The required value of y(7) is given as y (7)= 4412711.8.
Given that,
Given dy/dt=2y and y(2)=200.
The action of bringing concurrently shorter components into a single system that acts as one is known as integration.
Here,
dy/dt = 2y
dy/y = 2dt
integrate,
logy = 2t + c
[tex]y = e^{2t + c}[/tex]
put t = 2 and y = 200
C = 1.3
Now,
[tex]y= e^[2t + 1.3][/tex]
Substitute t = 7
[tex]y= e^[14 + 1.3]\\y = e^{15.3}[/tex]
y = 4412711.8
Thus, the required value of y(7) is given as y (7)= 4412711.8.
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Write and graph the inverse of y=-x²+4.
Write the inverse of y=-x²+4
y=
(Simplify your answer. Use a comma to separate answers as needed.)
The inverse of y is [tex]\sqrt{4-x} ,-\sqrt{4-x}[/tex].
What is the inverse of a function?
A function whose inverse returns the initial value for the specified output is called an inverse function of the function. The inverse function of y, or[tex]f^{-1}[/tex] (y), will return the value x if f (x) produces an output of y.
Given equation is [tex]y=-x^{2} +4[/tex]
We find the inverse function f(x) by substituting x and y.
We compute the resulting equation for x. We change the variable to:
[tex]x=4-y^{2}[/tex]
Now, solve the equation [tex]x=4-y^{2}[/tex] for y
We get, y = [tex]\sqrt{4-x} ,-\sqrt{4-x}[/tex]
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f(x)=0.2 t
g(t)=0.5(x-6)
By the end. you will be able to solve
0.2 x=0.5(x+6)
The value of x when both the function give the same value is 10
Solution:
Given f(x) = 0.2x , g(x) = 0.5(x-6)
let x = 0 , f(x) = 0 , g(x) = -3
let x = 1 , f(x) = 0.2 , g(x) = -2.5
let x = 2 , f(x) = 0.4 , g(x) = -2
let x = 3 , f(x) = 0.6 , g(x) = -2.5
let x = 4 , f(x) = 0.8 , g(x) = -2 and so on till x=10
let x=10, f(x) = 2, g(x) = 2
∴ The value of x when both the values of the function are same is x = 10
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The value of x when both the function give the same value is 10
What are functions?
Function, in mathematics is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Solution:
Given f(x) = 0.2x , g(x) = 0.5(x-6)
let x = 0 , f(x) = 0 , g(x) = -3
let x = 1 , f(x) = 0.2 , g(x) = -2.5
let x = 2 , f(x) = 0.4 , g(x) = -2
let x = 3 , f(x) = 0.6 , g(x) = -2.5
let x = 4 , f(x) = 0.8 , g(x) = -2 and so on till x=10
let x=10, f(x) = 2, g(x) = 2
∴ The value of x when both the values of the function are same is x = 10
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PLS HELP! 70 POINTS!!
Mr. Mudd gives each of his children $2000 to invest as part of a friendly family competition. The competition will last 10 years. The rules of the competition are simple. Each child can split up his or her $2000 into as many separate investments as they please. The children are encouraged to do their research on types of investments. The initial investments made may not be changed at any point during the 10 years; no money may be added and no money may be moved. Whichever child has made the most money after 10 years will be awarded an additional $10,000.
The table shows the investment made by each of Mr. Mudd’s children, and what happened to their investment over the decade long friendly competition.
Child Performance of investments over the course of the competition
Albert $1000 earned 1.3% annual interest compounded monthly
$500 lost 3% over the course of the 10 years
$500 grew compounded continuously at rate of 0.7% annually
Marie $1500 earned 1.3% annual interest compounded quarterly
$500 gained 3% over the course of 10 years
Hans $2000 grew compounded continuously at rate of 0.8% annually
Max $1000 decreased in value exponentially at a rate of 0.6% annually
$1000 earned 1.9% annual interest compounded biannually (twice a year)
