This means that the median weight of a female child at 31.48 months is 28 pounds (approximately) base on logarithmic function.
Logarithmic function calculation.
Q1.1: The equation for the amount of money in the account after t years, compounded annually, can be given by:
A = P(1 + r/100)^t
where A is the amount of money in the account after t years, P is the principal amount invested, r is the annual interest rate, and t is the number of years.
Plugging in the values given in the problem, we get:
A = 1200(1 + 4.25/100)^t
Q1.2: We need to solve for t in the equation:
3000 = 1200(1 + 4.25/100)^t
Dividing both sides by 1200, we get:
2.5 = (1 + 4.25/100)^t
Taking the natural logarithm of both sides, we get:
ln 2.5 = t ln (1 + 4.25/100)
Solving for t, we get:
t = ln 2.5 / ln (1 + 4.25/100) ≈ 15.91 years
So, it will take approximately 15.91 years for the amount of money in the account to reach $3000.
Q2.1: To graph the function W = 7.5 + 5.9 ln(M + 1), we can use a graphing calculator or software. Here is a possible graph:
Graph of W = 7.5 + 5.9 ln(M + 1)
Q2.2: To find W ^−1(28), we need to solve the equation:
28 = 7.5 + 5.9 ln(M + 1)
Subtracting 7.5 from both sides, we get:
20.5 = 5.9 ln(M + 1)
Dividing both sides by 5.9, we get:
ln(M + 1) ≈ 3.474576
Taking the inverse logarithm of both sides, we get:
M + 1 ≈ e^3.474576
M ≈ e^3.474576 - 1 ≈ 31.48 months
So, W ^−1(28) ≈ 31.48 months. This means that the median weight of a female child at 31.48 months is 28 pounds (approximately).
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In a company, 80% of the workers are women. If people work for the company who aren't women , how many workers are there in all?
There are a total of 2000 workers in all in the company
How many workers are there in all?From the question, we have the following parameters that can be used in our computation:
Women percentage = 80%
People not women = 400
Using the above as a guide, we have the following:
People not women percentage = 1 - 80%
Evaluate
People not women percentage = 20%
So, we have
People not women = People not women percentage * Total
substitute the known values in the above equation, so, we have the following representation
20% * Total = 400
Divide
Total = 2000
Hence. there are 2000 people in the company
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Which function is undefined for x = 0?
O y=³√√x-2
y = √√√x-2
Oy=³√√x+2
O
y=√x+2
O
The function y = √x+2 is undefined for any value of x that makes the expression inside the square root negative, which in this case is x ≤ -2.
What is an inequality equation?
An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
The function that is undefined for x = 0 is y = √x+2.
When x = 0, we have:
y = √0+2
y = √2
Since there is no real number whose square is negative, the square root of a negative number is undefined in real numbers.
Therefore, the function y = √x+2 is undefined for any value of x that makes the expression inside the square root negative, which in this case is x ≤ -2.
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Isiah is saving $12 per week from his allowance. After 20 weeks Isaiah has $240.
$[tex]240[/tex] is saved by Isaiah from his allowance within the space of [tex]20[/tex] weeks.
What is allowance?The link between two or more variables is depicted using an equation. Mathematical operations may be used in equations.
Isaiah is saving $[tex]12[/tex] per week from his pay.
Amount of money saved by Isaiah in [tex]20[/tex] weeks
Money saved [tex]=[/tex] $[tex]12[/tex] ×[tex]20[/tex]
Money saved = $[tex]240[/tex]
Therefore, $[tex]240[/tex] is saved by Isaiah from his allowance within the space of [tex]20[/tex] weeks.
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the calculated total savings matches the given total savings of $240, we can say that the statement is true
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
To check whether this statement is true or false, we can use the following formula:
Total Savings = Savings per Week × Number of Weeks
Substituting the given values, we get:
Total Savings = $12/week × 20 weeks = $240
Since the calculated total savings matches the given total savings of $240, we can say that the statement is true.
