You are given the rate of investment dI/dt. Find the capital accumulation over a five-year period by evaluating the definite integral Capital accumulation = 5 dI dt dt 0 where t is the time in years. (Round your answer to two decimal places.) dI dt = 16,000t (t2 + 2)2
Evaluate the definite integral.
Evaluate the definite integral.
Use any basic integration formula or formulas to find the indefinite integral. (Use C for the constant of integration.)
Answers
capital accumulation is 3,973,910.14.
To evaluate the definite integral, we will have to find the indefinite integral. We use integral by substitution to find the indefinite integral.
Capital Accumulation = ∫ dI/dt dt
= ∫ 16,000t (t^2 + 2)^2dt
If u = t^2 + 2 then du = 2t dt so the integral is
Capital accumulation = ∫ 16,000t (t^2 + 2)^2 dt
= ∫ 16,000 × (u - 2) × u^2 du/2
= ∫ 16,000u^3 - 64,000u^2 + 64,000udu/2
= 8,000u^4/4 - 32,000u^3/3 + 32,000u^2/2 + C
= 2,000u^4 - 10,667.7u^3 + 16,000u^2 + C
Substituting u again gives us:
Capital Accumulation = 2,000(t^2 + 2)^4 - 10,667.7(t^2 + 2)^3 + 16,000(t^2 + 2)^2 + C
To evaluate the definite integral, we need to find the values of this expression at t=0 and t=5 and subtract the two.
Capital Accumulation = [2,000(5^2 + 2)^4 - 10,667.7(5^2 + 2)^3 + 16,000(5^2 + 2)^2] - [2,000(0^2 + 2)^4 - 10,667.7(0^2 + 2)^3 + 16,000(0^2 + 2)^2]
= [2000(27)^4 - 10667.7(27)^3 + 16000(27)^2] - [2000(2)^4 - 10667.7(2)^3 + 16000(2)^2]
= 4,607,143.47 - 1,333,333.33 + 691,200
= 3,973,910.14
Therefore, the five-year capital accumulation is 3,973,910.14.
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Related Questions
Choose the equation that satisfies the data in the table.
-15 0 15
х
[
y
0
2
4
Answers
Answer:
B. y = \(\frac{2}{15} X + 2\)
Step-by-step explanation:
I. Given x = 15 and y = 4
4 = \(\frac{2}{15}(15) + 2\)
4 = 2+2
4 = 4 true
II. Give x = 0 and y = 2
2 = \(\frac{2}{15}(0) + 2\)
2 = 0 + 2
2 = 2 true
III. Given x = -15 and y = 0
0 = \(\frac{2}{15}(-15) + 2\)
0 = -2 + 2
0 = 0 true
Good luck.
if $396 is invested at an interest rate of 13% per year and is compounded continuously, how much will the investment be worth in 3 years ?
Answers
Answer:
154.44
Step-by-step explanation:
What is 13% of 396?
Y is 13% of 396
Equation: Y = P% * X
Solving our equation for Y
Y = P% * X
Y = 13% * 396
Converting percent to decimal:
p = 13%/100 = 0.13
Y = 0.13 * 396
Y = 51.48
Now multiply by 3 (amount of continuous years)
51.48 * 3
=154.44
Hope it helps!
Celeste is planting a rectangular flower garden in which the width will be 4 feet less than its length. She has decided to put a birdbath within the garden that will occupy a space 3feet by 4 feet how many feet are now left for planting? Express your answer on factored form
Answers
Answer:
(L-6)(L+2)
Step-by-step explanation:
Let L be the length of the flower garden.
Then the width will be L-4.
The area of the flower garden = L*(L-4) =L²-4L
The area of the birdbath is 3*4 = 12 ft²
The area of the remaining space for planting is
= Area of flower garden - area of birdbath
L² - 4L - 12We can factor the expression as follows:
L² - 4L - 12 L²-(6-2)L-12L²-6x+2x-12taking common frome each two terms
L(L-6)+2(L-6)(L-6)(L+2)Therefore, the number of feet left for planting is (L-6)(L+2) in factored form.
A dairy farmer wants to mix a 70% protein supplement and a standard 20% protein ratio to make 1900 pounds of a high grade 55% protein ration how many pounds of each should he use
Answers
The dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ration.
To determine the amounts of the 70% protein supplement and the 20% protein ratio needed to make a 1900-pound high-grade 55% protein ration, we can set up a system of equations.
Let's assume x represents the pounds of the 70% protein supplement and y represents the pounds of the 20% protein ratio.
The total weight equation is given by:
x + y = 1900
The protein content equation is given by:
(0.70x + 0.20y) / 1900 = 0.55
Simplifying the second equation, we get:
0.70x + 0.20y = 0.55 × 1900
0.70x + 0.20y = 1045
Now, we can solve this system of equations to find the values of x and y.
