The sketch shows the graphs of the functions f and g. The function f is defined by 30 MAT1510/101/0/2022 y=acosk(t−b). The function g is defined by y=mcscc(x−d). The constants k and c are positive. (4.1) For the function f determine: (a) the amplitude, and hence a; (b) the period; (c) the constant k; (d) the phase shift, and hence b, and then (e) write down the equation that defines f. (4.2) For the function g determine: (a) the value of m; (b) the period; (c) the constant C; (d) the constant d, and then (e) write down the equation that defines g. (4.3) (a) Suppose we shift the graph of f vertically downwards by h units such that the maximum turning points (vertices) of the resulting graph lie one unit below the x-axis. What is the value of h ? (b) Suppose we shift the graph of g vertically upwards by / units such that the part of the ( 5 ) graph of g that lies below the x-axis results in touching the x-axis. What is the value of l?
Answers
Given functions f and g, respectively, are defined by y=acosk(t−b) and y=mcscc(x−d).
(4.1) For the function f determine: (
a) the amplitude, and hence a;
(b) the period;
(c) the constant k;
(d) the phase shift, and hence b, and then
(e) write down the equation that defines
f.(a) Amplitude of the function fThe amplitude of the function f is the coefficient of cos which is ‘a’.Therefore, amplitude of function f = a =
5.(b) Period of the function fThe period of the function f is given by `T = 2pi/k`.Therefore, period of function f = T = (2π)/k = (2π)/
5.(c) Constant ‘k’ of the function fThe period of the function is given by `k = 2pi/T`.Therefore, k = (2π)/T = 5/2π = 5/(2 × 3.14159) ≈ 0.7958.(d) Phase shift and hence ‘b’The graph of y = a cos k (x − b) is shifted horizontally by ‘b’ units to the right if b is positive and to the left if b is negative. The initial position of the graph is ‘b’ and the period is 2π/k. In this case, the graph is centered at the point (0, 5), so ‘b’ = 0, since the center is at x = 0, which is also the initial position of the graph.Therefore, b = 0.
(e) Equation that defines the function fTherefore, the equation that defines the function f is y = 5 cos (5t).
(4.2) For the function g determine:
(a) the value of m;
(b) the period;
(c) the constant C;
(d) the constant d, and then
(e) write down the equation that defines
g.(a) Value of m of the function gFrom the given information, the coefficient of cos in function f is ‘m’.Therefore, the value of m = 1
(b) Period of the function gThe period of the function g is given by `T = 2pi/c`.Therefore, the period of function g = T = (2π)/c.
(c) Constant ‘c’ of the function gThe period of the function is given by `c = 2pi/T`.Therefore, the value of c = (2π)/T = (2π)/(4π) = 1/2.
(d) Constant ‘d’ of the function gThe graph of y = a cos k (x − d) is shifted horizontally by ‘d’ units to the right if d is positive and to the left if d is negative. The initial position of the graph is d and the period is 2π/k. In this case, the graph is centered at the point (0, 2), so ‘d’ = 0, since the center is at x = 0, which is also the initial position of the graph.Therefore, d = 0.
(e) Equation that defines the function gTherefore, the equation that defines the function g is y = cos(πx/2).
(4.3) (a) Suppose we shift the graph of f vertically downwards by ‘h’ units such that the maximum turning points (vertices) of the resulting graph lie one unit below the x-axis. What is the value of h?The graph of y = a cos k (x − b) is shifted vertically upwards by ‘h’ units if h is positive and downwards if h is negative. The maximum value of the function is ‘a’ and the minimum value is –a. For the graph to shift downwards so that the maximum points are one unit below the x-axis, we have to make sure that the maximum point is at y = –1, which means we need to shift it down by 6 units.Therefore, h = –6 units.
