Step-by-step explanation:
dy/dt = (A − Be^(-t/5)) y
(a) Find the general solution by separating the variables and integrating.
dy / y = (A − Be^(-t/5)) dt
dy / y = [A + 5B (-⅕ e^(-t/5))] dt
ln |y| = At + 5B e^(-t/5) + C
y = e^(At + 5B e^(-t/5) + C)
y = Ce^(At + 5B e^(-t/5))
(b) As t approaches infinity, dy/dt approaches Ay. The rate of growth, A, is triple the initial rate of growth 0.02, so A = 0.06.
When t = 0, dy/dt = (A − B)y. The rate of growth, A−B, is 0.02. We know A = 0.06, so B = 0.04.
(c) Given that A = 0.06, B = 0.04, and y(0) = 50×10⁶ − 10×10⁶ = 40×10⁶:
40×10⁶ = Ce^(0.06(0) + 5(0.04) e^(-0/5))
40×10⁶ = Ce^(0.2)
C = 40×10⁶ e^(-0.2)
y = 40×10⁶ e^(-0.2) e^(0.06t + 0.2 e^(-t/5))
y = 40×10⁶ e^(-0.2 + 0.06t + 0.2 e^(-t/5))
(d) If A = 0.02 and B = 0, and there is no transformation (y(0) = 50×10⁶), then:
50×10⁶ = Ce^(0.02(0) + 0)
50×10⁶ = C
y = 50×10⁶ e^(0.02t)
Comparing to the answer from part (c):
40×10⁶ e^(-0.2 + 0.06t + 0.2 e^(-t/5)) = 50×10⁶ e^(0.02t)
e^(-0.2 + 0.04t + 0.2 e^(-t/5)) = 5/4
-0.2 + 0.04t + 0.2 e^(-t/5) = ln(5/4)
-5 + t + 5e^(-t/5) = 25 ln(5/4)
t + 5e^(-t/5) = 5 + 25 ln(5/4)
Solve with a calculator:
t = 9.886
The transformed economy surpasses the untransformed economy in the 10th year.
(e) In year t=5, the size of the transformed economy is:
y = 40×10⁶ e^(-0.2 + 0.06(5) + 0.2 e^(-5/5))
y = 47.6×10⁶
The percent growth is:
(47.6×10⁶ − 40×10⁶) / 40×10⁶ × 100% = 19%
The growth rate is greater than 4%, so the current government can expect to be reelected.
1.
Simplify: 2.6 x 8.4-5.4
A. 2.32
B. 7.8
C. 16.44
D. 21.3
Answer:
b
Step-by-step explanation:
A camera has a listed price of $670.98 before tax. If the sales tax rate is 8.25%, find the total cost of the camera with sales tax included.
Round your answer to the nearest cent, as necessary.
х
Answer:
$726.34
Step-by-step explanation:
Convert 8.25% to a decimal
8.25/100=0.0825
Multiply the cost by the decimal
670.98*0.0825=53.35585
Add the tax to the cost of the camera
53.35585+670.98=726.33585
Rounded to the nearest cent: 726.34
So, the total cost of the camera is $726.34
Hope this helps!
Answer:726.34
Step-by-step explanation: You have to multiply 670.98 x .0825 and the answer will be around 55. You take that answer and add it to 670.98. There you have to round to the nearest sent and the answer will be 726.335 rounded to 726.34
One cup of cooked spinach contains 377% of the recommended value of vitamin A. What fraction of the recommended daily value of vitamin A is in one cup of cooked spinach?
Answer:
[tex]\frac{337}{100}[/tex]
Step-by-step explanation:
It is given that one cup of cooked spinach contains 337% of the recommended value of vitamin A.
Therefore, vitamin A is present in one cup of cooked spinach by 337%.
Hence, to represent the fraction of the recommended daily value of vitamin A in one cup of cooked spinach, it will be [tex]\frac{337}{100}[/tex]. (Answer)
{Converting the percentage into fraction}
Use the graph of the polynomial function to find the factored form of the
related polynomial. Assume it has no constant factor.
Please help with #48
Step-by-step explanation:
Among the three sides of length 9cm,11cm and 13cm;
9cm is the shortest and 13cm is the longest
the shortest of the corresponding i.e 9cm real - life distance= 125 km
Therefore, the longest of the corresponding i.e 13cm real - life distance= 125 ×13/9
= 180.55
= 180.6 km
In the diagram ABCD is a rectangle and PQ is parralell to AD
For the given rectangles, [tex]f=4[/tex] cm and [tex]g = 6[/tex] cm.
Step-by-step explanation:
Step 1:
The area of a rectangle is calculated by multiplying its length with its width. Both the rectangles APQD and PBCQ have the same width.
The second rectangle PBCQ has a length of 9 cm. Its area is determined by subtracting the area of APQD from the area of ABCD.
The area of the rectangle PQBC [tex]= 60 - 24 = 36[/tex] [tex]cm^{2}[/tex].
Step 2:
The length of rectangle PBCQ is 9 cm and the area is 36 [tex]cm^{2}[/tex] so the width can be determined.
[tex]Width = \frac{area}{length} = \frac{36}{9} = 4[/tex] cm. So [tex]f=4[/tex] cm.
Step 3:
The width of the rectangle APQD is also 4cm.
The width of the rectangle APQD is 4 cm and the area is 24 [tex]cm^{2}[/tex].
[tex]length = \frac{area}{width} = \frac{24}{4} = 6[/tex] cm. So [tex]g = 6[/tex] cm.
Your math test has 38 questions and is worth 200 points. The test consists of
multiple-choice questions worth 4 points each and open-ended questions
worth 20 points each. How many of each type of question are there?
The test has 35 multiple-choice questions and 3 open-ended questions.
To solve this, we can set up a system of linear equations. Let x represent the number of multiple-choice questions and y represent the number of open-ended questions.
Equation 1: x + y = 38 (total questions)
Equation 2: 4x + 20y = 200 (total points)
By solving this system of equations, we can find the values of x and y. First, multiply equation 1 by 4 and subtract it from equation 2:
4(x + y) = 4(38) => 4x + 4y = 152
4x + 20y = 200 - (4x + 4y = 152) gives: 16y = 48 or y = 3.
Substituting y = 3 into equation 1 gives: x = 38 - 3 = 35.
Therefore, there are 35 multiple-choice questions and 3 open-ended questions on the test.
What is the distance between the two points located at (14, 27) and (14, −8)?
The distance between the 2 given points is 35 units
Step-by-step explanation:
Step 1 :
Let A be the point (14, 27) and B be the point (14, −8).
Distance between any 2 points is obtained by the taking root of the sum of squares of the difference between the x co ordinates and the y co ordinates and is given by the formula
[tex]\sqrt({x_{2} - x_{1}) ^{2} + ({y_{2} - y_{1}) ^{2} }[/tex]
Where [tex](x_{1} , y_{1}) and (x_{2} , y_{2})[/tex] are the 2 points
Step 2 :
Using the above formula , we get the distance between the 2 given points as
[tex]\sqrt({14-14)^{2} + {((-8)-27)^{2} }[/tex] = [tex]\sqrt{(-35)^{2} }[/tex] = 35 units
Step 3 :
Answer:
The required distance of the 2 given points is 35 units
Find the slope of the line that passes through the points A(-3,1) and B(2,-5)
Answer:
Slope=-6/5
Step-by-step explanation:
Formula for calculating slope is y2-y1/x2-x1
y1=1
y2=-5
x1=-3
x2=2
Apply the above formula
-5-1/2-(-3)
-5-1/2+3
-6/5
what is the measure of a? ab=15, bc=15,ac=15
Answer:
5 or 3
Step-by-step explanation:
I need help on something on my Math assignment. In this problem, they already have the final answer to the volume of a half-sphere (1,071.79) in^3. the problem wants me to find the radius of the half-sphere, so I figured if I want to find radius, I must do the formula backward. But I only end up with a number like 0.00195311892566 and I don't think that is the correct answer.
Can you help me?
Sarah has a pond in the shape of a half sphere in her back yard. The pond currently holds 1,071.79 cubic inches of water. What is the radius of the pond?
Show your work and explain your answer.
Answer:
Hi I am cool
Step-by-step explanation:
Answer:
Don't you just divided that by 3?
Step-by-step explanation:
How do i solve this if i dont pass my math i lose my phone for a week got till tomorrow
what is the slope of the line that contains points (-3, 1) and (4, -2)?