Rearrange the first equation to solve for x:
x = 1900 - y
Substitute this expression for x in the second equation:
0.70(1900 - y) + 0.20y = 1045
1330 - 0.70y + 0.20y = 1045
1330 - 0.50y = 1045
-0.50y = 1045 - 1330
-0.50y = -285
y = -285 / -0.50
y = 570
Now substitute this value of y back into the first equation to find x:
x + 570 = 1900
x = 1900 - 570
x = 1330
Therefore, the dairy farmer should use 1330 pounds of the 70% protein supplement and 570 pounds of the 20% protein ratio to make a 1900-pound high-grade 55% protein ratio.
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Write a pair of integers whose sum is- -8
Answers
Answer:
-3+(-5)
Checking our answer:
Adding this does indeed give -8
(−20,F1) , (−10,F2) Step 1 of 2 : Compute the missing y values so that each ordered pair will satisfy the given equatio
Answers
\((-20, -4)\) and are all of the ordered pairings that fulfil this equation \(F = 9/5C + 32. (-10, 14)\).
What exactly are equation, and what varieties exist?Lines come in two varieties: identities and dependent equations. All possible values of the parameters result in an identity. Only certain combinations of the variables' values render a conditional equation true. Two expressions joined by the equals symbol ("=") form an equations.
What basic equation structure is used?Ax+By=C is the classic pattern for two-variable linear equations. A typical form linear equation is, for instance, 2x+3y=5. Finding all intercepts of a solution in this format is not too difficult. The approach additionally proves useful when trying to solve solutions combining two linear systems.
To find the missing y values, we need to substitute the given \(x\) values into the equation \(F = 9/5C + 32\) and solve for \(F\).
For the first ordered pair (-20, F1):
\(F1 = 9/5(-20) + 32\)
\(F1 = -36 + 32\)
\(F1 = -4\)
So the missing y value is \(-4\), and the complete ordered pair is \((-20, -4)\).
For the second ordered pair (-10, F2):
\(F2 = 9/5(-10) + 32\)
\(F2 = -18 + 32\)
\(F2 = 14\)
So the missing y value is \(14\), and the complete ordered pair is \((-10, 14)\).
Therefore, the complete set of ordered pairs that satisfy the equation \(F = 9/5C + 32\) is:
\((-20, -4)\) and \((-10, 14)\).
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The complete question is:
Given the equation
F=9,5
C+32
F=95C+32
where C is the temperature in degrees Celsius and F is the corresponding temperature in degrees Fahrenheit, and the following ordered pairs:
(−20,F1)
(−20,F1),(−10,F2)(−10,F2)
Step 1 of 2 : Compute the missing y values so that each ordered pair will satisfy the given equation.
Solve triangles: angle bisector theorem
DAC = BAD.
What is the length of CD?
Round to one decimal place.
Answers
Answer:
Step-by-step explanation:
CD/6.5 = 2.6/4.9 This is the result of the angle bisector theorem.
The theorem basically says that the side opposite the angle being bisected is divided the ratio of the sides enclosing the angle.
Multiply both sides of the proportion by 6.5
CD = 2.6 * 6.5 / 4.9
CD = 3.4489
CD = 3.4 rounded.
In order to solve the equation shown for x what would be the best first step? y=8 x-7
(A) Add 7 to each side
(B) Subtract 7 from each side
(c) Add 8 to each side
(D) Subtract 8 from each side
Answers
Answer:
A
Step-by-step explanation:
The first step is to add 7 to each side
y+7 = 8x -7 +7
= y + 7= 8x
Select the best estimate that would help you check the answer to
778
×
23
.
A.
700
×
30
B.
700
×
20
C.
800
×
20
D.
800
×
30
Answers
Answer: C. 800x20
Step-by-step explanation:
Answer:
The answer would be C
Step-by-step explanation:
778 is greater than 750, therefore the estimate for that would be 800. Then for 23, it is less 25 therefore, 23 would estimate to 20
Bro can someone please help? I’ll give you brainliest, I’m struggling really bad.
Answers
Answer:
has to be B
Step-by-step explanation:
3 would give you a horizontal line so that wouldnt be it
3/4 would give you a positive slope and you would need a fraction to get a slope like this and needs to be negative so B. -3/4
The value of y is directly proportional to the value of x. Given y = 12 when x = 36.
What is the value of y when x = 60?
Enter your answer in the box.
y =
Answers
p+aw=b make w the subject of the formula
Answers
Answer: To make "w" the subject of the formula "P+aw=b", we need to isolate "w" on one side of the equation.
First, we can subtract "P" from both sides of the equation to get:
aw = b - P
Next, we can divide both sides of the equation by "a" to get:
w = (b - P) / a
Therefore, the solution is:
w = (b - P) / a
Step-by-step explanation:
In this figure m∠A=(2x-2)°, m∠C=(4x-6)°,and m∠DBC=(5x+4)° What is m∠C
SHOW YOUR WORK will give 100 points!!
Answers
Answer:
answer 500
Step-by-step explanation:
2x2-40x33 divided by 2 and boom answer 500
Anser:
m∠C=42
Step-by-step explanation:
(2x - 2) + (4x - 6) = (5x + 4)
(6x - 8) = (5x + 4)
-4 -4
6x - 12 = 5x
-5x -5x
1x = 12
So 4 * 12 - 6 = 42
m∠C=42
How many 50ml can be filled from 5L
Answers
please help me!!!!!
Answers
Answer:
y=1
-4x + y= -3
-3 + 12= 9
y= {4}x + {3}
Step-by-step explanation:
*there is always a inviable 1 in front of a virable by it's self.*
What is the volume of the tri angular right prism?
Answers
Answer:
140 ft³
Step-by-step explanation:
imagine the prism is standing on one of its triangular sides.
then it becomes a regular object with the volume
base area × height
the base area is the area of the triangle
baseline × inner height / 2
in our case
4 × 7 / 2 = 14 ft²
so for the volume we have
14 × 10 = 140 ft³
A deck of cards has 52 cards with 4 suits (Hearts, Diamonds, Spades, and Clubs) and 13 cards in each suit (Ace thru 10, Jack, Queen, and King; the last three are considered face cards). A card is drawn at random from a standard 52-card deck. What is the probability that the card is not an Ace
Answers
Answer:
12/13
Step-by-step explanation:
P(card is not an Ace) =
(# of ways to not pick an ace) / (# of ways to pick a card from the deck) =
(52 - 4)/(52) =
48/52 =
12/13
Complete this sequence of numbers such that the difference between any two adjacent numbers is the same : 3/k, _, _, 9/2k.
Answers
The completed sequence is: 3/k, 3/k, 3/k, 9/2k.To complete the sequence of numbers with a constant difference between adjacent numbers, we can calculate the common difference by subtracting the first term from the second term.
Let's denote the missing terms as A and B.
The given sequence is: 3/k, A, B, 9/2k.
The common difference can be found by subtracting 3/k from A or B. Therefore:
A - 3/k = B - A = 9/2k - B.
To simplify, we can equate the two expressions for the common difference:
A - 3/k = 9/2k - B.
Next, we can solve for A and B using this equation.
Adding 3/k to both sides gives:
A = 3/k + 9/2k - B.
Now, we can substitute the value of A into the equation:
3/k + 9/2k - B - 3/k = 9/2k - B.
Simplifying further, we have:
9/2k - 3/k = 9/2k - B.
Cancelling out the common terms, we find:
-3/k = -B.
Multiplying both sides by -1, we get:
3/k = B.
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In a test with a mean of 100 and a standard deviation of 10, what is the standard deviation for a test score of 120
Answers
This question is incomplete
Complete Question
In a test with a mean of 100 and a standard deviation of 10, what is the standard score for a test score of 120?
Answer:
The standard score = 2
Step-by-step explanation:
The formula for Test (T) score is given as:
T score = zσ + μ
z = Standard or z score = ??
Standard deviation (σ) = 10
Mean (μ) = 100
Test score = 120
120 = 10z + 100
120 - 100 = 10z
20 = 10z
z = 20/10
z= 2
Therefore, the standard score = 2
Part 1: 12% annual interest on 132000 for 8 days
Part 2: 12% annual interest on 106,750 for 20 days.
If it helps, it's a 5 year note. Assuming 365 days in a year.
Answers
The interest for Part 1 is approximately $385.10.
The interest for Part 2 is approximately $709.31.
To calculate the interest for Part 1 and Part 2The formula is as follows:
Interest is calculated as follows: Principal * Rate * Time
Where
Principal represents the starting sumThe interest rate is rateTime measures length in years.Part 1:
$132,000 is the principal.
(Decimal) Rate = 12% = 0.12
Time = 8 days/365 days.
How much interest is there in Part 1?
Interest is calculated as follows : $132,000 * 0.12 * (8/365) = $385.10
Therefore, the interest for Part 1 is approximately $385.10.
Part 2:
$106,750 as the principal
(Decimal) Rate = 12% = 0.12
Time = 20 days / 365 days.
How much interest will there be in Part 2
Interest is calculated as follows : $106,750 * 0.12 * (20/365) = $709.31
Therefore, the interest for Part 2 is approximately $709.31.
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help please im really confused
Answers
Check the picture below.
so following the inscribed quadrilateral conjecture, let's get those equations that add up to 180°.
\((2y+74)+(7x+1)=180\implies 2y+7x+75=180\implies \underline{2y+7x=105} \\\\[-0.35em] ~\dotfill\\\\ (2y+100)+(6x-10)=180\implies 2y+6x+90=180\implies \underline{2y+6x=90} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{2y+7x=105}\implies 2y=105-7x \\\\\\ \stackrel{\textit{using the 2nd equation}}{2y+6x=90}\implies 2y=90-6x\implies \stackrel{\textit{substituting from above}}{105-7x=90-6x} \\\\\\ 105=90+x\implies \boxed{15=x}\)
\(\stackrel{\textit{since we know that}}{2y+7x=105}\implies 2y+7(15)=105\implies 2y+105=105 \\\\\\ 2y=0\implies y=\cfrac{0}{2}\implies \boxed{y=0}\)
How many square centimeters are in an area of 3.30in
Answers
Answer:
8.382 cm
Step-by-step explanation:
1in = 2.54 cm
3.30 x 2.54 = 8.382 cm
A rectangular patio has a length of (1 + 2x) yards and a width of (2 - 3x) yards. Which correctly describes the area and perimeter of the patio?
Answers
Area of the patio is -6x² + x + 2 square yards and perimeter of the patio is 6 - 2x yards.
What is a yard?A yard is a unit of measurement used to measure length or distance in both the US customary system and the British imperial system. One yard is equal to 3 feet or 36 inches. In the US customary system, a yard is equal to 0.9144 meters, while in the British imperial system, it is equal to 0.9144 meters or 3 feet. Yards are commonly used for measuring larger distances, such as in construction or landscaping, as well as in some sports like American football and cricket.
The area of the rectangular patio is given by multiplying its length by its width, so the area is:
A = (1 + 2x)(2 - 3x)
Now using distributive property we get,
A = 2 - 3x + 4x - 6x²
Simplifying further, we get:
A = -6x² + x + 2
Therefore, the area of the patio is described by the quadratic equation -6x² + x + 2.
To find the perimeter of the patio, we add up the lengths of all four sides. The length and width are given as (1 + 2x) and (2 - 3x), respectively, so the perimeter is:
P = 2(1 + 2x) + 2(2 - 3x)
Simplifying this expression, we get:
P = 2 + 4x + 4 - 6x
P = 6 - 2x
Therefore, the perimeter of the patio is described by the linear equation 6 - 2x.
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Convert.
5 days =
lao
hours
Answers
Answer:
120 Hours
Step-by-step explanation:
24 hours in a day
5 days
24 x 5 = 120
Simplify the expression. (2+1)×42÷2
Answers
Answer:
63
Step-by-step explanation:
Simplifying the expression,
→ (2+1) × 42 ÷ 2
→ 3 × 42 ÷ 2
→ 126 ÷ 2 = 63
Hence, the answer is 63.
solve this equation
3/5x-2=2/3x-1
Answers
The solution to the equation 3 / 5x-2 = 2 / 3x-1 is x = 1.
What is the solution to the given equation?Given the equation in the question;
3 / 5x-2 = 2 / 3x-1
To solve for x, cross multiply the equation
3 / 5x-2 = 2 / 3x-1
3( 3x - 1 ) = 2( 5x - 2 )
Apply distributive property
3( 3x - 1 ) = 2( 5x - 2 )
3×3x + 3×-1 = 2×5x + 2×-2
9x - 3 = 10x - 4
Subtract 10x from both sides
9x - 10x - 3 = 10x - 10x - 4
9x - 10x - 3 = - 4
Add 3 to both sides
9x - 10x - 3 + 3 = - 4 + 3
9x - 10x = - 4 + 3
-x = -1
Divide both sides by -1
-x/-1 = -1/-1
x = 1
Therefore, the value of x is 1.
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What is the value of i^97 - i
Answers
Answer:
0
Step-by-step explanation:
i^1 = i
i^2 = - 1
i^3 = i^2 * i = - 1
i^4 = i^2 * i^2 = -1 * -1 = 1
Now the circle just repeats itself. So what you do is find out the remainder of i^97 which you divide by 4. What you get is 24 with a remainder of 1.
So i^97 = i
i - i = 0
The answer is 0
Answer:
b
Step-by-step explanation:
Find the value of p.
-25 = -4p + 19
Answers
4p= 19+25
2. Add 19 and 25
4p= 44
3. Divide by 4
p= 11
Answer:
9.75
Step-by-step explanation:
-25 = -4p + 19
-25 - 19 = -4p
-39 ÷ -4 = p
9.75 = p
7+2x/3=5 need help aspa
Answers
Answer:
x = –3
Step-by-step explanation:
7 + 2x/3 = 5
2x/3 = 5 – 7
2x/3 = –2
multiply both sides by 3
2x = –6
divide both sides by 2
x = –6/2
x = –3
please rate as brainliest i need to move to the next rank
Help me and I’ll give you brainliest
Answers
Answer:
49
Step-by-step explanation: