Answers
Answer:
y = Ce⁻ᵗ − 7
Step-by-step explanation:
dy/dt = -y − 7
dy/dt = -1 (y + 7)
Separate the variables.
dy / (y + 7) = -1 dt
Integrate both sides.
ln│y + 7│= -t + C
Solve for y.
y + 7 = e⁻ᵗ⁺ᶜ
y + 7 = eᶜ e⁻ᵗ
eᶜ is another arbitrary constant, so:
y + 7 = Ce⁻ᵗ
y = Ce⁻ᵗ − 7
Related Questions
Examine the equation. 4(x – 3) = 4x – 12 Which of the following is true? (Check all that apply.) It is a true statement. Any input will result in an equivalent equation. It is equivalent to an equation of the form a = a. It has no solution. Only one input will result in a true statement.
Answers
Answer:
A, B, and C.
Step-by-step explanation:
We have the equation:
[tex]4(x-3)=4x-12[/tex]
Let’s distribute the left. This yields:
[tex]4x-12=4x-12[/tex]
Let’s add 12 to both sides:
[tex]4x=4x[/tex]
And subtract 4x from both sides:
[tex]0=0[/tex]
We get the true statement 0=0.
Hence, A is correct.
Because it is a true statement, any input will yield an equivalent output.
Hence, B is also correct.
We also have the form a=a, where a is 0.
Hence, C is also correct.
Therefore, our correct answers are A, B, and C.
Answer:
It is a true statement.
Any input will result in an equivalent equation.
It is equivalent to an equation of the form a = a.
HELP ME PLEASE Find the slope of the line and write it as a rate of change.
Answers
A slope is also known as the gradient of a line. The rate of change is $0.13/ mile.
What is Slope?A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
Given two of the points on the line of the function (7000, 900) and (20000, 2600). Now, The rate of change for the given function is the slope of the line as shown in the graph. Therefore, the rate of change will be,
Rate of change = ($2600 - $900)/(20,000 miles - 7,000 miles)
= 1700 / 13000
= $0.13/ mile
Hence, the rate of change is $0.13/ mile.
Learn more about Slope of Line here:
https://brainly.com/question/14511992
#SPJ2
What type of number is 739?.
A. Neither
B. Prime
C. Composite
Answers
ANSWER
For 739, the answer is: prime anslo written as B
Step-by-step explanation:
739 is a prime number because it has only two distinct divisors: 1 and itself (739).
HAVE A GOOD DAY!
Answer:
its neither
Step-by-step explanation:
Which of the following rates are proportional to $3.85 per 1 pound? Select all that apply.
HELP STAT
A) 5 pounds for $19.25
B) $7.70 for 2 pounds
C) 4 pounds for $15.10
D) $10.00 for 3 pounds
E) 10 pounds for $38.50
F) $28.75 for 9 pounds
Answers
A:$19.25/5=$3.85
B:$7.70/2=$3.85
E:$38.50/10=$3.85
Solve the equations:
2^(3x−4) = −2
Answers
Answer:
x=NaN your welcome hehe
Lou deposited $3,500 into a savings account. The simple interest rate is 4%. How much interest will the account earn in 10 years?
Answers
Answer:
2 years : $280
10 years: $1400
Step-by-step explanation:
The amount of interest earned in 10 years will be $1,400.
What is simple interest?Let P be the principal, R be the rate of interest, and T be the time. Then the interest rate is given as,
The formula for interest is written as,
I = (PRT)/100
$3,500 was put into a savings account Lou. 4% is the simple interest rate.
The amount of interest after 10 years is calculated as,
I = ($3,500 x 4 x 10) / 100
I = $1,400
The amount of interest earned in 10 years will be $1,400.
More about the simple interest link is given below.
https://brainly.com/question/2793278
#SPJ7
a pump moves 42 gallons in 7 minutes
Answers
Answer:
The correct answer is 6
Step-by-step explanation:
Divide 42 divided by 7 to get 6.
Answer:
What is the question?
Step-by-step explanation:
The pump moves 6 gallons in 1 minute
Divide 42 by 7 = 6
But I don't know the question so I can't tell you the best correct answer.
I just took a guess at what you wanted
Complete the steps to solve 4.5 ÷ 0.5
Answers
Answer:
9
Step-by-step explanation:
4.5/0.5=9
9*0.5=4.5
hope this helps :3
if it did pls mark brainliest
Answer:
4.5 ÷ 0.5
45/10 ÷ 5/10
45/10 × 10/5
450/50
45/5
= 9
Step-by-step explanation:
Please help me please
Answers
Answer:
Step-by-step explanation:
110_5
PLEASE HELP URGENT WILL GOVE BRAINLIEST
Answers
Simplify each term. please help!! 30 points + brainliest :)
1. -(-3y)³
2. (2c)⁵
3. (-2m)⁴
4. (4g)³
5. (7j)²
6. (-5z)⁵
Answers
Answer:
1. 27y^3
2. 32c^5
3. 16m^4
4. 64g^3
5. 49j^2
6. -3125z^5
Step-by-step explanation:
Can you help answer my question too, please?
