get five To double check you would do the same thing with 20 by 4, 30 by 6 and 40 by 8, and they all equal 5 dollars.
-if you use this answer be sure to reword it so you dont get copy write and integrity. have a great day or night.
Graph the line through the points (-6,4) and (0,-4)
Solve the pair of linear equations....
Please help me by solving this!
Simplify the following
(1 1/2) ^-2
Answer:
1/2.25 or 4/9
Step-by-step explanation:
Someone please help me!! I will mark as brainliest
Answer:
if it's not on a test, just guess
Step-by-step explanation:
8th grade math. Solve and check. 2x + 3x + 5 = 4(x - 2)
Answer:
x=−13
Step-by-step explanation:
Combine the like terms:
2+3+5=4(−2)5+5=4(−2)
Distribute:
5+5=4(−2)
5+5=4−8
Subtract 5 from both sides
5+5=4-85+5−5=4−8−5
Then simplify:
x=−13
Answer:
x=−13
What is the slope of the linear equation represented by the table. NEEDED PLSS
Answer:28/4
Step-by-step explanation:
Change of y over the change of x.
Y is +28
X is +4
HELP IT WOULD MEAN A LOT IT'S DUE TODAY IN 7 MINUTES
Answer:
39
Step-by-step explanation:
39 + 32 = 71
hope this helps have a good day!!
PLEASE MARK BRAINLIEST!! :)
Shown is a square garden with a triangular pond.
Find the area of the garden that is grass
The area of the garden that is grass is 30 square meters.
The square garden has a side length of 6 meters.
The triangular pond has a base of 4 meters and a height of 3 meters.
The area of the garden that is grass.
The area of the square garden is 6 x 6 = 36 square meters.
The area of the triangular pond is (1/2) x 4 x 3 = 6 square meters.
Therefore, the area of the garden that is grass is 36 - 6 = 30 square meters.
The area of the garden that is grass is 30 square meters.
Here are the steps in detail:
Calculate the area of the square garden: 6 m * 6 m = 36 square meters
Calculate the area of the triangular pond: (1/2) * 4 m * 3 m = 6 square meters
Subtract the area of the pond from the area of the square to find the area of the grass: 36 square meters - 6 square meters = 30 square meters
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Ethan is designing a new board game, and is trying to figure out all the possible
outcomes. How many different possible outcomes are there if he spins a spinner with
three equal-sized sections labeled Walk, Run, Stop and rolls a fair die in the shape of
a cube that has six sides labeled 1 to 6?
Answer:
18
Step-by-step explanation:
3x6
if I have 100 baskets and I have 400 hundred apples how many apples will go into each basket
Answer: 4 apples will go into each basket if you want all the baskets to be filled with an equal amount.
Step-by-step explanation:
100x=400
dividing through by 100 we get
x=4
Simplify: i^69
Please help fast
Answer: it's just "i"
Step-by-step explanation:
PLEASE HELP ME ASAP.
Answer:
use pathway but with an M instead of P
Step-by-step explanation:
BRAINLIEST GOES TO THE CORRECT ANSWER!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
11.99
Step-by-step explanation:
Which statement is true for brainliest
Answer:
<A≅<Z
Step-by-step explanation:
Hope This Helps!
[tex] \sqrt{ x} = \sqrt{2} + 1 \: then \: x = [/tex]
helpppp asap
edit:help guys i have examm
Answer:
3+2√2Step-by-step explanation:
Given the expression
√x = √2 + 1
To get x, we will have to square both sides
(√x)² = (√2 + 1)²
x = (√2 + 1)(√2 + 1)
x = √4+√2+√2+1
x = 2+2√2+1
x = 3+2√2
Hence the value of x is 3+2√2
Jack invested $7,600 in an account paying an interest rate of 6\tfrac{1}{4}6 4 1 % compounded continuously. John invested $7,600 in an account paying an interest rate of 6\tfrac{3}{4}6 4 3 % compounded quarterly. After 19 years, how much more money would John have in his account than Jack, to the nearest dollar?
Answer: John would have $1371.33 more in his account than Jack.
Step-by-step explanation:
Formula to calculate amount after t years if compounded continuously:
[tex]A=Pe^{rt}[/tex]
Formula to calculate amount after t years if compounded quarterly:
[tex]A=P(1+\dfrac{r}{4})^{4t}[/tex]
, where P= Principal amount, r= rate of interest.
Given: P= $7,600
t=19 years
For Jack, [tex]r=6\dfrac{1}{4}\%=\dfrac{25}{4}\%=\dfrac{25}{400}=0.0625[/tex]
For John, [tex]r=6\dfrac{3}{4}\%=\dfrac{27}{4}\%=\dfrac{27}{400}=0.0675[/tex]
Amount in Jack's account after 19 years= [tex]7600e^{0.0625(19)}[/tex]
[tex]=7600e^{1.1875}\\\\=7600(3.27887376794)\\\\\approx\$24,919.44[/tex]
Amount in John's account after 19 years= [tex]7600e^{0.0675(19)}[/tex]
[tex]=7600(1+0.0675)^{19}\\\\=7600(3.45931245291)\\\\\approx\$26,290.77[/tex]
Difference = 26290.77-24919.44 = $ 1,371.33
John would have $1371.33 more in his account than Jack.