The slope of the line is [tex]m=-\frac{3}{7}[/tex]
Explanation:
The points are [tex](-3,1)[/tex] and [tex](4,-2)[/tex]
We need to find the slope of the line that contains the points [tex](-3,1)[/tex] and [tex](4,-2)[/tex]
The slope of the equation can be determined using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting the points [tex](-3,1)[/tex] and [tex](4,-2)[/tex] in the slope formula, we have,
[tex]m=\frac{-2-1}{4-(-3)}[/tex]
Simplifying the expression, we have,
[tex]m=\frac{-2-1}{4+3}[/tex]
Adding the terms in both numerator and denominator, we have,
[tex]m=\frac{-3}{7}[/tex]
The slope of the line that contains the points [tex](-3,1)[/tex] and [tex](4,-2)[/tex] is [tex]m=-\frac{3}{7}[/tex]
Thus, the slope of the line is [tex]m=-\frac{3}{7}[/tex]
What is the net force on this object?
0 newtons
8 newtons
22 newtons
36 newtons
Answer:
8 Newtons
Step-by-step explanation:
Friction and Gravity are both known to be negative forces such as -20 and -14
So doing the math
22 + 20 = 42
42 - 20 = 22
22 - 14 = 8
8 is your answer, hope this helped!
Answer:
8 N to the right.
Step-by-step explanation:
Resolving vertical forces
upwards = 20 N, down = 20 N
- so the Net Force = 0.
Resolving horizontally :
Net force = 22 - 14 = 8 Newtons.
Q1: Solve for x : 5x - 7=3
Answer:
x=2
Step-by-step explanation:
5x - 7=3
Add 7 to each side
5x -7+7 = 3+7
5x = 10
Divide each side by 5
5x/5 = 10/5
x =2
May someone please help me?
Answer:
532m^2
Step-by-step explanation:
Please see the attached pictures for full solution.
Are the expressions (5+5+5+5) + (x+x+x+x) and 4(5+x) equivalent? If so, write another expression that is equivalent to both of them. If not, explain why not.
Answer:
Yes, they are equivalent. Something that is not equivalent is 5(9+10x)
Both expressions simplify to 20 + 4x. Distributing 4 in 4(5+x) yields the same result, confirming their equivalence.
Sure, let's break it down step by step:
1. **Start with the first expression**: (5+5+5+5) + (x+x+x+x)
- First, simplify the terms inside each set of parentheses:
= (20) + (4x)
- Then, add the simplified terms together:
= 20 + 4x
2. **Proceed to the second expression**: 4(5+x)
- Apply the distributive property, which states that multiplying a number by a sum is the same as multiplying the number by each term in the sum and then adding the results:
= 4 × 5 + 4 × x
- Multiply each term inside the parentheses by 4:
= 20 + 4x
3. **Compare the results**:
Both expressions simplify to 20 + 4x.
In both cases, we ended up with the same simplified expression, 20 + 4x. This confirms that the original expressions are equivalent.
To write another equivalent expression, we can distribute the 4 to both terms inside the parentheses in the expression 4(5+x), which results in 20 + 4x. Therefore, the expression 20 + 4x is equivalent to both (5+5+5+5) + (x+x+x+x) and 4(5+x).
Mr. Allen bought a new computer. His monthly payment plan is shown in the table.
Mr. Allen starts with a higher initial amount ($560) compared to Mr. Jessup ($400).
Mr. Allen pays off a larger amount each month ($80) compared to Mr. Jessup ($40).
The initial values and rates of change for Mr. Allen's and Mr. Jessup's payment plans can be compared based on the given information.
1. Initial Values:
- Mr. Allen's initial amount S: $560
- Mr. Jessup's initial amount: $400
Difference in initial values: $560 - $400 = $160
Mr. Allen's initial value is $160 more than Mr. Jessup's.
2. Rates of Change:
- Mr. Allen's rate of change: $80 per month
- Mr. Jessup's rate of change: $40 per month
The rate of change represents the amount by which the owed amount decreases each month. Mr. Allen's rate of change is greater because he pays off $80 per month, while Mr. Jessup pays off $40 per month.
In summary:
Mr. Allen starts with a higher initial amount ($560) compared to Mr. Jessup ($400).
