Answers
Answer:
y' = -4eˣ sin⁵(eˣ)
Step-by-step explanation:
Part 1 of the Fundamental Theorem of Calculus simply says that the definite integral of a function is equal to the antiderivative evaluated between the limits.
∫ₐᵇ f(x) dx = F(b) − F(a), where F(x) = ∫ f(x) dx.
y = ∫ₑₓ⁰ 4 sin⁵(t) dt
To integrate, use Pythagorean identity.
y = 4 ∫ₑₓ⁰ (1 − cos²(t))² sin(t) dt
Ignoring the limits for the moment, let's say u = cos(t) and du = -sin(t) dt.
y = 4 ∫ (1 − u²)² (-du)
y = -4 ∫ (1 − 2u² + u⁴) du
y = -4 (u − ⅔u³ + ⅕u⁵) + C
y = -4 (cos(t) − ⅔ cos³(t) + ⅕ cos⁵(t)) + C
Evaluate between t = eˣ and t = 0.
y = -4 (cos(0) − ⅔ cos³(0) + ⅕ cos⁵(0)) + C − [-4 (cos(eˣ) − ⅔ cos³(eˣ) + ⅕ cos⁵(eˣ)) + C]
y = -4 (1 − ⅔ + ⅕) + 4 (cos(eˣ) − ⅔ cos³(eˣ) + ⅕ cos⁵(eˣ))
Now take derivative with respect to x.
y' = 0 + 4 (-sin(eˣ) eˣ − 2 cos²(eˣ) (-sin(eˣ) eˣ) + cos⁴(eˣ) (-sin(eˣ) eˣ))
y' = -4eˣ sin(eˣ) (1 − 2 cos²(eˣ) + cos⁴(eˣ))
y' = -4eˣ sin(eˣ) (1 − cos²(eˣ))²
y' = -4eˣ sin⁵(eˣ)
This can be more easily calculated using the Second Fundamental Theorem of Calculus.
Related Questions
A refrigerator is priced at $525.50. There is a 6% sales tax rate. What is the sales tax for the refrigerator in dollars and cents?
Be sure to use the correct place value.
Answers
Answer:
Sales tax=$31.53
The total price is: $557.03
Step-by-step explanation:
$525.50*0.06=$31.53
Suppose there are two scale drawings of the same house. One uses the scale of 1 cm to 2 m, and the other uses the scale 1 cm to 4 m. Which drawing is larger?
Answers
Answer:
it's 1 cm to 2 m
Step-by-step explanation:
Sometimes two different scales are actually equivalent, such as 5 cm to 10 m and 1 cm to 2 m. It is common to write a scale so that it tells you what one unit on the scale drawing represents (for example, 1 cm to 2 m).
(3 x 10) x 8 = x(10 x 8)
Answers
Answer:
Here you go
Step-by-step explanation:
(3 x 10) x 8 = x(10 x 8)
What you do the distributive property so multiply 3x10 and you get 30 and multiply by 8 you get 240 so one side is solved. Now multiply 10x8 you get 80 and remember to multiply the variable x so you get 80x=240 now divide 80 both sides and you will get 3 as your total answer
Answer:
3
Step-by-step explanation:
(3x10)=30
30x8=240
(10x8)=80
240/80=3
Solve for x
-2x + 7 = 25
Answers
Answer:
-9
Step-by-step explanation:
Step 1:
-2x + 7 = 25
Step 2:
-2x = 18
Step 3:
-18 = 2x
Answer:
-9
Hope This Helps :)
Answer: -9
Step-by-step explanation: hope this helped ❤️
what is f(g(13)) ? A mapping diagram is shown.
Answers
Answer:
im about 90% sure its 32
Step-by-step explanation:
At a grocery store, almonds are on sale for $3.78 per pound. What is the price of 4.5 pounds? Please show explanation
Answers
$17.01
Step-by-step explanation:
To find the the price, you must find price per pound x how many pounds you will be priced for
price per pound x how many pounds you will be priced for
This is represented by 3.78 x 4.5
3.78 x 4.5 = 17.01
$17.01 is the cost of 4.5 pounds of almonds
Answer:
17.01 pounds
Step-by-step explanation:
3.78 x 4.5 = 17.01
Hope this helps!
Need some help on this question Select the polynomial that is divisible by (x-1).