Answer:668
Step-by-step explanation: I just did it.
(5 + 3) ÷ 2 + (52 - 3) Simplify:
Answer:
53
Step-by-step explanation:
To add fractions find the LCD and then combine
What value of x makes the equation below true 5(x − 8) + 26 = −9? A 1 B -1 C 15 D -15
Solve -3.5=x-4 for x using the multiplication propertiy of equality
Answer:
Hello! :) have a good day!
X= 0.5
Answer:
x = 0.5
Step-by-step explanation:
Please Help!
if these two shapes are similar, what is the measure of missing length q?
Answer:
40
Step-by-step explanation:
96 ÷ 60 = 1.6
25 × 1.6 = 40
Disclaimer: Yay, okay. The person above me got the same answer so this is right.
Pete is choosing his clothes for the day. His bottoms will be either cargo shorts(C) or jeans (J). His top will be T shirt (T), sweatshirt (S), or long sleeved shirt (L)
The question is incomplete. Here is the complete question.
Pete is choosing his clothes for the day. His bottoms will be either cago shorts (C) or jeans (J). His top will be T-shirt (T), sweatshirt (S) or long sleeved shirt (L).
Which is a complete list of the possilbe outfits he can choose from?
CT, CS, CL, JT, JS, JL
CJ, CT, CS, CL
CJT, CJS, CJL
CT, TC, JS, SJ, CL, LC
Answer: CT, CS, CL, JT, JS, JL
Step-by-step explanation: The Fundamental Counting Principle is a method of determining a number of ways independents events can occur, i.e., it states that if there are t ways of doing something and w ways of doing another, then there are t x w ways of doing both things.
For example:
Peter has 2 choices of bottom and 3 choices of top. So, according to the principle, he will have 2 x 3 choices of clothing.
And the choices are:
shorts and t-shirt = CT
shorts and sweatshirt = CS
shorts and long sleeved = CL
jeans and T-short = JT
jeans and sweatshirt = JS
jeans and long sleeved = JL
The order he chooses doesn't matter.
So, the right alternative is CT, CS, CL, JT, JS, JL.
A triangle has side lengths of 11 cm and 7cm. Which could be the value of the third side, 19cm or 17 cm
Answer:
use the Pythagoras theorem..you will got the solution
Answer:
The answer is 17
Step-by-step explanation:
Simplify this algebraic expression.
9k + 7 - K + 4 =
Answer:
8k+11
Step-by-step explanation:
Combine like terms
9k-k
7+4
9k-k=8k
7+4=11
8k+11
Beniceo Skis 748yd in 3 mins. At this rate, How many miles does beniceo ski in an hour? (1 mi= 1,760 yd). mi=miles yd= yards
Answer:
8.5 miles
Step-by-step explanation:
3x20=60, 60 minutes also being an hour so if you multiply 748 by 20 then it gives you 14,960 annndd now you have to divide by the amount of yards in a mile 14,960/1,760=8.5
Which equation correctly uses the law of cosines to solve for the length s?
Answer: Choice D
s^2 = 9^2 + 10^2 - 2(9)(10)cos(100)
==========================================================
Explanation:
Consider the pythaorean theorem
a^2 + b^2 = c^2
which is the same as saying
c^2 = a^2 + b^2
If we tack on "-2ab*cos(C)", then we end up with
c^2 = a^2 + b^2 - 2ab*cos(C)
which is one form of the law of cosines. The side c is opposite angle C, and the two are on opposite sides of the equation. The 'a's and 'b's are on the right side with the angle C.
Note if C = 90 degrees, then cos(C) = cos(90) = 0 which means the whole "-2ab*cos(C)" term goes to 0 and we'd be left with the pythagorean theorem again.
In this case, we replace c with s, replace 'a' with 9, replace b with 10, and C with 100.
Answer:
Option (4)
Step-by-step explanation:
Cosine rule states,
(UT)² = (SU)² + (ST)² - 2(SU)(ST)cos(∠UST)
Here, UT is the opposite side of angle UST and two sides SU and ST are the adjacent sides.
∠UST is the included angle between SU and ST.
By this formula,
s² = 9² + 10² - 2(9)(10)cos(100°)
Therefore, Option (4) will be the answer.
I really need help
-21a+35
Answer:
-7 (3a - 5)
Step-by-step explanation:
Answer:
[tex] - 7(3a - 5)[/tex]
Step-by-step explanation:
you just have to factor out the common term 7.
Please help with this it is due today
Answer:
24
Step-by-step explanation: