Answer:
dp/dt = 0.02P-N
Step-by-step explanation:
[tex]\frac{p(t+t)}{nt}[/tex]
The differential equation that describes the relationship between P and t is:
dP/dt = rP - N
where P is the balance in dollars, t is time in years, r is the annual interest rate, and N is the rate of withdrawals in dollars per year.
What is a differential equation ?A differential equation is an equation that relates an unknown function to its derivatives (or differentials) with respect to one or more independent variables. In other words, it is an equation that involves derivatives of an unknown function.
The rate of change of the balance P in the bank account is equal to the difference between the rate of interest earned on the account and the rate at which money is withdrawn from the account.
The rate of interest earned on the account is given by the continuous compounding formula:
dP/dt = rP
where r is the annual interest rate, P is the balance in dollars, and dP/dt is the rate of change of P with respect to time.
On the other hand, the rate at which money is withdrawn from the account is given by the expression:
dN/dt = N/T
where N is the rate of withdrawals in dollars per year, and T is the time interval in years between withdrawals.
If we assume that Ana withdraws money from the account continuously at a rate of N dollars per year, we can write:
N = dN/dt
Substituting this into the first equation, we get:
dP/dt = rP - dN/dt
Substituting the expression for dN/dt, we get:
dP/dt = rP - N/T
Simplifying, we get:
dP/dt = rP - N
which is the differential equation that describes the relationship between P and t.
The differential equation
dP/dt = rP - N
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Gino wants to leave at least 20% tip on his restaurant bill of $197.40. Approximately how much tip should he add to the bill?
1 point
Every five years in March, the population of a certain town is recorded. In
1995, the town had a population of 4500 people. From 1995 to 2000, the
population increased by 15%. From 2000 to 2005, the population
decreased by 4%. What was the town's population in 2005? *
4527
4968
4995
5382
Answer:
So, the town had a population on 4,500 people in 1995. Then from 1995 to 2000, the population increased by 15%.
Convert 15% to a decimal by dividing it by 100. Then, the population in 1995 by this decimal.
15% ÷ 100 = 0.15
4,500 × 0.15 = 675
Now, add this to the population in 1995.
4,500 + 675 = 5,175
This means that the town had a population of 5,175 people in 2000.
To calculate the town's population in 2005, repeat the same steps we took to find the population in 2000, except this time we will subtract instead of add since the population DECREASED.
4% ÷ 100 = 0.4
5,175 × 0.4 = 207
5,175 - 207 = 4,968
FINAL ANSWER:
The town had a population of 4,968 in 2005.
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Step-by-step explanation:
A baker uses a circular pan with a 24-inch diameter to make a pizza. What is the area of the pizza? Round to the nearest hundredths
A. 37.68
B. 75.36
C. 1808.64
D. 452.16
Answer:
D
Step-by-step explanation:
A = πr^2
A = π12^2
A = π144
A ≈ 452.16
Answer:
The answer is 452.16
Step-by-step explanation:
If you don't believe me you can use a circle calculator
The ratio of children to adults is 4 to 3. How many children are there if there are 2700 adults?
Answer:
2025 children
Step-by-step explanation:
4 2700
-- = --------
3 x
cross multiply
4x = 8100
x = 2025
What is the solution to this equation? 3v(1/8-x)=-1/2
Answer:
v = −4/−24x+3
Step-by-step explanation:
Let's solve for v.
3v(1/8−x) = −1/2
Step 1: Factor out variable v.
v(−24x+3/8) = −1/2
Step 2: Divide both sides by (-24x+3)/8.
v(−24x+3/8)/−24x+3/8 = −1/2/−24x+3/8
v=−4/−24x+3
Shidjdjzjzjzjzjzjzjzjzjzjzzjzjzjzjzjzj
Answer:
14130 yd³
Step-by-step explanation:
The formula of volume of sphere
[tex] = \frac{4}{3} \pi {r}^{3}[/tex]
The volume of the sphere
[tex] = \frac{4}{3} \times 3.14 \times {(30 \div 2)}^{3} [/tex]
[tex] = \frac{4}{3} \times 3.14 \times {15}^{3} [/tex]
[tex] = \frac{42390}{3} [/tex]
= 14130 yd³
Allen has a piece of wood that is 10.5 feet long. He decides to cut it into 3 equal pieces to repair his deck. How long should he cut each piece?
Answer:
3.5 feet
I think is right
You are buying shoes online. The selling price is $29.99. The sales tax is 6.5% What is the total cost? Round to the nearest penny, if necessary.
Answer:
$31.94
Step-by-step explanation:
29.99 x 0.065 = 1.95
29.99 + 1.95= 31.94 :)
Answer:
$31.94
Step-by-step explanation:
maths question solve it quick pls
Answer:
(a)2 1/4
(b)1 1/2
(c)1 1/18
(d)5 7/12
Step-by-step explanation:
(a) 11/3 - 17/12 = 44/12 - 17/12 = 27/12 = 9/4 = 2 1/4
(b) 33/10 - 18/10 = 15/10 = 3/2 = 1 1/2
(c) 41/9 - 7/2 = 82/18 - 63/18 = 19/18 = 1 1/18
(d) 47/6 - 9/4 = 94/12 - 27/12 = 67/12 = 5 7/12
Hope it helped :)
What is a decimal that is equivalent to the fraction 44/100
Answer:
0.44
Step-by-step explanation:
44/100 as a decimal is 0.44.
Hope this helped!!!
The decimal equivalent to the fraction 44/100 is 0.44.
We have,
To find a decimal equivalent to the fraction 44/100, we can simply divide the numerator (44) by the denominator (100):
44 ÷ 100 = 0.44
The concept used to find the decimal equivalent of a fraction is division.
By dividing the numerator by the denominator, we obtain the decimal representation of the fraction.
Therefore,
The decimal equivalent to the fraction 44/100 is 0.44.
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What is the value of x?
Answer:
x = 21
Step-by-step explanation:
The two angles shown are supplementary.
3x + 10 + 6x - 19 = 180
9x - 9 = 180
9x = 189
x = 21
what is the unit price of 12 cupcakes for 25 dollars
Answer:
Unit price of 12 cupcakes for 25 dollars = 25/12
= 2.08 dollars
Answer:
The unit price would be $2.08 for a cupcake because if you divide 12 and 25, you would get 2.08.
Step-by-step explanation:
Can someone solve this?
Answer:
The answer is A.
Step-by-step explanation:
Because if you compare the two "y" section on both graphs you will notice that the "Speedy Delivery" charges way more than the "Lightning Delivery ."
Hope this helps ,have a good day.
Find the point on a circle that has a radius of 8 with an angle of rotation of 130 degrees centered at (-3,5)?
Express the relation in a table:(2,1),(4,5),(3,3),(1,(2)
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Once the data is entered into a spreadsheet, it is convenient to sort the table by the input values. The relation is unchanged, but it may be easier to work with that way.
The table is shown below.
find the area of the triangle
Answer:
133
Step-by-step explanation:
14 times 19 is 266 divided by 2 is 133
Area of a triangle is 1/2 x base x height
Base is given as 19 ft and height is given as 14 ft
Area = 1/2 x 19 x 14 = 133 square ft
Please help me with this ASAP ASAP please please help
Answer:
4ㅈr² is formula
so
4 × ㅈ× (16)²
= 1024ㅈ cm²
look at pic 10 pts will mark brainilest
Answer:
1,400
Step-by-step explanation:
Evaluate for x=2
100(2^3+2^2+2)
=1400
PLZ give me brainliest
name the quadrant in which the point (7,-10) is located PLEASE HELP I NEED IT NOW PLS
Step-by-step explanation:
the point (7,-10) is located in 1 at quadrant
Answer:
Quadrant 4
Step-by-step explanation:
To find this out, simply get a coordinate plane and plot the coordinate point.
OR
You can remember this formula for coordinate points:
Quadrant 1: (x,y)
Quadrant 2: (-x,y)
Quadrant 3: (-x,-y)
Quadrant 4: (x,-y)
Point (7,-10) has a positive x-coordinate and a negative y-coordinate. This means it belongs in quadrant 4.
Can someone explain me this
Answer:
area of circle - area of hexagon
Step-by-step explanation:
Installment Loan
Principal
$1500.00
Term Length
4 years
How much of the first
payment for the
installment loan
6% shown in the table will
go towards interest?
Interest Rate
Monthly Payment
$35.00
A. $27.50
B. $7.50
C. $2.10
D. $32.90
The amount of the first payment that will go towards interest is $7.50.
The answer is B. $7.50.
To calculate the amount of the first payment that will go towards interest for an installment loan, we need to consider the principal, term length, and interest rate.
Given:
Principal: $1500.00
Term Length: 4 years
Interest Rate: 6%
Monthly Payment: $35.00
To find the amount of interest paid in the first payment, we'll first calculate the total interest paid over the entire term and then divide it by the number of payments.
Calculate the total interest paid over the term.
Total Interest = Principal × Interest Rate × Term Length
Total Interest = $1500.00 × 6% × 4 = $360.00
Divide the total interest by the number of payments.
Interest in the First Payment = Total Interest / Number of Payments
Interest in the First Payment = $360.00 / (4 years × 12 months per year)
Interest in the First Payment = $360.00 / 48
Interest in the First Payment = $7.50
Therefore, the amount of the first payment that will go towards interest is $7.50.
The answer is B. $7.50.
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The figure is a ____.
1. Square
2. Rectangle
3. Triangle
The figure has _____ sides.
1. Three
2. Four
3. Five
The figure has the dimensions of _____.
1. Length, Width, and height
2. Length, Width, Base, and height
3. Length and Width
(also ignore my mouse)
The figure is a rectangle.
The figure has Four sides.
The figure has the dimensions of Length and Width.
Sorry if its wrong, I have bad memory
What would y be if x was equal to 410 billion?
Answer:
it would be any number because variables don't mean a certain,number
Make frequency tables for the following data sets. Include columns for relative frequency. Also, make a bar graph for the frequency
Final grades of 30 students in a math class: AAAAAABBBBBBCCCCCCCCCCFFF
Write down the integer values satisfied by the diagram
Answer:
{0, 1, 2, 3}Step-by-step explanation:
The diagram includes the interval:
(-1, 3]The integer values in the given interval are:
{0, 1, 2, 3}3.
A man has 6 packages. Their average weight is 18 kg. Find the total
weight of the 6 packages.
Answer:
108 kg for all 6 packages
Step-by-step explanation:
Answer:
=108
Step-by-step explanation:
18 × 6 will give you 108
Can someone help me with this, please!!!
Answer:
The answer is C
Step-by-step explanation:
Both triangles are very similar
What is the probability of choosing a king from a deck of cards? Type your answer as a fraction.
Answer:
4/52 or 1/13
Step-by-step explanation:
there are only 4 kings; diamond, Heart, Spades and Clubs.
4x+2y=16
3x+4y=17
i need help
Answer:
x = 3 , y = 2
Step-by-step explanation:
Nancy uses her $10 allowance to buy a dress. She got $2 bills and 2quarters in change. what was the price of the dress???
Answer:cdjbskbbN
Step-by-step explanation:2 2/4
Answer:
$7.50
Step-by-step explanation:
10 - 2.50 = 7.50