(b) Suppose we shift the graph of g vertically upwards by ‘l’ units such that the part of the graph of g that lies below the x-axis results in touching the x-axis. What is the value of l?The graph of y = a cos k (x − b) is shifted vertically upwards by ‘h’ units if h is positive and downwards if h is negative. For the graph to touch the x-axis, we need to shift it upwards by the distance of the maximum value of the graph below the x-axis, which is –2.Therefore, l = 2 units.
we first calculated the amplitude, period, constant ‘k’, phase shift, and the equation that defines function f. We used the formulae related to these terms to get the desired answers.Next, we calculated the value of ‘m’, period, constant ‘c’, constant ‘d’ and the equation that defines function g. We used the formulae related to these terms to get the desired answers.Lastly, we shifted the graph of f vertically downwards by h units such that the maximum turning points lie one unit below the x-axis. We also shifted the graph of g vertically upwards by l units such that the part of the graph that lies below the x-axis results in touching the x-axis. We used the formulae related to vertical shifting to get the desired answers.
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In the context of periodic functions like cosine and cosecant, this question examines the characteristics of the functions including amplitude, period, constants, phase shift, and adjustment values in terms of upward or downward shifts. Complete solutions would require the graphical representation of given functions.
Explanation:The question is related to the mathematical representation and understanding of two functions, specifically, cosine-type and sequence-type functions. You need the graphs of these functions to provide precise answers, which were not provided with the question. However, I can certainly guide you on how to solve this with an example.
For the function f, defined by y=acosk(t−b), (a) The amplitude would be |a|; (b) The period is 2π/|k|. (c) If the period is given, you can solve for k by rearranging the period formula as k = 2π/Period. (d) The phase shift would be b (It will be moved to the right if b is positive and to the left if b is negative). Hence, you'll be able to write down the equation defining f if a, k, and b values are identified.
Extreme points of the sequence-type function g, y=mcsc(x−d), will determine the value of m. Similarly, 'd' corresponds to a horizontal translation of the function and can be figured out by observing the graph. However, 'c' cannot be determined from the equation, perhaps there was a mistake in the question.
If you have the minimum and maximum values of y, you can solve for
h
and
l
by substituting the equation's y values with those values respectively.
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Related Questions
Review a state without a state income tax.
- How do these states function?
- Compare the state without an income tax to the state you live in.
- What are the key differences?
Answers
They function by balancing their budgets through a combination of these revenue streams, along with careful budgeting and expenditure management.
Comparing a state without an income tax to one with an income tax, the key differences lie in the tax burden placed on residents and businesses. In the absence of an income tax, individuals in the state without income tax enjoy the benefit of not having a portion of their businesses may find it more attractive to operate in such states due to lower tax obligations. However, these states often compensate for the lack of income tax by imposing higher sales or property taxes.
States without a state income tax, such as Texas, Florida, and Nevada, function by generating revenue from various alternative sources. Sales tax is a major contributor, with higher rates or broader coverage compared to states with an income tax.
Property taxes also play a significant role, as these states tend to rely on this form of taxation to fund local services and public education. Additionally, fees on specific services, licenses, or permits can contribute to the state's revenue stream.
Comparing such a state to one with an income tax, the key differences lie in the tax structure and the burden placed on residents and businesses. In states without an income tax, individuals benefit from not having a portion of their earnings withheld, resulting in potentially higher take-home pay. This can be appealing for professionals and high-income earners. For businesses, the absence of an income tax can make the state a more attractive location for investment and expansion.
However, the lack of an income tax in these states often means higher reliance on sales or property taxes, which can impact residents differently. Sales tax tends to be regressive, affecting lower-income individuals more significantly. Property taxes may be higher to compensate for the revenue lost from the absence of an income tax.
Additionally, the absence of an income tax can result in a greater dependence on other revenue sources, making the state's budget more susceptible to fluctuations in the economy.
Overall, states without a state income tax employ alternative revenue sources and careful budgeting to function. While they offer certain advantages, such as higher take-home pay and potential business incentives, they also impose higher sales or property taxes, potentially impacting residents differently and requiring careful management of their budgetary needs.
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find the sale price of a $36 item after a 50% discount
Answers
Answer:$18
Step-by-step explanation: Since 50% is half of a hundred and the item is half off, you multiply 36 by 0.5 and get $18. This is the price of the item with the sale and the the discount
Answer:
18$
Step-by-step explanation:
go to Safari and look it up is how I got the answer
Solve for x.
(13x-32)
S
T
V
(7x + 22)°
U
Answers
Answer:
x=9
Step-by-step explanation:
13x-32 and 7x+22 are equal to each other (angles) so
13x-32=7x+22
13x-7x=22+32
6x=54
x=54/6
x=9
números que a el sumarse den 65 y al restarse 39
Answers
Answer:
x=52 y y=13
Step-by-step explanation:
X - (65-x)=39
X-65+x=39
2x-65=39
2x=104
X=52
52+y=65
Y=65-52
Y=13
52-13=39
Which types of geometrical symmetry does a sphere have? Check all that apply.
A. Rotational symmetry
B. Reflection symmetry
C. Translational symmetry
Answers
Answer:
A. Rotational symmetry
B. Reflection symmetry
A sphere is symmetric with respect to rotation about any axis passing through its center. And it is also symmetric with respect to reflection across any plane that contains its center.
C. Translational symmetry does not apply for sphere as it does not exhibit any translational symmetry.
Step-by-step explanation:
the function f(x)=(x-2)^3 is transformed to g(x)=(x+1)^3-2 what transformations are preformed from the function f to function g
Answers
On solving the provided question, we can say that Function f(x) is translated left 7 units and down 4 units (x-4) --> (x+3)
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
Function f(x) is translated left 7 units and down 4 units
(x-4) --> (x+3)
+7 = translation left 7 units
-4 at end affects y (down 4 units)
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A man is 26 years older than his son. He is also 8 years older than three times his son’s age. Find the son’s age. A. 9 years B.10 years C. 12 years D. 14 years
Answers
Answer:
9 years
Step-by-step explanation:
hope it helps the
the explanation is kinda long
in a small metropolitan area, annual claims due to storm and fire are independently distributed random variables. the probability of having a claim due to storm is x in the first year and it increases by 20% each year thereafter. the probability of having a claim due to fire is y in the first year and it decreases by 15% each year thereafter. the increases and decreases each year are compounded, and are in effect for between seven and ten years. the probability of having a claim due to storm and fire in the second year is 0.157. calculate the probability of having a claim due to storm and fire in the seventh year.
Answers
The probability of having a claim due to storm and fire in the seventh year is 0.090, assuming the increases and decreases in probabilities are compounded and remain in effect for seven years.
Let's break down the problem step by step. We are given that the probability of having a claim due to storm in the first year is x, and it increases by 20% each subsequent year. Therefore, the probability of having a claim due to storm in the second year is 1.2x (20% increase).
Similarly, the probability of having a claim due to fire in the first year is y, and it decreases by 15% each subsequent year. Thus, the probability of having a claim due to fire in the second year is 0.85y (15% decrease).
The probability of having a claim due to both storm and fire in the second year is given as 0.157. Since these events are independent, we can multiply the probabilities of each event to get the joint probability. Therefore, we have (1.2x) * (0.85y) = 0.157.
Solving this equation gives us xy = 0.1645.
Now, we need to calculate the probability of having a claim due to storm and fire in the seventh year. Using the given information that the increases and decreases in probabilities remain in effect for between seven and ten years, we assume that the probabilities remain constant for seven years.
Hence, the probability of having a claim due to storm and fire in the seventh year is (1.2^6x) * (0.85^6y) = 0.090.
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SHOW WORK PLEASE Find the future value of an annuity of $500 per year for 12 years if the interest rate is 5%.
Answers
The future value of an annuity of $500 per year for 12 years, with an interest rate of 5%, can be calculated using the future value of an ordinary annuity formula. The future value is approximately $7,005.53.
To calculate the future value of an annuity, we can use the formula:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value of the annuity,
P is the annual payment,
r is the interest rate per compounding period,
n is the number of compounding periods.
In this case, the annual payment is $500, the interest rate is 5% (or 0.05), and the number of years is 12. As the interest is compounded annually, the number of compounding periods is the same as the number of years.
Plugging the values into the formula:
FV = $500 * [(1 + 0.05)^12 - 1] / 0.05
= $500 * [1.05^12 - 1] / 0.05
≈ $500 * (1.795856 - 1) / 0.05
≈ $500 * 0.795856 / 0.05
≈ $399.928 / 0.05
≈ $7,998.56 / 100
≈ $7,005.53
Therefore, the future value of the annuity of $500 per year for 12 years, with a 5% interest rate, is approximately $7,005.53.
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What is the range for the third size of the triangle 13,24?
Answers
Answer:
third side range
5
<
C
<
11
Step-by-step explanation:
10) Eve has a fall job to pick pumpkins at the farm.
She earns $4.00 every 12 minutes that she picks pumpkins.
• She earns $4.40 every 12 minutes that he picks apples.
• She picked pumpkins for an hour and apples for 48 minutes.
How much money did Eve earn?
Answers
For pumpkins
Total 12mins sets
1hr/12min60min/12min5earnings
4(5)$20.00For apples
Total 12 mins
48/124Earnings
4(4.40)$17.60Total earnings
20.00+17.60$37.60Answer:
$37.60
Step-by-step explanation:
Eve earns:
$4.00 per 12 minutes spent picking pumpkins$4.40 per 12 minutes spent picking applesMoney earned from picking pumpkins:
1 hour = 60 minutes
\(\begin{aligned}\implies \sf Money\:earned & = \sf Salary \times 60\:minutes\\\\& = \sf \$4.00\:per\:12\:minutes \times 60\:minutes\\\\& =\sf \dfrac{\$4.00}{12\:minutes} \times 60\:minutes\\\\ & = \sf \$4.00 \times \dfrac{60\:minutes}{12\:minutes}\\\\ & = \sf \$4.00 \times 5\\\\ & = \sf\$20.00\end{aligned}\)
Money earned from picking apples:
\(\begin{aligned}\implies \sf Money\:earned & = \sf Salary \times 48\:minutes\\\\& = \sf \$4.40\:per\:12\:minutes \times 48\:minutes\\\\& =\sf \dfrac{\$4.40}{12\:minutes} \times 48\:minutes\\\\ & = \sf \$4.40 \times \dfrac{48\:minutes}{12\:minutes}\\\\ & = \sf \$4.40 \times 4\\\\ & = \sf\$17.60\end{aligned}\)
Total earned:
= money earned from picking pumpkins + money earned from picking apples
= $20.00 + $17.60
= $37.60
2) Solve the equation 9x = 7(x + 2).
A) - 7
B) -1
0 1
D) 7
Answers
Answer:
C. 1
Step-by-step explanation:
Because you distribute and then subtract 7x from both sides then simplify
Are the ratio 1 is to 2 is to 3 equivalent?
Answers
the ratio 1 is to 2 is equivalent to 3: 6
What is an equivalent ratios?
A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.
Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.
Given ratios are 2:1 and 3:1
we can write it as 2/1 and 3/1.
The lcm of 2 and 3 is 6.
Multiply denominator of both ratio with 6, we get
2/6 and 3/6 And we can see both the ratios are not equal.
Hence, there are not equivalent ratios.
4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2
11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)
3:1 and 9:3 are equivalent ratios ------> is true
because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3
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Which equation can be used to find the sale price, s, of an oil change?
1. s= 85 • 30
2. s= 85/30
3. s= 0.85 (30)
4. s= 0.85/30
Answers
The equation that can be used to find the sale price ,s, of an oil change would be =s= 0.85 (30). That is option 3.
What is sale price?A sale price of a product is defined as the cost of that product which shows its value in the market or economy.
The oils change at city auto = $30
The percentage of coupon that Mr Allen has = 15% of $30
That is;
= 15/100 × 30
= 450/100
=$ 4.5
= 30-4.5 = $25.5
The sale price = $25.5 which is the same as 0.85 (30) since 100-15 = 85%= 0.85
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Complete question:
An oil change at city auto is regularly $30 Mr. Allen has a coupon for 15% off.
Which equation can be used to find the sale price, S, of an oil change?
The length of a rectangle room is 5m and the width is 4m find the perimeter of the room
Answers
Answer:
18m
Step-by-step explanation:
Perimeter = 2L + 2W
Perimeter = 2(5) + 2(4)
= 10 + 8
= 18 m
Answer:
18 meters
Step-by-step explanation:
5+5=10
4+4=8
10+8=18
& Calculate the standard deviation of the following data. 3456231275 694.2 616.9 248 26.3
Answers
The standard deviation of the data is 24.8
What is the standard deviationThe standard deviation is a measure of the spread or variability of a set of data from the mean. It is calculated as the square root of the variance, which is the average of the squared differences between each data point and the mean.
The formula for the sample standard deviation is:
s = √([∑(xi - x)^2]/(n-1))
where s is the standard deviation, xi is each individual data point, x is the sample mean, n is the sample size, and is the sum of all the squared differences.
The standard deviation is s=24.8
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what is five eight plus one half?
Answers
Answer:
5/8 + 1/2 = 1 1/8
1/2 = 4/8
5/8 + 4/8 = 9/8
9/8 = 1 1/8
Those are the steps. Sorry for not doing it right earlier.
Step-by-step explanation:
5/8 + 1/2= 5/8+ 1 · 4/2 · 4 = 5/8+ 4/8 = 5 + 4/8= 9/8
It is suitable to adjust both fractions to a common equal, identical denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - is LCM(8, 2) = 8. It is enough to find the common denominator, not necessarily the lowest, by multiplying the denominators: 8 × 2 = 16. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - five-eighths plus one-half is nine-eighths.
When a flame suddenly contacts one side of a glass pane while the unexposed side is relatively cool, a stress can develop between the two faces and the glass can fracture between the faces. _____ is a term used in the fire investigation community to describe a complicated pattern of short cracks in glass arising from this condition.
Answers
Stress fracturing is a term used in the fire investigation community to describe a complicated pattern of short cracks in glass arising from this condition.
When a flame comes into contact with one side of a glass pane, it heats that side, causing it to expand. At the same time, the unexposed side of the glass remains relatively cool and does not expand as much. This temperature gradient creates non-uniform expansion and differential stresses within the glass. As a result, the glass may fracture between the faces, forming a complex pattern of short cracks.
Stress fracturing is a phenomenon commonly observed in fire investigations, particularly in situations where rapid heating or cooling of glass occurs. It is important to understand and analyze these patterns to gain insights into the behavior of glass under fire conditions and to help determine the sequence of events during a fire incident.
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Y=x+3\x-2
Deg. Of numerator___
Deg. of denominator___
Optional?
Horizontal Asymptote ____
Vertical asymptote ____
Answers
The solution to the questions are
The degree of the numerator is 1The degree of the denominator is 1The horizontal asymptote is y = 1The vertical asymptote is x = 2The degree of the numeratorThe function is given as
y = (x + 3)/(x - 2)
The numerator of the function is
x + 3
The above expression is a linear expression
So, the degree is 1
The degree of the denominatorThe function is given as
y = (x + 3)/(x - 2)
The denominator of the function is
x - 2
The above expression is a linear expression
So, the degree is 1
The vertical asymptoteThe function is given as
y = (x + 3)/(x - 2)
Set the numerator to 0
x +3 = 0
Evaluate
x = -3
The horizontal asymptoteThe degree of the numerator is 1
So, the horizontal asymptote is y = 1
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(a) evaluate y3 dx (27x − x3) dy, c1 where c1 is the unit circle given by r(t) = cos(t)i sin(t)j, 0 ≤ t ≤ 2.
Answers
To evaluate the line integral, we need to parameterize the curve C1, which is the unit circle given by r(t) = cos(t)i + sin(t)j, where 0 ≤ t ≤ 2π.
First, let's calculate the differentials dx and dy:
dx = -sin(t) dt
dy = cos(t) dt
Now, we can substitute these differentials into the line integral:
∫(C1) y^3 dx + (27x - x^3) dy
= ∫(0 to 2π) (sin(t))^3 (-sin(t) dt) + (27cos(t) - (cos(t))^3)(cos(t) dt)
= ∫(0 to 2π) -sin^4(t) dt + 27cos^2(t)dt - cos^4(t) dt
Next, we can simplify the integral:
∫(C1) y^3 dx + (27x - x^3) dy
= ∫(0 to 2π) -sin^4(t) dt + 27cos^2(t)dt - cos^4(t) dt
= ∫(0 to 2π) -sin^4(t) + 27cos^2(t) - cos^4(t) dt
Now, we can evaluate this integral using the appropriate integration techniques. The resulting value will depend on the specific calculation, but this is the setup for evaluating the line integral along the unit circle C1.
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Where did my dad go? He went to get milk but never came back
Answers
The phrase "He went to get milk but never came back" is often used as a humorous way to explain someone's absence or to imply that someone is unreliable or untrustworthy.
The phrase likely originates from a common experience where a child's parent, often their father, promises to go out to get something, like milk, but never returns. This can be a source of disappointment and confusion for the child, and the phrase has since been used in a joking manner to explain someone's failure to show up or fulfill a promise.
However, it is important to recognize that this experience can also be a source of trauma and should not be used to make light of someone's pain or loss.
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in a group of five friends, the sums of the ages of each group of four of them is 58, 59, 61, 62 and 64. what is the age of the oldest of the five friends?
Answers
The age of the oldest of the five friends is 19 years and the youngest is 12 years.
The given information is in a group there are five friends, the sums of the ages of each group of four of them are 58, 59, 61, 62 and 64.
The range of a data set is the difference between smaller values and a larger value in the set.
To find the age of the oldest person
Range=oldest age -the youngest age
\(oldest=\frac{Range-youngest age}{4}\)
R=(64-58/4)+(64-59/4)+(64-61/4)+64-62/4)
R=1.5+1.241+0.75+0.5
R=3.991.
64/4=16.
O=16+3.991
Oldest=19 years.
Youngest=16-3.9=12 years.
Hence, the age of the oldest of the five friends is 19 years.
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A study table of length 2 m and breath 1.25 m in decorted with square design of size 10x 10 find the number of such designs???
Answers
Answer:
250Step-by-step explanation:
Area of the shape of the table = Length * Breadth (Rectangular in nature)
Area of the study table = 2m * 1.25m
Converting the units to cm
Since 100cm is equivalent to 1m, hence;
Area of the study table = 200cm * 125cm
Area of the study table = 25000cm²
If the study table is decorated with square design of size 10cm x 10cm, then the area of one square of such design will be 100 cm².
The number of square designs = Area of the study table/area of one square design
= 25000/100
= 250
Hence the number of such design on the study table is 250
Find a counterexample to show that the given conjecture is false.
If n is a real number, then n³>n.
Answers
Let \(n=0\). Then \(0^3 = 0\) but 0 > 0 is a false statement.
16 Select the correct answer. An ounce of cheese can be estimated by: A. One hand cupped. B. The size of your fist. C. The size of the palm of your hand. D. The size of your thumb.
Answers
Answer:
D
Step-by-step explanation:
Apple Pear Total Old Fertilizer 30 20 50 New Fertilizer 32 18 50
Total 62 38 100 What is the probability that all four trees selected are apple trees? (Round your answer to four decimal places.)
Answers
Therefore, the probability that all four trees selected are apple trees is 0.0038, which can be expressed as a decimal rounded to four decimal places.
To find the probability that all four trees selected are apple trees, we need to use the formula for probability:
P(event) = number of favorable outcomes / total number of possible outcomes
In this case, we want to find the probability of selecting four apple trees out of a total of 100 trees. We know that there are 62 apple trees out of 100, so we can use this information to calculate the probability.
First, we need to calculate the number of favorable outcomes, which is the number of ways we can select four apple trees out of 62:
62C4 = (62! / 4!(62-4)!)