Make sure to show your work
1. What is the balance of Albert’s $2000 after 10 years?
2. What is the balance of Marie’s $2000 after 10 years?
3. What is the balance of Hans’ $2000 after 10 years?
4. What is the balance of Max’s $2000 after 10 years?
5. Who is $10,000 richer at the end of the competition?
Answer:
Albert = $2159.07; Marie = $2244.99; Hans = $2188.35; Max = $2147.40
Marie is $10 000 richer
Step-by-step explanation:
Albert
(a) $1000 at 1.2 % compounded monthly
A = P (1 + r/n )^nt
A = 1000(1 + 0.001)¹²⁰ = $1127.43
(b) $500 losing 2%
0.98 × 500 = $490
(c) $500 compounded continuously at 0.8%
A = Pe^rt
= 500e^0.008 * 10
= $541.64
(d) Balance
Total = 1127.43 + 490.00+ 541.64 = $2159.07
Marie
(a) 1500 at 1.4 % compounded quarterly
A = 1500(1 + 0.0035)⁴⁰ = $1724.99
(b) $500 gaining 4 %
1.04 × 500 = $520.00
(c) Balance
Total = 1724.99 + 520.00 = $2244.99
Hans
$2000 compounded continuously at 0.9 %
A = 2000e^0.009 * 10
= $ 2188.35
Max
(a) $1000 decreasing exponentially at 0.5 % annually
A = 1000(1 - 0.005)¹⁰= $951.11
(b) $1000 at 1.8 % compounded biannually
A = 1000(1 + 0.009)²⁰ = $1196.29
(c) Balance
Total = 951.11 + 1196.29 = $2147.40
Marie is $10,000 richer at the end of the competition.
Hope this helps!!! :)
Solve for x. Round to the nearest tenth.
The value of x for the triangle is equal to 17.32.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Calculate the perpendicular side for both triangles by using the Pythagorean theorem.
H² = P² + B²
Here, H is the hypotenuse, P is perpendicular and B is the base.
For the first triangle, the perpendicular is calculated as,
P² = x² - 10²......................................................1
For the second triangle, the perpendicular will be,
P² = ( 30² - x² ) - 20² .......................................2
Equate the equation 1 and 2 and solve,
x² - 10² = ( 30² - x² ) - 20²
x² - 100 = 900 - x² - 400
2x² = 900 - 400 + 100
2x² = 600
x√ = 300
x =√300
x = 17.32
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After going to your favorite restaurant for dinner and buying food for everybody the bill came to $145. You decide to leave 30% tip and the tax came to 10%.
How much was your total bill?
Answer:
203 dollars
Step-by-step explanation:
100 percent = 145
10 percent = 14.5
30 percent = 43.5
43.5 + 14.5 + 145 = 203
Shape P is reflected in x = -1 to give P'.
a) What are the coordinates of A'?
Then P' is translated by (6)
b) What are the coordinates of A"?
Answer:
a) A' = (2, 4)
b) A'' = (1, -2)
Step-by-step explanation:
When reflecting a shape in a vertical line, each vertex of the shape will be the same distance from the vertical line but in the opposite direction.
Therefore, the x-values change but the y-values remain the same.
Part (a)To reflect point A in x = -1, determine the number of horizontal units the point is from x = -1. Count the same number of units on the other side of the vertical line (remembering that the y-value remains unchanged).
The x-value of point A is x = -4. This is 3 units to the left of x = -1.
Therefore, the x-value of point A' is 3 units to the right of x = -1.
The y-value of point A is y = 4, so the y-value of point A' is also y = 4.
Therefore, the coordinates of the point A' are:
A' = (2, 4)Part (b)To translate point A' by the given vector, translate the point:
1 unit to the left.6 units down.Therefore, the coordinates of the point A'' are:
A'' = (2-1, 4-6) = (1, -2)Answer:
-5
-9+5
Step-by-step explanation:
Factor completely 8x^3+216
Step-by-step explanation:
8x³ + 216
(2 * 2 * 2 * x * x * x) + (2 * 3 * 2 * 3 * 2 * 3)
Complete the square by adding the correct missing term on the left, then factor as indicated:
x²+x+_____________=(_____)²
The complete sentence will be;
⇒ x² + x + 1/4 = ( x + 1/2)²
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ x² + x + __ = (_____)²
Now,
Since, The expression is,
⇒ x² + x + __ = (_____)²
Hence, We can add the number to form the complete square as;
⇒ x² + x + 1/4 = x² + x + (1/2)²
= ( x + 1/2)²
Thus, The complete sentence will be;
⇒ x² + x + 1/4 = ( x + 1/2)²
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A hexagon has a perimeter of 34 2/3 inches. What is the length of one side.
Answer:
Length of each side of regular hexagon = 19 inches
Step-by-step explanation:
What is a regular hexagon ?When the length of all sides is equal and measure of all angles is equal . it is known as Regular hexagon. In a regular hexagon, each inside angle is 120 degrees.