Answers
Answer:
A
Step-by-step explanation:
p(x)=5x^3−4x^2−x
what is equalvent to neagative -8
Answers
The endpoints of RS are R(−4,3) and S(16,18). Complete each statement using a fraction.
a. (8,12) is the point ___ of the way from R to S.
b. (0,6) is the point ___ of the way from R to S.
Answers
Answer:
a) (8,12) is the point [tex]\frac{3}{5}[/tex] of the way from R to S, b) (0, 6) is the point [tex]\frac{1}{5}[/tex] of the way from R to S.
Step-by-step explanation:
Let be [tex]X[/tex] a point in the line between endpoints [tex]R[/tex] and [tex]S[/tex]. The ratio of the line segment [tex]RX[/tex] to the line segment [tex]RS[/tex] is given by:
[tex]r = \frac{RX}{RS}[/tex]
Where:
[tex]RX = \sqrt{(x_{X}-x_{R})^{2}+(y_{X}-y_{R})^{2}}[/tex]
[tex]RS = \sqrt{(x_{S}-x_{R})^{2}+(y_{S}-y_{R})^{2}}[/tex]
Let be [tex]x_{R} = -4[/tex], [tex]y_{R} = 3[/tex], [tex]x_{S} = 16[/tex] and [tex]y_{S} = 18[/tex].
a) If we know that [tex]x_{X} = 8[/tex] and [tex]y_{X} = 12[/tex], the ratio of the line segment [tex]RX[/tex] to the line segment [tex]RS[/tex] is:
[tex]RX =\sqrt{[8-(-4)]^{2}+(12-3)^{2}}[/tex]
[tex]RX = 15[/tex]
[tex]RS =\sqrt{[16-(-4)]^{2}+(18-3)^{2}}[/tex]
[tex]RS = 25[/tex]
Then,
[tex]r = \frac{15}{25}[/tex]
[tex]r = \frac{3}{5}[/tex]
(8,12) is the point [tex]\frac{3}{5}[/tex] of the way from R to S.
b) If we know that [tex]x_{X} = 0[/tex] and [tex]y_{X} = 6[/tex], the ratio of the line segment [tex]RX[/tex] to the line segment [tex]RS[/tex] is:
[tex]RX =\sqrt{[0-(-4)]^{2}+(6-3)^{2}}[/tex]
[tex]RX = 5[/tex]
[tex]RS =\sqrt{[16-(-4)]^{2}+(18-3)^{2}}[/tex]
[tex]RS = 25[/tex]
Then,
[tex]r = \frac{5}{25}[/tex]
[tex]r = \frac{1}{5}[/tex]
(0, 6) is the point [tex]\frac{1}{5}[/tex] of the way from R to S.
solve for x
x/3 + 14 = 35
Can you help?
Answers
Answer:
X=63
Step-by-step explanation:
Im pretty sure at least
Under normal conditions, 1.5 feet of snow will melt into 2 inches of water. After a recent snowstorm, there were 4 feet of snow. How many inches of water will there be when the snow melts?
Answers
Answer:
The answer im pretty sure is 5.33 inches of water.
Step-by-step explanation:
In which number 2 worth one-tenth as much as it is in the number 378,215 A.439,592 B.657,423 C.872,551 D.939,264
Answers
Answer:
i would say b since its 1 placement lower
Step-by-step explanation:
Round 491,778 to the nearest hundred
Answers
Answer:
491,800!
Step-by-step explanation:
Rounding 491,778 to the nearest hundred we get 491,800 as our answer.
Given,
491,778
We need to round 491,778 to the nearest hundred.
What is the place value of a given number?The different place value is given below:
Example: 468975
4 - hundred thousands
6 - ten thousands
8 - thousands
9 - hundreds
7 - tens
5 - ones
Which number 491,778 is in the hundred place value.
= The number 7 in 491,778 is in the hundred place value.
Round 491.778 to its nearest hundreds.
= 491,778
Since 7 is in the hundred place value we need to round 778 to its nearest hundred.
It is either 700 or 800.
Since 778 is greater than or equal to 750.
We will round it to 800.
491,800 is our answer.
Thus rounding 491,778 to the nearest hundred we get 491,800 as our answer.
