Find the solution of the initial value problem. dp/dt=5e^t, p(0)=25
The equation is [tex]p = 5e^{t} +20[/tex].
IntegrationIt is a method of summing up parts to find the whole. It is a reverse process of differentiation.
Given
dp/dt=5e^t
To findThe value of p.
How to get the value of p?dp/dt=5e^t is given
[tex]\begin{aligned} \dfrac{dp}{dt} &= e^{t} \\\int dp &= \int {5e^{t} } \, dt \\\int dp &= 5 \int {e^{t} } \, dt \\p &= 5e^{t} +c\\\end{aligned}[/tex]
It is given that at t=0, p will be 25, then
[tex]p = 5e^{t} + c\\c = p - 5e^{t}\\c= 25 - 5e^{0}\\c= 25 - 5 * 1\\c= 20[/tex]
Hence the equation will be [tex]p = 5e^{t} +20[/tex].
Thus, the equation is [tex]p = 5e^{t} +20[/tex].
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PLEASE HELP!!!! WILL GIVE 99 PTS! :)Sam is observing the velocity of a car at different times. After two hours, the velocity of the car is 54 km/h. After four hours, the velocity of the car is 58 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the car at different times. Show your work and define the variables used. (5 points)
Part B: How can you graph the equation obtained in Part A for the first six hours? (5 points)
t = time
v = velocity
you have (2,54) & (4,58)
v-54 = (58-54) / (4-2) *(t-2)
v=4/2(t-2)+54
v =2(t-2)+54
v = 2t-4+54
b - Graph by plotting the given points (2,54) & 4,58) and drawing a straight line through them
The length of a rectangle is 5 in. more than twice its width. its area is 102 in2. find the length of the rectangle
At Taft high school 59% of all students participate in after school sports and 23% participate in both after school sports and volunteer activities. What is the probability that a student participates in volunteer activities given that the student participates in after school sports. A. 82% B. 36% C. 59% D. 39%
how to solve bh+hr=25 when solving for h
Four more than the quotient of a number and 3 is at least 9
Explanation of an inequality involving addition and division
The given inequality is: 4 + (x/3) ≥ 9
To express the statement algebraically:
Add four to the quotient of a number and 3.
Set the expression greater than or equal to 9.
Solve for x to find the number that satisfies the inequality.
the teacher separated her class of twenty-eight students into two groups. One group has 4 more than twice as many students as the other group. How many students are in each group?
PLEASE HELP!!!!!!!!!!!
Whats the value of x?
4x=5x-12
x=
Two buses are traveling to a state park. One bus leaves the terminal at 4:00 p.m. and travels at 40 miles per hour. The second bus leaves the terminal at 5:00 p.m. and travels at 60 miles per hour.
How much time passes until the second bus catches up with the first bus?
Final answer:
The second bus catches up with the first bus in 2 hours.
Explanation:
To calculate how much time passes until the second bus catches up with the first bus, we need to find the distance between them when the second bus starts and the relative speed between the two buses.
When the second bus starts, the first bus has already traveled for 1 hour (from 4:00 p.m. to 5:00 p.m.) at a speed of 40 mph. Therefore, the first bus has covered a distance of 40 miles.
The relative speed between the two buses is the difference in their speeds, which is 60 mph - 40 mph = 20 mph.
Using the formula: t = d / v, where t is the time, d is the distance, and v is the speed, we can calculate the time it takes for the second bus to catch up with the first bus:
t = 40 miles / 20 mph = 2 hours.
Therefore, it takes 2 hours for the second bus to catch up with the first bus.
Do I solve this by equaling both equations to each other?
Kiko is coasting on her bicycle down a hill. After 3 s, her speed is 10 m/s. After 8 s, her speed is 25 m/s. What is her acceleration during this time?
Kiko is coasting on her bicycle down a hill. After 3 s, her speed is 10 m/s. After 8 s, her speed is 25 m/s. Her acceleration during this time will be 5 m/s².
What is acceleration?Acceleration is the rate of change in both speed and direction of velocity over time. When anything moves faster or slower in a straight line, it is said to have been accelerated. Because the direction is always shifting, motion on a circle accelerates even while the speed is constant.
It is given that, Kiko is coasting on her bicycle down a hill. After 3 s, her speed is 10 m/s. After 8 s, her speed is 25 m/s.
Acceleration is found as the ratio of the change in speed to the change in a time interval.
Acceleration = change in speed/ change in a time interval
Acceleration = (25-10) / (8-5)
Acceleration = (15)/(3)
Acceleration = 5 m/s²
Thus, Kiko is coasting on her bicycle down a hill. After 3 s, her speed is 10 m/s. After 8 s, her speed is 25 m/s. Her acceleration during this time will be 5 m/s².
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if 1 inch = 2.54 centimeters how many inches is equal to 254 centimeters
I need help solving this!!!
Numbers 3 and 4, solve algebraically. I don't get #5 question.
please help i will give a brainlist if you get it right
Evaluate the expression 14.3-2×5^2÷5
Your cruise ship is leaving for a 610 league adventure. how many nautical miles is this
Final answer:
A 610-league adventure is equivalent to 1830 nautical miles, calculated by multiplying the number of leagues by the conversion factor, where one league is equal to approximately 3 nautical miles.
Explanation:
To convert the distance from leagues to nautical miles, we need to know the conversion factor. One league is approximately 3 nautical miles. Thus, by multiplying the given number of leagues by this factor, we can determine the distance in nautical miles.
If the cruise ship is embarking on a 610-league adventure, we calculate the equivalent distance in nautical miles as follows:
Multiply the number of leagues (610) by the conversion factor (3).
The calculation would be 610 leagues * 3 nautical miles/league = 1830 nautical miles.
Therefore, a 610-league voyage is equivalent to 1830 nautical miles.
A digital camera memory card is 1/4 full. The card is 2/3 full when 375 more pictures have been taken. How many pictures can the memory card hold?
Final answer:
The memory card can hold a total of 900 pictures.
Explanation:
The question asks us to find the total capacity of the memory card in a digital camera by using the information that it is 1/4 full before 375 pictures are added, and 2/3 full after these pictures are added.
Let's define the total capacity of the memory card as 'x' pictures.
If 1/4 of the card is full, then it contains x/4 pictures.
After adding 375 pictures, the card becomes 2/3 full, which means:
x/4 + 375 = (2/3)x
To solve for x, we need to get all the x's on one side of the equation and the numbers on the other side:
Multiply both sides of the equation by 12 to get rid of the fractions: 12(x/4) + 12(375) = 12(2/3)xSimplify the equation: 3x + 4500 = 8xSubtract 3x from both sides: 4500 = 5xDivide both sides by 5: 900 = xTherefore, the memory card can hold a total of 900 pictures.
Help me with this please
The gross income of Abelina Bennett is $215 per week. Her deductions are: $15.16, FICA tax; $29.33, income tax; 2% state tax; 1% city tax; and 3% retirement fund. What is her net income?
To calculate Abelina Bennett's net income, subtract her deductions from her gross income. Her net income is $157.61 per week.
Explanation:To calculate Abelina Bennett's net income, we need to subtract her deductions from her gross income. The deductions include FICA tax, income tax, state tax, city tax, and retirement fund.
Step 1: Add up all the deductions:
FICA tax: $15.16
Income tax: $29.33
State tax: 2% of $215 = $4.30
City tax: 1% of $215 = $2.15
Retirement fund: 3% of $215 = $6.45
Step 2: Calculate the total deductions: $15.16 + $29.33 + $4.30 + $2.15 + $6.45 = $57.39
Step 3: Subtract the total deductions from the gross income: $215 - $57.39 = $157.61
Abelina Bennett's net income is $157.61 per week.
A cube has a surface area of 900 cm what is the number of cubic cm in the volume of the cube
If there are 400 people in a room, what is the probability of at least 2 people sharing the same birthday?
The probability of at least 2 people out of 400 sharing the same birthday is almost certain due to the 'birthday paradox', due to there being only 365 days in the year but 400 people in the room.
Explanation:The probability that at least 2 people out of 400 sharing the same birthday is almost certain due to the 'birthday paradox.' This is because there are only 365 days in a year for birthdays, but we have 400 people in the room.
To calculate this probability, we assume that every person is equally likely to be born on any day of the year (ignoring leap years). The first person can have their birthday on any of 365 days. The second person has a 364/365 chance of not having the same birthday as the first. The third person has a 363/365 chance of not sharing a birthday with the first two, and so on. By the time we reach the 366th person, the probability of them not sharing a birthday with anyone else is zero, since all 365 possible birthdays have been taken.
So, the overall probability of at least 2 people sharing a birthday is 1 minus the probability of all 400 people having unique birthdays. When you calculate it with 400 people, the result is almost 1, which indicates that it's nearly certain at least 2 people share a birthday.
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Which expression is equivalent to the given expression?
13x – 29x
A.x(29 – 13)
B.13(x + 29)
C.x(13 – 29)
D.13(x – 29)
Let f (x) = 2x - 1, g(x) = 3x, and h(x) = x2 + 1. Compute the following: f (h(x)) and . g (f (x))
1) After striking a pair of arcs from each endpoint of a line segment, what is the next step in constructing the segment's perpendicular bisector?
C) Use a straight edge to draw a vertical line between the points where each pair of arcs intersect.
what is the common factor of 24a^3c and 3a
Please check my answer!
Hogan needs to rent a car while on vacation. The cost of the vehicle is $21 per day. He gives the office manager $180 up front. If x represents the number of days and y represents the total cost of the rental, which equation will help Hogan determine if he owes the agency money at the end of his trip or if the agency owes him money?
Answer:
[tex]y=21x-180[/tex]
Step-by-step explanation:
The cost of the vehicle is $21 per day. He gives the office manager $180 up front.
The upfront is a type of advance payment that is deducted from the final amount.
Let x represents the number of days and y represents the total cost of the rental.
So, the correct equation here is :
[tex]y=21x-180[/tex]
Given the system of constraints, name all vertices of the feasible region. Then find the maximum value of the given object function.
One number is 3 less than twice another. If their sum is 39, find the numbers.
Which of the following systems of equations represents the word problem?
A) y=2x-3 and y=x+39
B) y=2x-3 and x+y=39
C) y=2(x-3) and x+y=39
Find the range of the logarithmic function f(x) = log4 x.
estimate 63 times 39
estimate 62.93 times 73
estimate 34.44 times 57
Estimate of 63 times 39: Approximately 2400.
Estimate of 62.93 times 73: Roughly 4410.
Estimate of 34.44 times 57: About 2040.
To estimate the products, you can round the numbers and then perform the multiplication.
Here are the estimates for the given multiplication problems:
Estimate of 63 times 39:
Round 63 to 60 and 39 to 40.
Calculate 60 times 40, which is 2400.
Estimate of 62.93 times 73:
Round 62.93 to 63 and 73 to 70.
Calculate 63 times 70, which is 4410.
Estimate of 34.44 times 57:
Round 34.44 to 34 and 57 to 60.
Calculate 34 times 60, which is 2040.
These are rough estimates and may not be entirely accurate, but they provide a quick way to get an idea of the approximate result of the multiplication.
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