If h(x) = g[f(x)], use the table of values for f, g, f'and g' to find the value of h'(1).
x f(x) g(x) f'(x) g'(x)
1 3
2
2
6
2 1
00
5
7
3
7
2
7
9
your answer goes here
Answers
Answer:
Hey there :)
h ( x ) = f [ g ( x ) ]
To find h ' ( x )
We do → f ' [ g ( x ) ] × g ' ( x )
This is called the chain rule
Given;
g ( 1 ) = 2 → f ' ( 2 ) = 5
g ' ( 1 ) = 6
Apply the formula
h ' ( 1 ) = f ' [ g ( 1 ) ] × g ' ( 1 )
= f ' ( 2 ) × 6
= 5 × 6
h ' ( 1 ) = 30
If h(x) = g[f(x)], the value of h'(1) from the given table is calculated as 18.
To find the value of h'(1), we need to apply the chain rule. The chain rule states that if we have a composite function h(x) = g[f(x)], then its derivative h'(x) is given by [tex]\(h'(x) = g'(f(x)) \cdot f'(x)\)[/tex].
Let's use the table of values to find h'(1):
1. f(1) = 3
2. g(f(1)) = g(3) = 2
3. f'(1) = 2
4. g'(f(1)) = g'(3) = 9
Now, we can find h'(1) using the chain rule:
[tex]\[h'(1) = g'(f(1)) \cdot f'(1) = 9 \cdot 2 = 18.\][/tex]
Therefore, the value of h'(1) is 18.
To know more about value, refer here:
https://brainly.com/question/33648788
#SPJ2
The equation below describes a proportional relationship between x and y. What is the constant of proportionality? y=3/5x The constant of proportionality is______
Answers
Answer:inversely proportional
Step-by-step explanation:
As the value of x increase the value of y decrease
A newborn giraffe weighs about 65 kilograms. How much does it weigh in grams?
Answers
Answer:
65,000 grams
Step-by-step explanation:
1 kilogram = 1,000 grams
The giraffe weighs 65,000 grams.
What is the scale factor from the original triangle to its copy?
.
Original
Copy
Answers
Solve four and three fourths minus one and one third.
(GIVING EXTRA POINTS ON THIS ONE AND A BREAINLIEST!!)
A) Two and two sevenths
B) two and two twelfths
C) three and five twelfths
D) three and five sevenths
(Here is an image if needed) :
Answers
Explanation: The first thing you do when you subtract mixed numbers is convert them into improper fractions. 4 3/4 can be converted to 19/4 and 1 1/3 can be converted into 4/3. To be able to subtract or add fractions they need to have the same denominator a number in which both denominators can go into and that number is 12. 4 can equally go into 12 and so can 3. Now that you have found the common denominator (12) you have to find out what kind of operation you need to do in order for 4 to be 12 and for 3 to also be 12. And that is by multiplying. If you multiply 4 by 3 and get 12 and 3 by 4 to get 12 as well. Whatever you do to the bottom of the fraction you also do to the top so 19 x 3 / 4 x 3 = 57/12. Do the same to the other improper fraction: 4 x 4/ 3 x4 = 16/12. They both now have the same denominator but you have to subtract so,,57/12 - 16/12 = 41/12 you have the answer to the subtraction problem but you can probably tell that it isn’t any of the options on the question. Simplifying 41/12 will give you the mixed number 3 5/12.
Answer:
c
Step-by-step explanation:
The cost of medical care abroad is often significantly less than in the United States. In 2014, the cost of knee replacement surgery in the United states was $34,000. This cost was $4000 more than four times the cost of knee replacement surgery in India. Find the cost of Knee replacement surgery in India.
Answers
Answer:
Cost in India: $7500
Step-by-step explanation:
Represent cost in India with I and cost in United States as U.
Given
[tex]U = 3400[/tex]
[tex]U = 4000 + 4 * I[/tex]
Required
Find I
Simply substitute 34000 for U in the second equation
[tex]34000 = 4000 + 4 * I[/tex]
[tex]34000 = 4000 + 4I[/tex]
Solve for 4I
[tex]4I = 34000 - 4000[/tex]
[tex]4I = 30000[/tex]
Solve for I
[tex]I = 30000/4[/tex]
[tex]I = 7500[/tex]
Hence, the cost in India is $7500
If I had 4 eggs
Leslie gives me 3 eggs
My farm rooster lays 5 eggs
How many eggs do I have?
Answers
Answer:3 eggs
Step-by-step explanation:
You HAD 4 eggs
Leslie gives you 3 eggs
Roosters don’t lay eggs,
Therefore, you have 3 eggs.
I have 12 eggs
Addition is the the process of determining the total sum of two or more numbers. Addition is a basic mathematical operation. The other basic operations are subtraction, multiplication and division.
The number of eggs I have would increase with the number of eggs I am given and the number of eggs the farm rooster lays. This means I would have to add these numbers together.
The number of eggs I have = number of eggs I has initially + number of eggs Leslie gives me + number of eggs the farm rooster lays
4 + 3 + 5 = 12 eggs
A similar question was solved here: https://brainly.com/question/17472003?referrer=searchResults
2. Multiply the following:
a. 3.5(x)
Answers
Answer:
3.5x
Step-by-step explanation:
3.5(x)=3.5x
The mean lifetime of a tire is 48 months with a standard deviation of 77 months. If 147 tires are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 0.83 months?
Answers
Answer:
0.55199
Step-by-step explanation:
When we have a random number of samples, We solve using z score formula
z = (x-μ)/σ/√n where
x is the raw score
μ is the population mean
σ is the population standard deviation
n is random number of samples
z = 0.83/77/√147
z = 0.13069
Probabilty value from Z-Table:
P(x<48.83) = 0.55199
The probability that the mean of the sample would differ from the population mean by less than 0.83 months is 0.55199
Keith wants to plot -8 and -9 and on a number line. Which statement is true? *
Answers
Sarah is training for a bike race. She rides her bike 5 3/4 miles in 1/3 hour. What is Sarah’s rate in miles per hour. Express your answer as a mixed number
Answers
Answer:no
Step-by-step explanation:
Answer:
17 [tex]\frac{1}{4}[/tex]
What is the constant of proportionality in the equation y = 5/9x
Answers
Answer: 5/9
This is assuming the equation is y = (5/9)x
Note it is in the form y = kx with k = 5/9 as the constant of proportionality.
The average monthly cost of basic cable TV was $9.73 in 1985 and has increased by about $1.35 each year since then. Let t be the number of years since 1985.
1. Use function notation to write an equation giving the monthly cost of basic cable TV as a function of t.
f(t)=____t+____
2. Using the function from above what is the average monthly cost of basic cable TV for this year?
3. Using the function from 1, what year was the average monthly cost of basic cable TV $23.23?
Answers
Answer:
$50.23
Step-by-step explanation:
f(t)=1.35(t)+9.73
First I found out how many years are after 1985 so you would do 2020-1985 which equals 30.
I plug it in for t.
f(t)=1.35(30)+9.73
Then you multiply 1.35 and 30 which would leave us with.
f(t)=40.5+9.73
Add them and you get $50.23
To demonstrate probabilities, a mathematics teacher had students draw cards from a bag which contained 26 red cards and
26 black cards. During class, the bag was dropped, and 5 red cards and 1 black card were lost.
Tell whether the loss of cards changes the probability of drawing a black card from the bag.
If so, was the probability increased or decreased? Support your answer by calculating the probability for each situation.
Answers
Answer:
decreased
Step-by-step explanation:
Maggie has a 2-gallon pitcher of lemonade. How many liters of lemonade did she make?
I'LL GIVE BRAINLIEST!
Answers
Answer:
2 gallons converted to liters is 7.57 or 8 liters rounded
Answer correctly and I will mark you brainless ❤️
Answers
A 2-column table with 6 rows. Column 1 is labeled Tables with entries 1, 2, 3, 4, 5, 6. Column 2 is labeled Chairs with entries 6, 12, 18, 24, 30, 36.
Rachel needs two tables for her birthday party. How many chairs will she need?
Answers
i think the answer is The 1st table represents a function
Lets explain how to solve the problem
- Function is a relation where each input has a single output
- The notation of the function is f(x) = y , where x is the input of the
function and y is the out put of the function
- The domain of the function is x and the range of the function is y
* Lets find which table represent a function
# First table:
x y
-3 -1
0 0
-2 -1
- In the first table
∵ -3 has only -1
∵ 0 has only 0
∵ -2 has only -1
∵ 8 has only 1
∵ Every x has a single y
∴ The table represents a function
∴ The 1st table represents a function
- In the second table
x y
-5 -5
0 0
-5 5
6 -6
∵ x = -5 has y = -5 and y = 5
∴ One x has two values of y
∴ The table doesn't represent a function
- In the third table
x y
-4 8
-2 2
-2 4
0 2
∵ x = -2 has y = 2 and y = 4
∴ One x has two values of y
∴ The table doesn't represent a function
- In the fourth table
x y
-4 2
3 5
-4 0
∵ x = -4 has y = 2 and y = 0
∴ One x has two values of y
∴ The table doesn't represent a function
Answer:
It is 12
Step-by-step explanation:
The length of a rectangle is 97 meters and the width is 14 meters. Find the area. Give your answer without units.
Provide your answer below:
Answers
The length is 97 and the width is 14
97•14=1358
The area of a rectangle is the product of length and width thus the area will be 1358 square meters.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
The perimeter of the rectangle = 2( length + width).
It is known that,
Area of rectangle = length × width.
Area = 97 x 14 = 1358 sqare meters
Hence "The area of a rectangle is the product of length and width thus the area will be 1358 square meters".
For more about rectangles,
https://brainly.com/question/15019502
#SPJ5
How many 1 6 cup servings are in 3 4 cups of popcorn? (in simplest fraction form)
Answers
Answer: 8/17
Step-by-step explanation: 16 ÷ 34 = 8/17
Hope this helps ^_^