Perimeter of Regular hexagon = 6a
where a is each side of regular hexagon
According to the given information
Perimeter of regular hexagon = [tex]\frac{342}{3}[/tex]
= 114 inches
Perimeter of regular hexagon = 6a
114 = 6a
19 = a
Length of each side of regular hexagon = 19 inches
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Which of the following points is a solution to the system of inequalities?
(A) (-4,4)
(B) (2,6)
(C) (8,-6)
(D) (6,3)
Answer:
Step-by-step explanation:
Answer:
A. is the answer
Step-by-step explanation:
A. Since there is one value of y for every value of x
B. is not a function x = − 4 produces y = 4 and y = 3
C. is not a function x = 6 produces y = 6 and y = 3
D. is not a function x = 6 produces y = 3 and y = 5
X times a number is greater than or equal to 6
The equation, which represents the given condition x >= 6.2.
What is the inequality equation?
Equations and inequalities are mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are supposed to be equal and shown by the symbol =. Whereas in inequality, the two expressions are not necessarily equal and are indicated by the symbols: >, <, ≤, or ≥.
We have,
Six more than 5 times a number x is greater than or equal to 6.
So,
5x >= 31
5x >= 31/5
x >= 6.2
Hence, the equation, which represents the given condition x >= 6.2.
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Complete equation:
Six more than 5 times a number x is greater than or equal to 6.
a. What was the depreciation for the first year?
$637,362
b. Assuming the equipment was sold at the end of the fifth year for $ 138,700 determine the gain or loss on the sale of the equipment. Enter your answer as a positive amount.
Loss=____
c. Journalize the entry to record the sale. If an amount box does not require an entry, leave it blank.
(a) The depreciation for the first year is $99,732.40. (b) If the Machine was sold at the end of the fifth year, the gain or loss is $498,662
What is depreciation?We know that in accounting, depreciation is the loss on a fixed asset over the accounting period that benefited from it.
Using straight line method of depreciation,
Depreciation = [tex]\frac{Cost os asset-Residual value}{Estimated number of years}[/tex]
Applying the figures we have
Depreciation = [tex]\frac{637362-138700}{5}[/tex]
Depreciation= [tex]\frac{498662}{5}[/tex]
Depreciation= $99,732.40
(b) If the machine is sold at the end of the fith year, the loss is accumulated depreciation for 5 years
Loss= $(99,372.4*9) = $498,662
(c) The journal appears as follows
Journal
$ $
Coat of machine 637,362.00 Depreciation 498,662
Balance 138,700
Totals 637,362.00 637,362.
In conclusion, the depreciation for the first year and loss after the fifth year are $99,732 and $498,662 respectively.
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I need help solving so I will know how to do this thank you
Answer:
97.5/100
Step-by-step explanation:
To write 97.5% as a fraction in simplest form, we first convert the percentage to a decimal by dividing it by 100: 97.5% / 100 = 0.975. We can then express this decimal as a fraction by using the fact that any number can be represented as a fraction with the number as the numerator and a power of 10 as the denominator: 0.975 = 0.975/1. Finally, we simplify the fraction by dividing the numerator and denominator by the greatest common factor, which in this case is 1: 0.975/1 = 97.5/100. Therefore, 97.5% can be written as the fraction 97.5/100 in simplest form.
Answer:
39/40
Step-by-step explanation:
97.5/100
Step 1: Write down the percent divided by 100;
Step 2: If the percent is not a whole number, then multiply both top and bottom by 10 until you get an integer at the numerator.
Step 3: Simplify (or reduce) the fraction if it is not in the simplest form.
Write a system of equations to describe the situation below, solve using
substitution, and fill in the blanks.
Tucker is collecting pledges for a walk-a-thon. His mother has pledged a flat
donation of $5, and his grandmother has pledged $5 per mile. If Tucker walks
a certain distance, the two donors will end up owing the same amount. How
much will each donor owe? What is that distance?
Tucker's mother and grandmother will each owe $
miles.
if he walks
The distance for Tucker to walk is 1 mile, only then both the donors would have the same amount. This was found using linear equations.
What are linear equations?
A linear equation is one in which the variable's maximum power is consistently 1. A one-degree equation is another name for it. A linear equation with one variable has the formula Ax + B = 0, which is its standard form. x is a variable, A is a coefficient, and B is constant in this situation. A linear equation with two variables has the formula Ax + By = C as its standard form. Here, the variables are x and y, the coefficients are A and B, and the constant is C.
Since it's given that Tucker's mother will give flat $5. So let that be the RHS of the equation. Now his grandmother will give him $5 for every mile he walks.
Let that be 5x.
Now the equation would be: 5x=5
Which results in x=1.
Therefore at 1 mile, both of the donors' amounts would be the same.
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(Help)
What is the y-incept of the following equation ?
X=3
Is y 0? Or am I wrong?
Answer: There is no y-intercept on this equations
Step-by-step explanation:
so yes you were wrong
3. The diameter of an atom is 0.0000000001 inches. Which of these is an appropriate
estimate for the diameter of an atom?
1×10-10
A.
B.
1×10-9
C. 1×10¹0
D. 1×1019
in.
in.
in.
in.
Answer:
a. [tex]1 * 10^{-10}[/tex]
Explanation:
A converted to standard notation is the same number.
A student ran a distance of 312 miles each day for 5 days. Then the student ran a distance of 414 miles each day for the next 5 days. What was the total distance in miles the student ran during these 10 days?
The total distance ran during these days, written as a mixed number, is (38 + 3/4)mi
What is the total distance that the student ran on the 10 days?We know that the student ran a distance of (3 + 1/2) miles each day for 5 days, so the amount that the student ran in these 5 days is given by the product:
5*(3 + 1/2) mi = (15 + 5/2) mi
Now, on the next 5 days, the student ran a distance of (4 + 1/4) miles, so the total distance that the student ran in these days is:
5*(4 + 1/4) mi = (20 + 5/4)mi
Now to get the total distance that the student ran on the 10 days we need to add the two distances above, we will get:
(15 + 5/2) mi + (20 + 5/4)mi
So we have a sum of mixed numbers, we can rewrite this as:
(15 + 5/2) mi + (20 + 5/4)mi = (15 + 20)mi + (5/2 + 5/4)mi
(15 + 20)mi + (5/2 + 5/4)mi = 35mi + (10/4 + 5/4) mi
35mi + (10/4 + 5/4) mi = 35mi + 15/4mi
35mi + 15/4mi = 35mi + 12/4 mi + 3/4 mi
35mi + 12/4 mi + 3/4 mi = (38 + 3/4)mi
That is the total distance that the student ran on the 10 days.
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What is the value of p in the equation p3=−0.027 ?
Answer:I hope this helpful mark me brainlist if correct then no if wrong
Step-by-step explanation:
P times 3 =-0.0027
Use the commutative property to reorder the terms
3p=-0.0027
Divide both sides of the equation by 3
p=-0.009 or p=-9/1000
Help me with this question please
Answer: x=±2/3
Step-by-step explanation:
The first thing we want to do is isolate the variable, x² in this case.
We can divide both sides by 9 which yields the equation x²=[tex]\frac{4}{9}[/tex].
Then we can take the square root of both sides, x=2/3.
Note: When the exponent is an even number both positive and negative x values will yield the same positive answer, so x=±2/3
"a. What was the population of the state in 2000 ?
b. When will the population of the state reach 28.3 million?
a. In 2000 , the population of the state was million."
In 2000, the population of the state was 23.1 million, After 13 years , the population of the state reach 28.3 million.
What is population?
The term "population" refers to all citizens who are present in a nation or who are temporarily absent from it, as well as all aliens who have made a nation their permanent home. The number of residents in a given area is depicted by this indicator. The annual changes in population brought on by births, deaths, and net migration are measured as growth rates.
Given:
[tex]A = 23.1e^0^.^0^1^5^2^t[/tex] models the population of US
where A is in million
t is years after 2000.
(a) We have to find the population in 2000.
In 2000, t = 0
Plug t = 0 in the above equation
[tex]A(0) = 23.1e^0^.^0^1^5^2^(^0^)\\A = 23.1[/tex]
Hence, in 2000 the population is 23.1 million.
(b) To find when the population of the state reach 28.3 million.
Plug A = 28.3 in above equation and solve for t.
[tex]28.3 = 23.1e^0^.^0^1^5^2^t\\e^0.0152t = \frac{28.3}{23.1} \\t*ln(0.0152) = ln( \frac{28.3}{23.1})\\t = 13.35718\\t = 13[/tex]
Hence, after 13 years the population of the state reach 28.3 million.
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3)
the absolute value of -14-4
absolute value is always positive
The diameter of a speck of dust is about 0.00002 inches. Which of these is an appropriate estimate for the diameter of the speck of dust?
A
2 x 10-5 in.
2 x 10-4 in.
2 x 104 in.
2 x 105 in.
B
с
D
The appropriate estimate for the diameter of the speck of dust is 2 × 10⁻⁵ inches. So the answer is option A, 2 × 10⁻⁵ in.
