Answer:
a. The equation is separable, as we can write it as (1 - y²) dy = x² dx. Integrating both sides, we have (1/2)*ln|1 - y²| = (1/3)*x³ + C, where C is the constant of integration. Solving for y, we get an equation for the integral curves: y = ±sqrt(1 - exp(2/3*x³ + 2C)).
b. Rearranging the equation, we get (2/(y - 1)) dy/dx = (3x² + 4x + 2). This is separable, so integrating both sides, we have 2 ln|y - 1| = x³ + 2x² + 2x + C, where C is the constant of integration. Solving for y, we get y = 1 + Ce^(x³+2x²+2x)/2. Using y(0) = -1, we have -1 = 1 + C, so C = -2. Thus, the solution to the initial value problem is y = 1 - 2e^(x³+2x²+2x)/2. The solution exists for all values of x.
How many combinations of poker hands are in a deck of cards?
find the value of k , if x =1, y=2 is a solution of the equation 2x+3y=k
Answer:
k=8
Step-by-step explanation:
2(1)+3(2)=k
2+6=8
k=
The answer is:
k = 8
Work/explanation:
If x = 1, and y = 2, we can plug these values into the equation 2x+3y = k:
[tex]\bf{2(1) + 3(2) = k}[/tex]
Multiply
[tex]\bf{2 + 6 = k}[/tex]
Add
[tex]\bf{8 = k}[/tex]
Hence, k = 8.no explanation needed would be nice ytho thnks
The average rate of change in the population between 2002 and 2004 is one thousand per year, and between 2002 and 2006 is 1.75 thousand per year.
Rate of changeTo calculate the average rate of population change, we need to find the difference in population between the given years and divide it by the difference in years.
Between 2002 and 2004:
Population change = 80 - 82 = -2 (decrease of 2, as the population decreased)
Year difference = 2004 - 2002 = 2
Average rate of change = Population change / Year difference
Average rate of change = -2 / 2 = -1 (thousands per year)
Between 2002 and 2006:
Population change = 75 - 82 = -7 (decrease of 7, as the population decreased)
Year difference = 2006 - 2002 = 4
Average rate of change = Population change / Year difference
Average rate of change = -7 / 4 = -1.75 (thousands per year)
Therefore, the average rate of change of population between 2002 and 2004 is 1 thousand per year, and between 2002 and 2006 is 1.75 thousand per year.
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Pie chart values
20%. Rice
15%. Others
Pulses. 30%
maize 20%
wheat 15%
Percentage distribution of products in exports of the
given countries.
(a) What is the value (in $ billion) of pulses export
by US? on a billion
(6)
What is the ratio of wheat export of UK to
maize export of IND? 4:10
(e) By what percentage is the maize export of
JAP more than the rice export of AUS?
(d) If the export of AUS is doubled and that of US is
halved but percentage distribution of products of
export remains the same, then find the value of
Export of Rice by US
Export of Pulses by AUS
In USSR, find the ratio of maize export to the
rice export.
a.) The value of pulses exported by US in billion would be=30 billion.
b.) The ratio of wheat export of UK to maize export of IND would be= 6:5
How to calculate the value of pulses exported?For question a.)
To calculate the pulses, the following steps should be taken as follows:
From the bar chart, the value of pulses in billions = 30 billions.
For question b.)
The ratio of wheat export at UK and maize export at IND would be calculated as follows:
The quantity of wheat export at UK = 24
The quantity of maize export at IND = 20
Therefore, the ratio of wheat to maize = 24:20= 6:5
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HELP ASAP IVE BEEN STUCK ONNTHIS 20 PTS
Answer:
[tex] \sqrt{ {( - 4 - 2)}^{2} + {(1 - 0)}^{2} } = \sqrt{ {( - 6)}^{2} + {1}^{2} } = \sqrt{36 + 1} = \sqrt{37} [/tex]
The number 37 goes beneath the radical symbol.
What’s the answer please I’m so behind
Answer:
2
Step-by-step explanation:
3x - 12 is inside the root.
The smallest value of √(3x - 12) is 0.
The greatest value of √(3x - 12) is infinity.
Since the function includes +2, then the range is from 2 to infinity.
Answer: 2
Solve the right triangle.
b=1.98 c=4.63
[tex] \sf \hookrightarrow \: {(BC)}^{2} + {(AC)}^{2} = {(AB)}^{2} [/tex]
[tex] \sf \hookrightarrow \: {a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] \sf \hookrightarrow \: {a}^{2} + {(1.98)}^{2} = {(4.63)}^{2} [/tex]
[tex] \sf \hookrightarrow \: {a}^{2} + (1.98 \times 1.98)= (4.63 \times 4.63) [/tex]
[tex] \sf \hookrightarrow \: {a}^{2} + (3.9204)= (21.4369)[/tex]
[tex] \sf \hookrightarrow \: {a}^{2}= (21.4369) - (3.9204)[/tex]
[tex] \sf \hookrightarrow \: {a}^{2}= 17.5165[/tex]
[tex] \sf \hookrightarrow \: a= \sqrt{ 17.5165}[/tex]
[tex] \sf \hookrightarrow \: a= 4.18. Approx[/tex]
Answer: To solve the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's label the sides of the triangle as follows:
The length of the hypotenuse is c = 4.63.
One of the legs is b = 1.98.
Using the Pythagorean theorem, we can find the length of the other leg, which we'll label as a:
a^2 + b^2 = c^2
a^2 + (1.98)^2 = (4.63)^2
a^2 + 3.9204 = 21.4369
a^2 = 21.4369 - 3.9204
a^2 = 17.5165
Taking the square root of both sides, we find:
a ≈ √17.5165
a ≈ 4.1833
So, the length of the other leg (side a) is approximately 4.1833.
Therefore, the sides of the right triangle are approximately:
Side a ≈ 4.1833
Side b = 1.98
Side c = 4.63
Step-by-step explanation:
In a hockey Skills competition, Olga scored on 3 of 5 breakaways. Tara scored on 5 of 7 breakaways. Whose performance was better?
Answer:
Step-by-step explanation:
Olga scoring 3/5 breakaways means she scored a fraction of 3/5 or 60 percent of the breakaways. Tara scored a fraction of 5/7 or around 71 percent. That means Tara's performance was better as she scored a higher percentage of the breakaways.
After college, you get a job with a starting salary of $37,000. You have a cousin that works at the same company, but he was hired three years before you. Your contract states you will receive a pay raise each year of 6%. Your cousin tells you that his starting salary three years ago was $50,000 and he has been guaranteed a 4% pay raise each year.
1. Make a table showing your salary for your first five years on the job
1. A table showing your salary for the first five years on the job is shown below.
2. Your cousin's salary would be $56243.2 in the year you started working.
3. A formula for your salary is [tex]P(t) = 37000(1.06)^t[/tex]
A formula for your cousin's salary is [tex]P(t) = 50000(1.04)^t[/tex]
4. A graph of your salary and your cousin's salary is shown below.
It would take about 16 years before your salary exceed your cousin's salary.
How to write an exponential function to model the situation?In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
[tex]P(t) = I(1 + r)^t[/tex]
Where:
P(t) represent the future value.t represent the time or number of years.I represent the initial amount.r represent the exponential growth rate.Part 1.
We can create a table of values to model your salary for the first five years on the job as follows;
Years 1 2 3 4 5
Salary ($) 39,220 41,573.2 44,067.6 46,711.7 49,514.4
Part 2.
For your cousin's salary three years after, we have:
y = 50,000(1.04)³
y = $56243.2.
Part 3.
We can write a formula for your salary as follows;
[tex]P(t) = 37000(1 + 0.06)^t\\\\P(t) = 37000(1.06)^t[/tex]
For your cousin's salary, we have:
[tex]P(t) = 50000(1 + 0.04)^t\\\\P(t) = 50000(1.04)^t[/tex]
Part 4.
In order to plot a graph of your salary and your cousin's salary, we would use an online graphing tool with a scale of 1 units for 1 year on the x-axis and a scale of 50 units for 1000 dollars on the y-axis.
Since the lines representing both salaries intersect at 15.808, we can logically deduce that it would take approximately 16 years for your salary to exceed your cousin's salary.
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la edad de Ana es la mitad de jose y dentro de 10 años seran dos tercios ..cual es la edad de jose
La edad actual de José es de 30 años.
Para resolver este problema, primero debemos establecer ecuaciones basadas en la información proporcionada. Llamemos "x" a la edad actual de José y "y" a la edad actual de Ana. Según la primera condición, la edad de Ana es la mitad de la edad de José, por lo que podemos escribir la ecuación: y = (1/2)x.
La segunda condición nos dice que dentro de 10 años, sus edades serán dos tercios de sus edades actuales. Esto se puede expresar como: (x + 10) * (2/3) = y + 10.
Reemplazando el valor de y en la segunda ecuación con la primera ecuación, obtenemos: (x + 10) * (2/3) = (1/2)x + 10.
Resolviendo esta ecuación, podemos simplificarla y llegar a: 2(x + 10) = 3[(1/2)x + 10].
Al resolver la ecuación resultante, encontramos que x = 30.
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PLEASE HELP PLEASE HELP
Answer:
22
Step-by-step explanation:
You can do it by 220 divided by 10, which gives an answer of 22.
3
2
1
-1
-2
-3
Determine the period.
V
MAN
6 8 10 12 14
2 4
The period of the function in this problem is given as follows:
5 units.
How to obtain the period of the function?A periodic function is a function that has the behavior repeating over intervals in the domain of the function.
Then the period of the function has the concept defined as the difference between two points in which the function has the same behavior.
The distance between peaks of the function in this problem is of 5 units, which represents the period of the function.
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solve the following problem
a. The maximum population of the squirrels is 1800.
b. The number of squirrels that were introduced to the island are 200 squirrels.
What is an exponential function?In Mathematics and Geometry, a logistic growth function can be represented by using the following mathematical equation:
[tex]f(x) = \frac{L}{1\;+\;e^{-k(x-x_0)}}[/tex]
Where:
L represents the carrying capacity, maximum value or supremum.x represents the x-value of midpoint.k represents the rate of change or growth rate.Based on the information provided above, the population of squirrels can be modeled by the following logistic growth function;
[tex]P(t) = \frac{1800}{1\;+\;8e^{-0.3t}}[/tex]
Part a.
By comparison, the maximum value or supremum population of the squirrels is 1800 squirrels.
Part b.
When t = 0, the initial number of squirrels that were introduced to this island can be calculated as follows;
[tex]P(t) = \frac{1800}{1\;+\;8e^{-0.3t}}\\\\P(0) = \frac{1800}{1\;+\;8e^{-0.3(0)}}[/tex]
P(0) = 1800/9
P(0) = 200 squirrels.
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If the HCF of two numbers is 36 and their LCM is 1260 . If one number is 72 find the other one
Hence, The other Number is: B = 630
Step-by-step explanation: EUCLIDS ALGORITHMIf the HCF of two numbers is 36 and their LCM is 1260. If one number is 72 find the other one:
PRIME FACTORS of 1260 are:2, 2, 3, 3, 7
PRIME FACTORS of 72 are:2, 2, 2, 3, 3
Write the formula for HCF and LCM:HCF * LCM = a * b
HCF = 2 * 2 * 3 * 3
= 36
Substitute The Given Values:36 * 1260 = 72 * b
36 * 1260 = 72b
45360 = 72b
Divide Both Sides by 36:1260 = 2 * b
45360 / 72 = 72b/72
b = 630
Divide Both Sides by 2:B = 630
Draw the conclusion:Hence, The other Number is: B = 630
I hope this helps you!
Determine the perimeter of a field that has a length of 97 metres and a width of 69 metres
Answer:
Step-by-step explanation:
2(97+69)=332(m)
1. Consider a simple random sample of 25 newts. The mean tail length of our sample is 5 cm. If we know that 0.2 cm is the standard deviation of the tail lengths of all newts in the population, then what is a 90% confidence interval for the mean tail length of all newts in the population ?
The 90% confidence interval for the mean tail length of all newts in the population is approximately (4.9342 cm, 5.0658 cm).
How to find 90% confidence interval for the mean tail length of all newts in the populationTo calculate the 90% confidence interval for the mean tail length of all newts in the population, we can use the formula:
Confidence Interval = Sample Mean ± Margin of Error
Given:
- Sample size (n) = 25
- Sample Mean (xbar) = 5 cm
- Standard Deviation of the population (σ) = 0.2 cm
- Confidence level = 90% (which corresponds to a z-score of 1.645 for a two-tailed test at a 90% confidence level)
First, we need to calculate the margin of error:
Margin of Error = (Critical Value) * (Standard Deviation / √Sample Size)
In this case, the critical value for a 90% confidence level is 1.645. Let's substitute the values:
Margin of Error = 1.645 * (0.2 / √25)
Margin of Error = 1.645 * 0.04
Margin of Error ≈ 0.0658
Now, we can calculate the confidence interval:
Confidence Interval = Sample Mean ± Margin of Error
Confidence Interval = 5 ± 0.0658
Confidence Interval ≈ (4.9342, 5.0658)
Therefore, the 90% confidence interval for the mean tail length of all newts in the population is approximately (4.9342 cm, 5.0658 cm).
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Which of the following could be a real world description of 3x-15
Answer:
three times a number minus fifteen
or
fifteen is less than three times a number
Find the sum of the first 50 terms
t1=91 and t25=374
In an arithmetic sequence where t1=91 and t25=374, the sum of the first 50 terms is 18,425.
How to find sum of arithmetic sequenceFormula for the sum of an arithmetic sequence is given as
[tex]Sn = (n/2) x [2a1 + (n-1)d][/tex]
where
Sn is the sum of the first n terms,
a1 is the first term
d is the common difference and
n is the number of terms.
Given that t1 = 91 and t25 = 374.
To find d, we can use the formula for the nth term of an arithmetic sequence:
[tex]tn = a1 + (n-1)d[/tex]
Substitute n = 25, t25 = 374, and a1 = 91, we get:
374 = 91 + 24d
d = 11
Substitute d in the Sn formula
S₅₀ = (50/2) x [2(91) + (50-1)(11)]
S₅₀ = 25 x [182 + 49 x 11]
S₅₀= 25 x 737
S₅₀ = 18,425
Therefore, the sum of the first 50 terms is 18,425.
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Create a table of values for the function graphed below using the plotted points. Remember, table of values are written with the x
-values in order from least to greatest (read the graph from left to right).
there are 5 rows for both problems x,y and 45 points for helping me with this
The table of values of the graphs are
x -2 -1 0 1 2
y -8 -6 -4 -2 0
and
x -7 -2 2 3 4
y 1 -8 3 5 -5
Writing the table of values of the graphs.from the question, we have the following parameters that can be used in our computation:
The graph
A linear equation is represented as
y = mx + c
Where
c = y when x = 0
So, we have
y = mx - 4
Using the points, we have
2m - 4 = 0
This gives
2m = 4
So, we have
m = 2
This means that the equation is y = 2x - 4
So, we have the following table of values
x -2 -1 0 1 2
y -8 -6 -4 -2 0
For the second table, we have
x -7 -2 2 3 4
y 1 -8 3 5 -5
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what is 4.5x-100>125
Answer:
4,5x>225--> x>225:4,5
Step-by-step explanation:
The answer is:
x > 50Work/explanation:
To solve this inequality, begin by adding 100 on each side:
[tex]\sf{4.5x-100 > 125}[/tex]
[tex]\sf{4.5x > 125+100}[/tex]
[tex]\sf{4.5x > 225}[/tex]
Now, divide each side by 4.5.
[tex]\sf{x > 50}[/tex]
Hence, the answer is x > 50.how many time can 457 go into 600
Answer:
Once
Step-by-step explanation:
Simple, once. If you do 600-457, you get an answer of 143, which you cannot subtract another 457 because it will turn negative.
How to calculate your bi-weekly paycheck based on 20 hour weeks at a rate of $9.00 per hour. Also, You will need to deduct Federal Income Tax (11.9%) , State Income Tax (3.6%), F.I.C.A (7.65%), and professional dues. Lastly you will need to look determine whether or not you will be able to pay your monthly car insurance bill of $200.00?
To calculate your bi-weekly paycheck, follow these steps:
Step 1: Calculate the gross earnings:
Multiply the number of hours worked per week by the hourly rate.
20 hours/week * $9.00/hour = $180.00/week
Step 2: Calculate the total earnings for two weeks:
Multiply the weekly earnings by the number of weeks in a bi-weekly pay period.
$180.00/week * 2 weeks = $360.00
Step 3: Calculate the deductions:
Calculate each deduction separately and subtract them from the gross earnings.
Federal Income Tax: $360.00 * 11.9% = $42.84
State Income Tax: $360.00 * 3.6% = $12.96
F.I.C.A: $360.00 * 7.65% = $27.54
Professional Dues: Amount varies depending on the specific dues.
Total Deductions: $42.84 + $12.96 + $27.54 + Professional Dues
Step 4: Calculate the net earnings:
Subtract the total deductions from the gross earnings.
Net Earnings = Gross Earnings - Total Deductions
Once you have the net earnings, you can determine if it is sufficient to cover your monthly car insurance bill of $200. If your bi-weekly net earnings are greater than or equal to $200, you will be able to pay your car insurance bill.
It is important to note that these calculations are based on the information provided, and actual tax rates and deductions may vary depending on your specific circumstances and location.
Additionally, professional dues may differ depending on your profession. It is recommended to consult with a tax professional or payroll department for precise calculations.
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An environmental group is tracking a fast-growing algae's coverage on a nearby pond. When
the group first measured the algae, it covered 3 square meters of the pond. They expect the
area of the pond covered by algae will double each day.
Write an exponential equation in the form = a(b)^x that can model the area of the pond
covered by algae, y, in x days.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =
How much of the pond is expected to be covered by algae after 4 days?
Answer:
y = 3(2^x)48 m² after 4 daysStep-by-step explanation:
You want an exponential function of the form y = a(b^x) that models algae growth that initially covers 3 square meters of a pond and doubles in area each day.
Exponential functionThe function y = a(b^x) has an initial value of 'a', which the problem statement tells us is 3 (square meters). The value 'b' is the growth factor, which the problem statement tells us is 2 each day.
The desired exponential equation is ...
y = 3(2^x)
4 daysWhen x=4, the function evaluates to ...
y = 3(2^4) = 3(16) = 48 . . . . square meters
After 4 days, 48 square meters of the pond is expected to be covered by algae.
<95141404393>
Can I get a help with the second one please!
Answer:
897
Explanation:
Start with replacing all the [tex]t[/tex] with 2.
[tex](t^{2} + 6t+7)(3t^{2} +3)[/tex]
[tex](2^{2} + 6(2)+7)(((3)(2))^{2} +3)[/tex]
Deal with the exponent before multiplying and adding.
[tex](2^{2} + 6(2)+7)(((3)(2))^{2} +3)[/tex]
[tex](4 + 6(2)+7)(((3)(2))^{2} +3)[/tex]
[tex](4 + 12+7)(((3)(2))^{2} +3)[/tex]
[tex](23)(((3)(2))^{2} +3)[/tex]
Now I believe here is where you made your mistake, you should first multiply 3 and 2 instead of evaluating the exponent straight away, because [tex]3t[/tex] was squared together.
[tex](23)(((3)(2))^{2} +3)[/tex]
[tex](23)(6^{2} +3)[/tex]
[tex](23)(36 +3)[/tex]
Then after adding, just multiply to get your answer, 897.
[tex](23)(36 +3)[/tex]
[tex](23)(39) = 897[/tex]
If a varies as square root of y, how x is affected when y is increased by 44%
Answer: 16.7%
Step-by-step explanation:
x/(root y) =x
root y is increased by 44%
x/(44+root y)=16.7%
Solve 5 ≥ -5x > 25 and graph the solution set on a number line
I need help please.
Answer:
false
Step-by-step explanation:
Its All Real Numbers
Classical determination of the probability of an event. There are 8 red, 5 white and
6 black balls. One ball is randomly taken from the urn. What is the probability that it will be black?
The probability of drawing a black ball from the urn, with a total of 19 balls (8 red, 5 white, and 6 black), is approximately 0.3158 or 31.58%.
To determine the probability of drawing a black ball from the urn, we need to consider the total number of balls and the number of black balls.
In this case, the total number of balls in the urn is 8 + 5 + 6 = 19, as there are 8 red, 5 white, and 6 black balls.
The probability of drawing a black ball can be calculated by dividing the number of black balls by the total number of balls:
Probability = Number of black balls / Total number of balls = 6 / 19 ≈ 0.3158 (rounded to four decimal places)
Therefore, the probability of drawing a black ball from the urn is approximately 0.3158, or 31.58%.
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Consider the function h(x)=12x−3 with a restricted domain of {−2, 0, 2, 10} . What is the range of the function? Responses {−2, 0, 2, 10} {−2, 0, 2, 10} all real numbers all real numbers {−4, −3, −2, 2} {−4, −3, −2, 2} the set of integers the set of integers
The range of the function h(x) with the restricted domain of {-2, 0, 2, 10} is {-27, -3, 21, 117}. Therefore, the correct response is {−27, -3, 21, 117}.
To find the range of the function h(x) = 12x - 3 with the restricted domain of {-2, 0, 2, 10}, we need to evaluate the function for each value in the domain and determine the corresponding range values.
For x = -2:
h(-2) = 12(-2) - 3 = -24 - 3 = -27
For x = 0:
h(0) = 12(0) - 3 = 0 - 3 = -3
For x = 2:
h(2) = 12(2) - 3 = 24 - 3 = 21
For x = 10:
h(10) = 12(10) - 3 = 120 - 3 = 117
The range of the function h(x) with the restricted domain of {-2, 0, 2, 10} is {-27, -3, 21, 117}. Therefore, the correct response is {−27, -3, 21, 117}.
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Simplify one over four n-1/2 divided by n over five minus one over 20 n
The simplified expression is (400n)/(320n^3 - 52n - 40n^2 + 2).
First, let's focus on simplifying the numerator and denominator separately:
Numerator:
The numerator is 1 divided by (4n - 1/2). We can simplify this by finding a common denominator. The denominator of 1/2 is 2, so we rewrite the expression as:
1/(4n - 12) = 1/(4n - 2/4) = 1/(4n - 2/4) = 1/((16n - 2)/4) = 4/(16n - 2)
Denominator:
The denominator is (n/5 - 1/20n). To simplify this, we find a common denominator. The denominator of 1/20n is 20n, so we rewrite the expression as:
n/5 - 1/20n = (20n^2)/(5 * 20n) - 1/(20n) = (20n^2 - 1)/(100n)
Now, let's simplify the entire expression by dividing the numerator by the denominator:
(1/(4n - 1/2)) ÷ (n/5 - 1/20n) = (4/(16n - 2)) ÷ ((20n^2 - 1)/(100n))
To divide by a fraction, we multiply by its reciprocal:
(4/(16n - 2)) ÷ ((20n^2 - 1)/(100n)) = (4/(16n - 2)) * (100n/(20n^2 - 1))
Next, we can simplify the numerator and denominator separately:
Numerator:
4 * 100n = 400n
Denominator:
(16n - 2) * (20n^2 - 1) = 320n^3 - 52n - 40n^2 + 2
Finally, we substitute the simplified numerator and denominator back into the expression:
(4/(16n - 2)) * (100n/(20n^2 - 1)) = (400n)/(320n^3 - 52n - 40n^2 + 2)
Thus, the simplified expression is (400n)/(320n^3 - 52n - 40n^2 + 2).
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answer QUESTION DOWN BE;LOW IN MID EXPLANANTION TAHNKS
The solution to the composite functions from the graph are:
(f * g)(2) = 16
(f - g)(0) = -5
How to interpret the Function Graphs?Composite functions are defined as when the output of one function is used as the input of another. If we have a function f and another function g, then the function “ f of g of x”, is the composition of the two functions.
a) Using the concept of composite functions, we can say that:
(f * g)(x) = f(x) * g(x)
Thus:
(f * g)(2) = f(2) * g(2)
f(2) = 4
g(2) = 4
Thus:
(f * g)(2) = 4 * 4
(f * g)(2) = 16
b) Using the concept of composite functions, we can say that:
(f - g)(x) = f(x) - g(x)
Thus:
(f - g)(0) = f(0) - g(0)
f(0) = 1
g(0) = 6
Thus:
(f - g)(0) = 1 - 6
(f - g)(0) = -5
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