Learn more about comparing place values in numbers here:
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11. If a square has an area of 121 square meters, what is the side length? A. 60.5 m B. 12 m C. 11 m D. 484 m
Answers
Answc
Step-by-step explanation:
answer= C. 11m
simplify 5(x – 2) + 11
Answers
Answer:
1/5
Step-by-step explanation:
Step 1:
5x - 10 + 11
Step 2:
5x = 1
Answer:
x = 1/5
Hope This Helps :)
Plz help 7th grade math
Answers
Find the volume of the solid shown or described. If necessary round to the nearest tenth. Find the volume of the figure below. Round to the nearest tenth. M
Answers
Answer:
C) 3057.6 cm³
Step-by-step explanation:
Rectangular prism: 20x11x9=1980
Cylinder: [tex]\pi[/tex]r²h = [tex]\pi[/tex]X7x7x7=1077.57
1980+1077.57=3057.57
I need help please it’s really hard and I don’t understand it
Answers
The line segment HI has length 3x - 5, and IJ has length x - 1.
We're told that HJ has length 7x - 27.
The segment HJ is made up by connecting the segments HI and IJ, so the length of HJ is equal to the sum of the lengths of HI and IJ.
This means we have
7x - 27 = (3x - 5) + (x - 1)
Solve for x :
7x - 27 = (3x + x) + (-5 - 1)
7x - 27 = 4x - 6
7x - 4x = 27 - 6
3x = 21
x = 21/3
x = 7
Select the correct answer from each drop-down menu. Ashton works as a marketing manager for a consumer products firm. His total earnings, A, in x months is given by the function A(x) = 2,400x + 40x2. His total savings, S, in x months is given by the function S(x) = 250x + 500. The function E(x) = represents Ashton’s total expenses in x months. Ashton’s expenses for 3 years total $
Answers
Answer:
E(x) = 40x² + 2150x - 500E(36) = $128740Step-by-step explanation:
Earnings = A(x)Savings = S(x)Expenses = E(x)Savings = Earnings - Expenses ⇒ Expenses = Earnings - Savings
E(x) = A(x) - S(x)E(x) = 2400x + 40x² - (250x + 500) E(x) = 2400x + 40x² - 250x - 500 E(x) = 40x² + 2150x - 500E(3 years) = E(36 months)
E(36) = 40*36² + 2150*36 - 500= $128740The school needs to buy new computers for four classrooms. If the school needs 20 new computers in each classroom, how many computers does it need to buy in total? Explain
Answers
Answer:
80 computers
Step-by-step explanation:
For 1 class=20 computers
For 4 classes=20x4=80 computers
Warehouse Club Membership If the annual fee for a warehouse club membership is $100 and the reward rate is 2% on club purchases for the year, then the linear equation y = 100 - 0.02x models the actual annual cost of the membership y, in dollars. Here x represents the annual amount of club purchases, also in dollars. (a) Determine the actual annual cost of the membership if club purchases for the year are $2400 (b) What amount of club purchases would reduce the actual annual cost of the mem bership to $50? ) How much would a member have to spend in annual club purchases to reduce the annual membership cost to $0?
Answers
Answer:
(a) $52
(b) $2500
(c) $5000
Step-by-step explanation:
(a) y = 100 - 0.02x
x = 2400
y = 100 - 0.02(2400)
y = 100 - 48
y = 52
$52
(b) 50 = 100 - 0.02x
-50 = -0.02x
x = 2500
$2500
(c) 0 = 100 - 0.02x
0.02x = 100
x = 5000
$5000
Solve the equation for the indicated variable. A=r+rvf, for v
Answers
Answera=frv+r
Step-by-step explanationa=r+rvf
To solve for a variable in an equation means that we change the subject of the formula. The solution to the equation for variable v is:
[tex]\frac{A - r}{rf} = v[/tex]
Given that:
[tex]A = r + rvf[/tex]
Subtract r from both sides
[tex]A - r = rvf[/tex]
Divide both sides by rf
[tex]\frac{A - r}{rf} = v[/tex]
Rewrite as:
[tex]v=\frac{A - r}{rf}[/tex]
Hence, the solution to the equation for variable v is:
[tex]\frac{A - r}{rf} = v[/tex]
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On a recent quiz, the class mean was 70 with a standard deviation of 2.1. Calculate the z-score (to 4 decimal places) for a person who received score of 76.
Answers
So, in this case the equation would be
(76-70)/(2.1)
For,
X=76
Mean=70
Standard Deviation= 2.1
After solving we find that the z score equals 2.85714
or
2.8571
Story Problem
Joseph's lunch at a restaurant costs $13.00, without tax. He leaves the
waiter a tip of 15% of the cost of the lunch, without tax. What is the total cost
of the lunch, including the tip, without tax?
Answers
Please helppppp!!!!!!!
Answers
Answer:
K 2
J 4
Step-by-step explanation:
Solved it as an equation 2 x+x=6
x= number of miles Katie drives
If the Perimeter of the triangle 15 centimeters, what is the value of n
Answers
Answer:
Step-by-step explanation:
n+2n+1+5n-6=15
= 8n + 1 - 6= 15
= 8n + 1 - 6 + 6 = 15 + 6
= 8n +1 = 21
= 8n + 1 - 1 = 21 - 1
=8n = 20
= 8n / 8 = 20 / 8
= n = 2.5
the value of ‘n’ is 2.5
The value of n in the triangle is 2.5
How to determine the value of n?The perimeter of the triangle is the sum of its side lengths.
So, we have:
P = n + 2n + 1 + 5n - 6
Evaluate the like terms
P = 8n - 5
The perimeter is 15.
So, we have:
8n - 5 = 15
Add 5 to both sides
8n = 20
Divide by 8
n = 2.5
Hence, the value of n is 2.5
Read more about perimeter at:
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ILL GIVE YOU BRAINLIST !!
Flying L helicopter was flying 400 feet above sea level, then descended 100 feet to
avoid bad weather. When the clouds cleared, it ascended 200 feet. Write an expression, then determine the integer that represents Flying L's elevation now.
Answers
Answer:
500ft
Step-by-step explanation:
Elevation = 400ft-100ft+200ft
Elevation = 500ft
If you need an expression with only variables, set 400, 100, 200, and elevation as separate variables
Please solve 2x+6 > 20
Answers
Answer:
See below.
Step-by-step explanation:
So we have the inequality:
[tex]2x+6>20[/tex]
Subtract 6 from both sides:
[tex]2x>14[/tex]
Divide both sides by 2:
[tex]x>7[/tex]
So, the solution is all numbers greater than 7.
And we're done!
PLEASE HELP 15 POINTS!!!!!! What is the value of x?
Answers
Answer:
128 degrees
Step-by-step explanation:
Remember : Sum of all angles in a hexagon is 720°!
Thus,
128° + 100° + 120° + X + 112° + 133° =720°
=> 593 + X = 720
=> X = 127°235 people are at RSM summer camp. There are 35 more boys than girls, and 70 fewer adults than girls. How many people of each group are at the camp?
Answers
Answer:
The number of girls are 90 girls
The number of boys are 125 boys
The number of adults are 20 adults
There are 90 girls, 125 boys and 20 adults at the camp
Step-by-step explanation:
The total number of people is given as 235 people
The number of boys = 35 + The number of girls
The number of adults = The number of girls - 70
Let the total number of girls = G
Therefore, we have;
The number of boys = 35 + G
The number of adults = G - 70
The total number of persons = The number of boys + The number of adults + The number of girls
Therefore;
235 = The number of boys + The number of adults + The number of girls
Which gives;
235 = 35 + G + G - 70 + G = 3·G - 35
235 = 3·G - 35
3·G - 35 = 235
3·G = 235 + 35 = 270
G = 270/3 = 90
The number of girls = 90
The number of boys = 35 + The number of girls = 35 + 90 = 125
The number of boys = 125
The number of adults = The number of girls - 70 = 90 - 70 = 20
The number of adults = 20.
Answer:
There are 90 girls, 125 boys, and 20 adults.
Step-by-step explanation:
Let x be the number of girls. How many boys were there?
x + 35
How many adults were there?
x - 70
We know that 235 people are at RSM summer camp. Use this to make an equation.
x + (x + 35) + (x - 70) = 235
x + x + 35 + x - 70 = 235
3x - 35 = 235
3x - 35 + 35 = 235 + 35
3x = 270
3x ÷ 3 = 270 ÷ 3
x = 90
x, x + 35, x - 70
90, 125, 20