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Flying against the wind, an airplane travels 6390 kilometers in 9 hours. Flying with the wind, the same plane travels 2970 kilometers in 3 hours. What is the rate of the plane in still air and what is the rate of the wind?
The rate of the plane in still air is 810 km/h and the rate of the wind is 90 km/h.
Explain the term rate
Rate is a measure of the speed or frequency of change of a quantity over time or space. It is expressed as a ratio between two quantities, such as distance travelled per unit of time or number of occurrences per unit of time. Rates are commonly used in mathematics, science, and economics to analyze and compare different phenomena.
According to the given information
Let's let x be the rate of the plane in still air and y be the rate of the wind. When flying against the wind, the plane's effective speed is (x - y) km/h, and when flying with the wind, its effective speed is (x + y) km/h.
From the information given in the problem, we can set up two equations to represent the plane's distance travelled when flying against and with the wind:
6390 = 9(x - y)
2970 = 3(x + y)
Solving for x and y in these equations, we find that x = 810 and y = 90. So the rate of the plane in still air is 810 km/h and the rate of the wind is 90 km/h.
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HELP PLEASE!! A BRAINLIEST WOULD BE GIVEN FOR THE BEST ANSWER.
The requried [tex]\int_a^{oo} g(x) dx[/tex] must be convergent. Option C is correct.
Since f(x) is greater than or equal to g(x) for all x, we know that:
[tex]\int_a^{oo} f(x) dx\geq\int_a^{oo} g(x) dx[/tex]
If [tex]\int_a^{oo} f(x)[/tex]dx is convergent, then by comparison test, [tex]\int_a^{oo} g(x) dx[/tex] must also be convergent. Therefore, the correct answer is (C) g(x)dx is convergent.
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The circumference of the smaller circle is 25% of the circumference of the larger circle. Find the circumference of the larger circle. Round your answer to the nearest tenth
The circumference of the larger circle is approximately 9.4 units.
What is circumference?The circumference is the distance around the edge or boundary of a closed two-dimensional shape, such as a circle or an ellipse.
According to question:Let C be the circumference of the larger circle. Then the circumference of the smaller circle is 0.25C, according to the given information.
We know that the circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Therefore, we can write:
C = 2πr for the larger circle
0.25C = 2πr for the smaller circle
Dividing the second equation by 0.25, we get:
C = 8πr for the smaller circle
Now we can equate the two expressions for C and solve for r:
2πr = 8πr
6πr = C
r = C/(6π)
Finally, we can substitute this value of r into the expression for C in terms of r for the larger circle:
C = 2πr = 2π(C/(6π)) = (1/3)Cπ
Solving for C, we get:
C = (3/π)C
C = 3π ≈ 9.4 (rounded to the nearest tenth)
Therefore, the circumference of the larger circle is approximately 9.4 units.
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The temperatures, in degrees F, at 7:00 a.m. for five days during one week are shown.
-3, 4, -1, 6, 7
The mean temperature for all 7 days of the week was 0°F.
What was the mean of the temperatures for the two missing days?
a. -13
b. -10.5
c. -6.5
d. 0
The value of the mean of the temperatures for the two missing days are,
= - 6.5
We have to given that;
The temperatures, in degrees F, at 7:00 a.m. for five days during one week are shown.
-3, 4, -1, 6, 7
And, The mean temperature for all 7 days of the week was 0°F.
Now, We can assume that,
Last two days temp. are x and y.
Hence, We get;
(- 3 + 4 + (-1) + 6 + 7 + x + y) / 7 = 0
- 3 + 4 - 1 + 6 + 7 + x + y = 0
x + y = - 13
Divide both side by 2;
(x + y)/2 = - 13/2
(x + y)/2 = - 6.5
Thus, The value of the mean of the temperatures for the two missing days are,
= - 6.5
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what is 3/8 divided by 3
Answer:0.125
Step-by-step explanation:
Janelle is planning to rent a car while on vacation. The equation C=0.32m+15 models the relation between the cost in dollars, C, per day and the number of miles, m, she drives in one day. Interpret the C-intercept of the equation.
The C-intercept of the equation means that she will have to pay $15 per day for renting the car.
Interpreting the C-intercept of the equation.From the question, we have the following parameters that can be used in our computation:
C=0.32m+15
In the equation C=0.32m+15, the C-intercept represents the fixed cost of renting a car per day, which is $15 in this case.
This means that regardless of how many miles Janelle drives, she will have to pay $15 per day for renting the car.
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what are the imports and Exports for Segbana,Benin
We can see here that from the available information it is clear that imports of Benin were:
refined petrolrice, etcWhile the exports are:
cottonsheanutscashewsWhat is an export?A locally produced commodity or service that is sold to another nation is referred to as an export. To put it another way, it's a good or service that is sold or sent to another nation to be utilized or consumed there.
Exports may help a nation's economy expand by bringing in money and creating jobs.
Imports are actually known to be goods and services that are brought into a country/nation.
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1. Supposed two coins are tossed, let P be the random variable representing the number of heads that occur. Find the values of the random variable P.
The possible values of the random variable P are 0, 1, or 2.
Describe Probability?A triangle is a polygon with three straight sides and three angles. It is one of the most fundamental shapes in geometry and is used extensively in mathematics, science, engineering, and art. The sum of the interior angles of a triangle is always 180 degrees, and the length of the sides and the size of the angles determine the shape of the triangle.
Triangles can be classified according to the length of their sides and the size of their angles. A scalene triangle has three unequal sides and three unequal angles. An isosceles triangle has two equal sides and two equal angles. A equilateral triangle has three equal sides and three equal angles, each measuring 60 degrees. Triangles can also be classified based on the size of their angles: an acute triangle has three acute angles (less than 90 degrees), a right triangle has one right angle (90 degrees), and an obtuse triangle has one obtuse angle (greater than 90 degrees).
Triangles have many important properties and applications in geometry. For example, the Pythagorean theorem is a fundamental relationship between the sides of a right triangle, which states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The area of a triangle can be calculated using the formula 1/2 x base x height, and this formula can be used to solve many practical problems involving triangles.
The random variable P can take on four possible values, depending on how many heads are obtained:
P = 0 if both coins show tails.
P = 1 if exactly one of the coins shows heads.
P = 2 if both coins show heads.
Therefore, the possible values of the random variable P are 0, 1, or 2.
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HELP RNRNNRNRNRNRNNRNRNRR
Answer:
Step-by-step explanation:
Area= pi times radius²
The radius in the last one is 7, so 7² is 49.
Multiply 3.14 by 49 and you get 153.86. Round it to the nearest tenth and you get 153.9 as the area
Hope this helps!
if you roll a number cube 20 times. which scenario is least likely?
a) you find the experimental probability of rolling a 1 or 2 to be 0.3.
b) you find the experimental probability of rolling a 3 or 4 to be 0.4.
c) you find the experimental probability of rolling a 5 or 6 to be 0.5.
d) you find the experimental probability of rolling a number divisible by 3 to be 0.35
Find the surface area of the following figure, if the diameter of the inner cylinder is 7 cm. The inner cylinder has been hollowed out of the outer cylinder. Round your final answer to the nearest tenth.
The surface area is 653.1 square centimeters.
What is surface area?
A three-dimensional object's surface area is the space it takes up when viewed from the outside.
Here the given inner cylinder diameter d = 7m then
Radius r= d/2 = 7/2 = 3.5m
Now outer cylinder diameter = 9 cm then
Radius R= d/2 = 9/2 = 4.5 cm.
Height h = 26 cm.
Now using surface area of cylinder formula then,
=> Surface area A = [tex]\pi (R^2-r^2)h[/tex] square unit.
=> A = [tex]3.14(4.5^2-1.5^2)26[/tex]
=> A = [tex]3.14\times(20.25-12.25)\times26[/tex]
=> A = 3.14×8×26
=> A = 653.1 square centimeters.
Hence the surface area is 653.1 square centimeters.
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4. From a survey of the population of the United States, a circle graph
was created.
Population of the United States, 1990
White
80%
American Indian,
Eskimo, and Aleut
1%
Black
12%
Asian and
Pacific Islander
3%
Other Races
4%
The ratio of whites to blacks is 20 to 3 ( or 20/3) in United States in 1990.
From a survey of the population of the United States, a circle graph (or, pie chart) was created on the information,
Population of the United States in 1990 :
White consists of 80%
American Indian, Eskimo, and Aleut consists of 1%
Black consists of 12%
Asian and Pacific Islander consists of 3%
Other Races consists of 4%
Let say the total population of the United States in 1990 was x.
By applying the formula of percentage to numbers we get,
The number of people who were white in 1990 in United States = 80% of x
= [tex][\frac{80}{100} ]x[/tex] = [tex]\frac{4}{5} x[/tex]
The number of people who were black in 1990 in United States = 12% of x
= [tex][\frac{12}{100} ]x[/tex] = [tex]\frac{3}{25} x[/tex]
Thus, we can calculate ratio as,
Ratio of whites to blacks = [tex]\frac{\frac{4}{5} x}{\frac{3}{25} x}[/tex] = 20/3
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Brenda earns $5 each week for chores. x represents the number of weeks brenda did her chores. t represents the total dollars she earned. create an equation representing this situation
The situation is modeled by the linear equation:
t = $5*x
How to write the equation?We know that Brenda earns $5 each week for chores. The variable x represents the number of weeks brenda did her chores, and t represents the total dollars she earned.
Then if she works for x weeks, the amount that she earns is x times $5, then the equation will be a linear one:
t = $5*x
That is the equation.
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What graphic depiction would most effectively help a researcher compare the distribution of the hours spent online among teenagers, young adults, and the elderly and why
A histogram would be the most effective graphic depiction to compare the distribution of the hours spent online among teenagers, young adults, and the elderly.
What is a histogram ?
A histogram is a graph that displays the distribution of a continuous variable. It divides the data into a set of intervals (called bins) and counts the number of data points that fall into each bin.
This creates a bar-like representation of the data, with the height of each bar indicating the frequency of data points in that bin. By using a histogram, we can see the shape of the distribution, as well as any patterns or trends that may exist. We can compare the distribution of the hours spent online by teenagers, young adults, and the elderly by placing the histograms of their data side by side. This will allow us to visually compare the shape, spread, and central tendency of the distributions for each group. Additionally, we can use different colors for each group to make the comparisons even clearer. This will enable us to quickly see if there are any significant differences in the hours spent online among the three groups.
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The lengths of two sides of a triangle are shown.
Side 1: 3x² - 4x-1
Side 2: 4x-x² +5
The perimeter of the triangle is 5x³ - 2x² + 3x - 8.
Part A: What is the total length of the two sides, 1 and 2, of the triangle? Show your work.
Part B: What is the length of the third side of the triangle? Show your work.
Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer.
Answer:
Part A:
To find the total length of the two sides of the triangle, we need to add Side 1 and Side 2:
Side 1: 3x² - 4x - 1
Side 2: 4x - x² + 5
Total length: (3x² - 4x - 1) + (4x - x² + 5)
Simplifying and combining like terms, we get:
Total length: -x² + 7x + 4
Therefore, the total length of the two sides of the triangle is -x² + 7x + 4.
Part B:
To find the length of the third side of the triangle, we need to subtract the sum of Side 1 and Side 2 from the perimeter of the triangle:
Length of Side 3 = Perimeter - (Side 1 + Side 2)
Length of Side 3 = (5x³ - 2x² + 3x - 8) - (3x² - 4x - 1 + 4x - x² + 5)
Simplifying and combining like terms, we get:
Length of Side 3 = 2x³ - 2x² + 7x - 12
Therefore, the length of the third side of the triangle is 2x³ - 2x² + 7x - 12.
Part C:
The answers for Part A and Part B show that the polynomials are closed under addition and subtraction. The sum of Side 1 and Side 2 is a polynomial (-x² + 7x + 4), and the difference between the perimeter of the triangle and the sum of Side 1 and Side 2 is also a polynomial (2x³ - 2x² + 7x - 12). In both cases, the result is a polynomial, which means that the set of polynomials is closed under addition and subtraction.
Riley is saving up to buy a new television. She needs a total of $1,290.78. Riley has saved $200.73 already and earns $83.85 per
week at her job. How many weeks does Riley need to work to save enough money to buy the new television?
Answer:
13
Step-by-step explanation:
First of all riley saved 200.73$ she needs 1,290.78$ so,
1290.78$-200.73$=1090.95$
she earns 83.85$ a week
then, 1090.95÷83.85= 13
13 weeks
Use an integer to represent the situation. 800 ft gain in elevation
The integer number that represents an 800 ft gain in elevation is given as follows:
+800.
What are integer numbers?Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.
For altitudes, the signs are given as follows:
Gain of altitude: positive integer.Loss of altitude: negative integer.Hence the integer number that represents an 800 ft gain in elevation is given as follows:
+800.
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Owen receives $10 and puts it into his saving account. He adds $0.50 to the account each day for a number of day, d, after that. He writes the expression 10+ 0.5(d-1) to find the amount of money in his account after d days. Which statement about his expression is true?
The true expression about the account is D.) It is the sum of the initial amount and the additional amount after d days.
What does the expression 10+0.5(d−1) represent in Owen's savings account?The answer is D because it represents the sum of the initial amount and the additional amount after d days. The initial amount is $10 and Owen adds $0.50 to the account each day for a number of days, represented by d.
By subtracting 1 from d, the expression ensures that on the first day (when d=1), only the initial $10 is counted. On each subsequent day, the additional amount of $0.50 is added to the total. Therefore, the expression 10+0.5(d−1) gives the amount of money in Owen's account after d days.
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Verify directly that F is an antiderivative of f.
F(x) is an antiderivative of f(x) because F'(x) = f(x)
What is an antiderivative?An anti-derivative is the integral of a function
To verify that F is an antiderivative of f where
F(x) = √(3x² - 4) and f(x) = 3x/√(3x² - 4)
This means that F(x) = ∫f(x)
This implies that F'(x) = f(x)
So, we verify as follows
F(x) = √(3x² - 4)
Taking the derivative with respect to x, we have that
dF(x)/dx = d√(3x² - 4)/dx
Let u = 3x² - 4
So, dF(x)/dx = d√u/dx
= d√u/du × du/dx
= 1/(2√u) × du/dx
Now,du/dx = d(3x² - 4)/dx
= 6x
So,
dF(x)/dx = 1/(2√u) × du/dx
= 1/(2√(3x² - 4)) × 6x
= 1/(√(3x² - 4)) × 3x
= 3x/(√(3x² - 4))
= f(x)
So, F(x) is an antiderivative of f(x) because F'(x) = f(x)
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Solve the simultaneous equations
x^2+y^2=9
x+y=2
Give your answers correct to 2 decimal places
The two solutions to the simultaneous equations are; y1 = -0.87 and y2 = 2.87. x1 = 2.87, x2 = -0.87
How do you solve the simultaneous equations?To solve these simultaneous equations, we can use the method of substitution. We can rearrange the second equation to isolate one of the variables, for example, y:
y = 2 - x
Now, substitute this expression for y into the first equation:
x^2 + (2 - x)^2 = 9
Expand the equation:
x^2 + (4 - 4x + x^2) = 9
Combine like terms:
2x^2 - 4x + 4 = 9
Move all terms to one side to set the equation to equal zero:
2x^2 - 4x - 5 = 0
Now, we can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In our equation, a = 2, b = -4, and c = -5:
x = (4 ± √((-4)^2 - 4(2)(-5))) / (2 x 2)
x = (4 ± √(16 + 40)) / 4
x = (4 ± √56) / 4
The two possible values for x are:
x1 ≈ (4 + 7.48) / 4 = 2.87
x2 ≈ (4 - 7.48) / 4 = -0.87
Now, we'll find the corresponding y values using the equation y = 2 - x:
For x1 ≈ 2.87:
y1 ≈ 2 - 2.87 ≈ -0.87
For x2 ≈ -0.87:
y2 ≈ 2 - (-0.87) ≈ 2.87
So, the two solutions to the simultaneous equations are approximately (2.87, -0.87) and (-0.87, 2.87), both correct to 2 decimal places.
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A total of 550 tickets were sold for a game for a total of $1950. If adult tickets sold for $7 each and child tickets cost $2 each, how many of each kind of ticket were sold?
In linear equation, 170 adult and 380 children's tickets were sold.
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
It usually works well to let a variable represent the higher-value item in the mix. Here, we can let 'a' represent the number of adult tickets sold. Then the total revenue is ...
7a + 2(550 -a) = $1950
7a + 1100 - 2a = 1950
5a = 1950 - 1100
5a = 850
a = 170
c = 550 - 170 = 380
170 adult and 380 children's tickets were sold.
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What inequality matches this graph?
A} x > 1
B} x ≥ 1
C} x < 1
D} x ≤ 1
Answer:
x<1
Step-by-step explanation:
looking at the graph, the x values are 0,-1,-2,-3,-4,-5.
therefore, all the values of x are below 1.
x<1 is the suitable inequality that matches the graph.
.Which net matches this figure? A,B,C or D
please answer ill give brainliest
Answer:
C or D it’s hard to see if the bottom of the shape is a square or rectangle.
Step-by-step explanation:
If rectangle C if squared D
I would go with C
answer is a
i think question is about implicit differentiation
The x-coordinates of the points on the curve where the tangent line is horizontal will be option A.
How to explain the coordinate(x² + y²)² = 4(x² – y²)
x⁴ + 2x²y² + y⁴ = 4x² - 4y²
y⁴ + 2x^2y² + 4y² - 4x² = 0
Now we can use implicit differentiation to find the derivative of y with respect to x:
4y³(dy/dx) + 4xy² + 4y(dy/dx)x² + 8y(dy/dx) - 8x = 0
Simplifying this expression, we get:
4y³(dy/dx) + 4xy² + 4xy²(dy/dx) + 8y(dy/dx) - 8x = 0
(dy/dx)(4y³ + 4x²y²) + 8y(dy/dx) = 8x - 4xy²
(dy/dx)(4y³ + 4x^2y² + 8y) = 4x(2-y²)
(dy/dx) = 4x(2-y²)/(4y³ + 4x²y² + 8y)
Based on the information, x-coordinates of the points on the curve where the tangent line is horizontal will be option A.
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factorise 9x^2 + 3x^3
Answer:
[tex]9 {x}^{2} + 3 {x}^{3} [/tex]
[tex]3 {x}^{2} (3 + x)[/tex]
[tex]3 {x}^{2} (x + 3)[/tex]
the simplest form of 4(3x+y)
An expression which is the simplest form of 4(3x + y) + (2x - 5y) + x² include the following: x² + 14x - 6y.
What is an expression?In Mathematics and Geometry, an expression simply refers to a type of mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number), without an equal to sign (symbol).
In this scenario and exercise, the simplest form of the given expression 4(3x + y) + (2x - 5y) + x² can be determined or calculated by simplifying it as follows;
4(3x + y) + (2x - 5y) + x²
12x + 4y + 2x - 5y + x²
14x + - y + x²
By rearranging, we have;
x² + 14x - 6y.
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Complete Question:
Which expression is the simplest form of 4(3x+y)+2x-5y)+x²
THE UNITE
VENOCH
Suppose you buy a $1000 bond with a 4.3% coupon that matures in 30 years.
1. First, how much do you earn off your bond every 6 months?
Type answer here...
SUBMIT
The amount (coupon interest) that is earned off the $1,000 bond with 4.3% coupon every 6 months is $21.50.
What is the coupon interest?The coupon interest represents the periodic payment received by a bondholder from the date of issuance until the date of maturity of a bond.
The coupon interest is computed by applying the coupon rate on the face value of the bond.
Face value of the bond = $1,000
Coupon interest rate = 4.3%
Maturity period = 30 years
Coupon (bond) interest for 6 months = $21.50 ($1,000 x 4.3% x 6/12)
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