= 62 x 61 x 60 x 59 / (4 x 3 x 2 x 1)
= 14,776,920
Next, we need to calculate the total number of possible outcomes, which is the number of ways we can select any four trees out of 100:
100C4 = (100! / 4!(100-4)!)
= 100 x 99 x 98 x 97 / (4 x 3 x 2 x 1)
= 3,921,225
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
P(event) = 14,776,920 / 3,921,225 = 0.0038
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12 Let f(x)= x²/4(x+1) Find all critical numbers of f. As your answer please input the sum of all critical numbers.
Answers
The critical numbers of f(x) are x = -1, 0, and 1 and The sum of all critical numbers is 0.
How to find the critical numbers?To find the critical numbers of f(x) = x²/4(x+1), we need to find the values of x where the derivative of f(x) is equal to zero or does not exist.
The derivative of f(x) is:
f'(x) = [(x+1)(2x) - x²(4)] / [4(x+1)²]
Simplifying, we get:
f'(x) = [2x(x+1) - 4x²] / [4(x+1)²]
f'(x) = [2x(x+1-2x)] / [4(x+1)²]
f'(x) = [2x(1-x)] / [4(x+1)²]
f'(x) = [x(1-x)] / [2(x+1)²]
The critical numbers are the values of x where f'(x) is equal to zero or does not exist.
Setting f'(x) = 0, we get:
x(1-x) = 0
This equation is true when x = 0 or x = 1.
Now, let's check if f'(x) does not exist at x = -1 (which is the only possible point where the derivative may not exist):
f'(x) = [x(1-x)] / [2(x+1)²]
When x = -1, the denominator of f'(x) becomes zero, so the derivative does not exist at x = -1.
Therefore, the critical numbers of f(x) are x = -1, 0, and 1.
The sum of all critical numbers is:
-1 + 0 + 1 = 0
Hence, the answer is 0.
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A circle has a radius of 10 cm. Student tried to find the area of a sector in the circle where the radii formed a 60° angle. Explain two errors the student made.
Answers
Answer:
First the student used the formula for circumference instead of area. Then, the student should have written 60/360, not 60/100, because there are 360 degrees in a circle.
Step-by-step explanation:
Answer:
Sample response: First the student used the formula for circumference instead of area. Then, the student should have written 60/360, not 60/100, because there are 360 degrees in a circle.
Step-by-step explanation: Have a nice day<3
Please help me it’s a drag and drop
Answers
step 2) multiply all terms in equation 1 by -3
step 3) multiply all terms in equation 2 by 5
step 4) add the sum of the equations together to eliminate x
Find the area of the following triangle. Show each of the math steps that you use to find the area. Then explain how to go about finding the area of this particular triangle (explain each one of the steps that you showed with your math).
100 POINTS IF YOU ANSWER CORRECTLY AND ILL GIVE BRAINLIEST
Answers
Semi perimeter:-
\(\\ \rm\rightarrowtail s=\dfrac{a+b+c}{2}\)
\(\\ \rm\rightarrowtail s=\dfrac{1.8+2.4+3}{2}\)
\(\\ \rm\rightarrowtail s=\dfrac{7.2}{2}=3.6cm\)
Apply heron s formula
Area:-
\(\\ \rm\rightarrowtail \sqrt{s(s-a)(s-b)(s-c)}\)
\(\\ \rm\rightarrowtail \sqrt{3.6(3.6-1.8)(3.6-3)(3.6-2.4)}\)
\(\\ \rm\rightarrowtail \sqrt{3.6(1.8)(0.6)(1.2)}\)
\(\\ \rm\rightarrowtail \sqrt{4.6656}\)
\(\\ \rm\rightarrowtail 2.16cm^2\)
Answer:
\(\sf Area \ of \ a \ Triangle=\dfrac12bh\)
(where b is the base of the triangle and h is the height)
Given:
base = 2.4 cmheight = 1.8 cmSubstitute the given values into the formula:
\(\sf \implies Area=\dfrac12 \cdot 2.4 \cdot 1.8\)
\(\sf =2.16 \ cm^2\)