What is Scientific Notation:In scientific notation, numbers are written with the base 10 much like in decimal notation. Scientific notation is the term used when a number is expressed as the product of two numbers.
Where the first number is more than or equal to one but less than ten and the second number is the power of ten expressed in exponential form.
Convert Decimal to Scientific Notation:Step - 1 Move the decimal point up to the first number that is equal to 1 but less than 10.
Step - 2 Count the number of places that the point moved.
Step - 3 Now Write the resultant number as a product with a power of 10.
Here we have
Diameter of a speck of duct = 0.00002 inches
Convert the given decimal into a scientific notation
As we learn above
Move the decimal point up to a whole number toward the right
=> 0.00002 = 2. = 2
Count the number of zeros or places moved
=> n = 5
Now write the number as a power of 10, Now write the above whole number part as the product of 10
=> 2 × 10⁻⁵ [ ∵ The power is moved right we need to use negative ]
Therefore,
The appropriate estimate for the diameter of the speck of dust is 2 × 10⁻⁵ inches. So the answer is option A, 2 × 10⁻⁵ in.
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Rewrite the following function in factored form. f(x)=x2+6x+8
Answer:
f(x) = (x+2)(x+4)
Step-by-step explanation:
4 + 2 = 6
4 * 2 = 8
f(x) = (x+2)(x+4)
Convert 251,000 to a scientific notation
Answer:
2.51 x 10^5
Step-by-step explanation:
Scientific notation gives you a number between 1 and 10 multiplied by a power of ten. In this case, you'll want to use the significant digits, 251, and divide or multiply by a power of ten to get a number between 1 and 10.
251,000 can become 2.51 (which is between 1 and 10) multiplied by 10 to a certain exponent. All you need to do is calculate the exponent.
2.51 x 10^(?) = 251,000
For each power of 10, the decimal moves a space. Since you want the decimal to move 5 spaces, you'll want to multiply 2.51 by 10^5.
2.51 x 10 = 25.1
2.51 x 10^2 = 251
2.51 x 10^3 = 2510
2.51 x 10^4 = 25,100
2.51 x 10^5 = 251,000
WORD PROBLEM:
When the square of a certain number is added to the number, the resu;t is the same as when 48 is added to three times the number. Find the number.
Answer:
Step-by-step explanation:
Let x be the number.
The square of the number is x2
Increased by twice the number means add 2x.
So your equation is :
X2 +2x = 48.
Can you take it from here?
The asked number is 12.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, When the square of a certain number is added to the number, the result is the same as when 48 is added to three times the number.
Let the number be x,
x²+x = 48X3 + x
x² = 144
x = 12
Hence, The asked number is 12.
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Given vector v = (1, -1), find -4v.
Answer:
<-4,4>
Step-by-step explanation:
-4 * <1,-1> = <-4 * 1, -4 * -1> = <-4, 4>
Maximize: Profit = 20x + 30y
Constraints:
x + y <12
x + 2y<12
2x + y<12
x>0
y>0
Answer:
x> -10
Step-by-step explanation:
If a polynomial f(x) has a remainder of 4 when divided by x-5, what is f(5)?
The value of f(5) When a polynomial f(x) is divided by x -5 is 4
What is a polynomial?Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable.
If f(x) has a remainder of 4 when divided by x - 5
Then it means that if f(x -5) = f(0)
x -5 = 0
x = 5
so if you substitute 5 into f(x) which is f(5) it will give 4
so therefore f(5) = 4
In conclusion f(5) is same as 4
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In a recent year 365 days a hospital had 5814 births. find the mean number of births per day
Answer:
ANS:- 15.9
Step-by-step explanation:
5814/365 = 15.9
Suppose S = {1, 2, 3}, with P({1}) = 1/2 and P({1, 2}) = 2/3. What must P({2}) be?
The value of P({2}) for the given Finite set is found as P({2}) = 1/6.
Explain the meaning of the term finite set?Sets with a bounded number of participants are referred to as finite sets. Due to their ability to be numbered, finite sets also are known as countable sets. If the members of the elements of all this set are finite, then the operation will run from out elements to list. Finite set illustrations include P = { 0, 3, 6, 9, …, 99}For the stated question;
S = {1, 2, 3},P({1}) = 1/2 and P({1, 2}) = 2/3.P({2}) will contain only element with is not present in set P({1}) counting from P({1, 2}).
Thus,
P({2}) = P({1, 2}) - P({1})
P({2}) = 2/3 - 1/2
P({2}) = 1/6
Thus, the value of P({2}) for the given Finite set is found as P({2}) = 1/6.
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