Mr. Allen pays off a larger amount each month ($80) compared to Mr. Jessup ($40).
Complete question:
Mr. Allen bought a new computer. His monthly payment plan is shown in the table.
Month 0 1 2 3 4 5 6 7
Amount Mr. Allen Owes (S) 560 480 400 320 240 160 80 0
Mr. Jessup buys a new computer for $400. He makes monthly payments of $40 until the computer is paid for. Compare the initial values and rates of change of each function.
You can graph both functions to show that the amount Mr. Allen owes starts at $560 and decreases $80 per month. The amount that Mr. Jessup owes starts at $400 and decreases $40 each month.
Mr. Allen's initial value is $160 more than Mr. Jessup's. Mr. Allen's rate of change is greater than Mr. Jessup's rate of change.
To calculate Peter's monthly expenses, add up the amounts in row 5 of the table. Compare the total expenses with different salaries to determine if Peter can meet them. Advise Peter to create a budget and prioritize expenses if he wants to move out.
Explanation:To calculate Peter's monthly expenses, we need to add up all the amounts in row 5 of the table. Assuming each amount represents a monthly expense, we can sum them up to get the total monthly expenses. To determine if Peter can meet his expenses with different salaries, we compare the total expenses with each salary. If the salary is greater than or equal to the total expenses, Peter can meet his expenses. If the salary is less than the total expenses, Peter cannot meet his expenses.
If Peter wants to move out of his parent's house, I would advise him to create a budget and prioritize his expenses. He should also consider finding ways to increase his income or reduce his expenses to make moving out more affordable.
Given:
U=
[ 1 3 -57
2 14 11
L-8 05]
V=
[ 13 -1 -71
-6 1 19
[ 0 15 23
Solve:
X + U = V
X=
Answer:
answer is
[12 -4 -2]
[-8 -13 8]
[8 15 18]
Step-by-step explanation:
got it right on e2020
To solve the equation X + U = V, subtract the matrix U from both sides and simplify to find the solution for X. The solution is [12 - 4 - 14; -8 - 13 8; 8 15 18].
Explanation:To solve the equation X + U = V, we need to isolate X. Here is the step-by-step process:
First, subtract the matrix U from both sides of the equation: X = V - U.Next, subtract the corresponding elements of U from V. In this case, subtract the elements of U from the corresponding elements of V: X = [13 - 1 - 71; -6 1 19; 0 15 23] - [1 3 -57; 2 14 11; -8 0 5].Perform the subtraction and simplify: X = [12 - 4 - 14; -8 - 13 8; 8 15 18].The solution for X is the matrix [12 - 4 - 14; -8 - 13 8; 8 15 18].
what does have no change mean in math
Answer:
things are the same as they were
Step-by-step explanation:
"No change" in math means the same thing it does in English. Whatever it is you're looking at is the same now as it was before. It has not changed. The amount of change is zero.
Final answer:
In mathematics, 'no change' refers to a situation where a value or quantity remains constant over time or during certain operations. It can be used in various contexts, including functions, equations, and graphing to represent a static state.
Explanation:
In mathematics, the term 'no change' often refers to a situation where a value remains constant over time or through a particular process. For example, if a quantity does not increase or decrease, we can say that there has been no change in that quantity. Another way this might come up is in functions or equations, where certain operations have no effect on the input value, meaning the output remains the same as the input.
No change could also mean that a variable or a set of variables remains unaffected by certain transformations. In algebra, it might refer to a constant function where, regardless of the input, the output is always the same. No change might also be used in the context of graphing; if a graph stays flat without any increase or decrease, it represents no change in the value being graphed over the specified domain.
Translate this phrase into an algebraic expression. 13 more than twice Greg’s score. Use the variable g to represent Greg’s score
Answer:
2g + 13
Step-by-step explanation:
Times two plus 13.
Answer:
2g+13
Step-by-step explanation:
Since Greg's score id doubled, you would make it 2g.
More is an addition term, so 13 more signals to adding 13, therefore, your answer is
2g+13
The triangle cookie cutter has a base of 10 centimeters and a height of 8 centimeters. What is the area of each triangle cookie
Answer:
well im not sure but i think u multiply 8 times 10 which is 80 which might be the area hope this helps
what is 240,000,591 divides by 176
Answer:
240,000,591÷176= 1363639.72159
Answer:
1,363,639.721590909
Step-by-step explanation:
Solve the word problems. Round the answer to the nearest tenth.
Mark is on his way home for work. He drives 35 miles due North and then 42 miles due west. Find the shortest distance he can cover to reach home early.
54.7 miles
54.785 miles
547 miles
54 miles
Option A:
The shortest distance Mark can cover to reach home early is 54.7 miles.
Solution:
Towards North = 35 miles
Towards West = 42 miles
Using Pythagoras theorem,
In right triangle, squares of the hypotenuse is equal to the sum of the squares of the other two sides.
Let x be the hypotenuse.
[tex]x^2=35^2+42^2[/tex]
[tex]x^2=1225+1764[/tex]
[tex]x^2=2989[/tex]
Taking square root on both sides, we get
[tex]\sqrt{x^2}=\sqrt {2989}[/tex]
x = 54.67
x = 54.7
The shortest distance Mark can cover to reach home early is 54.7 miles.
Option A is the correct answer.
Thomas has purchased a $129,000 home with a 30-year mortgage at 5.25%.
He can make a monthly payment of $1050. If he were to make this payment
each month, how long will it take him to pay off his mortgage?
A. 217 months
B. 197 months
c. 177 months
D. 222 months
Answer: 177 months
Step-by-step explanation:
Answer: 177 months
Step-by-step explanation:
How do you answer this question??
Answer:
1) { 2,3,4,6,8,9,10,12,15} , {2,4,8,10}, { 2,4,8,10}
Step-by-step explanation:
£ = [ 1,2,3,4,6,8,12,16,24 48}
A = { 2,4,6,8,10}
B = { 3,6,9,12,15}
1) AUB = all members in A and B
= { 2,3,4,6,8,9,10,12,15}
2) AnB' = members in A not in B
{2,4,8,10}
3) A - B = take away members of B in A that is B from A
= { 2,4,8,10}
I hope this was helpful, please mark as brainliest
a relation contains the points (1,2),(2,-1),(3,0),(4,1), and (5,-1) which statement accurately describes this relation?
Answer: D
The relation represents _y_ as a function of x, because each value of _x_ is associated with a single value of _y_.
Step-by-step explanation:
The relation represents y as a function of x, because each value of x is associated with a single value of y.
We have given
A relation contains the points (1,2),(2,-1),(3,0),(4,1), and (5,-1).
What is the function relation?
A function is a relation that describes that there should be only one output for each input.
Here x is the input value and y is the output value of the functions.
A relation contains the points (1,2),(2,-1),(3,0),(4,1), and (5,-1)
for the given relation
The relation represents y as a function of x, because each value of x is associated with a single value of y.
To learn more about the function of the relation visit:
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Perform the indicated operation.
Answer:
your answer should be 7 1/24
In the diagram above, if the circle with the center A has an area of 72 pi, what is the area of the circle with center B?
18pi
24pi
30pi
36pi
48pi
Without additional information about the relationship between the two circles, it is not possible to definitively determine the area of circle B based on the area of circle A. If the circles are identical, the area of circle B is also 72 pi.
Explanation:Given the area of the circle with the centre A is 72 pi, we find the radius using the formula for the area of a circle: A = πr². Therefore, the radius of circle A, rA, can be found by rearranging the formula to rA = √(A/π). This gives us a radius of √(72) = 8.48 units. Without further information about the relationship between circle A and circle B, we cannot definitively determine the area of circle B. If the two circles are identical, then the area of circle B would also be 72 pi. However, if the radius or diameter of circle B is different, you would have to use that measurement to calculate the area using the formula A = πr².
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Subtract.
Your answer should be a polynomial in standard form.
(
6
y
2
−
9
y
+
4
)
−
(
−
7
y
2
+
5
y
+
1
)
Answer:
Step-by-step explanation:
(−8* y^2−9*y)+(8*y^3+9*y^2−2*y)
first, remove extraneous parentheses (or distribute if negative)
=−8* y^2−9*y+8*y^3+9*y^2−2*y
then group terms in decreasing degree of y (variable)
=+8*y^3 −8* y^2+9*y^2 −9*y−2*y
simply expression by adding/subtracting similar terms
=+8*y^3 +y^2 −11*y
to give the final answer.