Answer:
38
Step-by-step explanation:
perimeter = 2(l+b)
Where l is the length of the rectangle
b is the breadth of the rectangle
P = 2(15+4)
P = 2 × 19
P = 38
Expand log4 (4 / [7x^2 ] )
The expanded form of log4(4 / [7x^2]) is 1 - log4(7) - 2 * log4(x)
To expand the expression log4(4 / [7x^2]), we can use logarithmic properties to simplify it. First, we can rewrite the numerator as a power of the base 4:
log4(4) - log4(7x^2)
Since log4(4) is equal to 1 (since 4 raised to the power of 1 equals 4), the expression becomes:
1 - log4(7x^2)
Next, we can apply the logarithmic property log_a(b^c) = c * log_a(b) to simplify the logarithm of a product:
1 - (log4(7) + log4(x^2))
Using another logarithmic property log_a(b^c) = c * log_a(b), we can simplify the expression further:
1 - (log4(7) + 2 * log4(x))
Therefore, the expanded form of log4(4 / [7x^2]) is:
1 - log4(7) - 2 * log4(x)
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Let: R = It will rain this evening, B = The barometric pressure is dropping, T = The temperature is below 50 degrees F, S = It will snow this evening.
Choose the formula that represents the following probability: "The probability that it will not snow this evening conditional on the barometric pressure dropping."
Group of answer choices
P(¬S | B)
P( ¬ S & B)
P(B |¬ S)
P(S & ¬ B)
The Probability that it will not snow this evening conditional on the barometric pressure dropping, probability is P(¬S | B).
The components of the formula:
P(¬S | B): This formula represents the probability of "not snowing (¬S)" given that "the barometric pressure is dropping (B)." In other words, it calculates the likelihood of it not snowing this evening when we know that the barometric pressure is dropping.
P(¬S & B): This formula represents the probability of "not snowing (¬S)" and "the barometric pressure is dropping (B)" occurring simultaneously. It calculates the joint probability of these two events happening together.
P(B | ¬S): This formula represents the probability of "the barometric pressure is dropping (B)" given that "it is not snowing (¬S)." It calculates the likelihood of the barometric pressure dropping when we know that it is not snowing.
P(S & ¬B): This formula represents the probability of "snowing (S)" and "the barometric pressure is not dropping (¬B)" occurring simultaneously. It calculates the joint probability of these two events happening together.The probability that it will not snow this evening conditional on the barometric pressure dropping," the appropriate formula to represent this probability is P(¬S | B). It specifically considers the probability of it not snowing given that the barometric pressure is dropping.
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Determine whether there is a minimum or maximum value to the quadratic function. Find the value and the axis of symmetry. If your answer is not an integer please round to the nearest hundredth. f(x)=2x^2-10x+4
The Quadratic function has a minimum value of -8.5 at the axis of symmetry x = 2.5.
There is a minimum or maximum value to the quadratic function f(x) = 2x^2 - 10x + 4, we can look at the coefficient of the x^2 term, which is positive (2 in this case). A positive coefficient for the x^2 term indicates that the quadratic function opens upwards and has a minimum value.
To find the value of the minimum point and the axis of symmetry, we can use the formula:
Axis of Symmetry = -b / (2a)
Value at the Minimum Point = f(Axis of Symmetry)
In our quadratic function, a = 2 and b = -10. Plugging these values into the formulas, we get:
Axis of Symmetry = -(-10) / (2 * 2) = 10 / 4 = 2.5
To find the value at the minimum point, we substitute the axis of symmetry (x = 2.5) into the function:
f(2.5) = 2(2.5)^2 - 10(2.5) + 4
= 2(6.25) - 25 + 4
= 12.5 - 25 + 4
= -8.5
Therefore, the minimum value of the quadratic function f(x) = 2x^2 - 10x + 4 is -8.5. The axis of symmetry is x = 2.5.
the quadratic function has a minimum value of -8.5 at the axis of symmetry x = 2.5.
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Carly and Annie are making string bracelets. Carly's design needs 3.5 meters of string, Annie's needs 2.7 meters of string. How much string do they need together?
Answer:
6.2 meters
Step-by-step explanation:
Carly needs 3.5 meters of string.
Annie needs 2.7 meters of string.
Adding these two values together:
3.5 meters + 2.7 meters = 6.2 meters
15% OFF!
Gabe wants to buy a dog collar. The sale price is $3.91. What was the original price?
$
the original price was really "x", which oddly enough is the 100%, but today the collar is on sale at 15% off, that means the sale price is 100% - 15% = 85% of the original price, and we happen to know that's $3.91, so
[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} x & 100\\ 3.91& 85 \end{array} \implies \cfrac{x}{3.91}~~=~~\cfrac{100}{85} \\\\\\ \cfrac{x}{3.91} ~~=~~ \cfrac{20}{17}\implies 17x=78.2\implies x=\cfrac{78.2}{17}\implies x=4.6[/tex]
An sister is 6 years older than brother ,and their total age is 22 years what is the age of sister and brother
Answer:
Brother= 8 years old
sister= 14 years old
Step-by-step explanation:
S : B
x+6 : x
x+6+x=22
2x+6=22
2x=16
x=8
brother is 8 years old
x+6= sisters age
8+6=14 years old is the sister
You are a doctorate student in biology doing a dissertation about the insect Desmolithica Geogebra. This insect causes serious damage to plums, apricot and flowering cherries. The female insect lays as many as thirty to sixty eggs on the leaves of the host trees. The time when the insect larva hatches from its egg up to the moment in finding its host tree is called the searching period. Once the insect finds the plum, it squirms into the fruit and begin to ruin it. After approximately four weeks, the insect will crawl back under the bark of the plum tree or directly to the soil where it forms a cocoon. The observation regarding the behavior of the insect demonstrate the length of the searching period S(t), and the percentage of the larvae that survive this period N(t), depend on the air temperature denoted by t. The data from the observations suggest that if the air temperature is measure in degree celsius, where 20
S(t) = (-0.03t^2+1.6t-13.65)^(-1) days and N(t)= -0.85t^2+45.4t-547
S(25) in days N(25) in % T when ds/dt=0
0.1316 56.75 26.67
1. Explain comprehensively the models for S(t) and N(t). Elaborate mathematically these formulae in predicting for the length of searching period and percentage of larvae surviving the searching period when t=25.
2. Find the rate of change of the searching period with respect to temperature t. When does this rate equal to zero? What will happen when t=0?
3. Find the rate of change of the percentage of larvae surviving the searching period with respect to length of the searching period. What information does this provide?
The model for S(t) is given as:
S(t) = (-0.03t^2 + 1.6t - 13.65)^(-1)
This model predicts the searching period length in days. It is an inverse function of the quadratic equation (-0.03t^2 + 1.6t - 13.65). As the temperature increases, the searching period decreases, indicating that the larvae are more efficient at finding the host tree at higher temperatures.
To calculate S(25), we substitute t = 25 into the equation:
S(25) = (-0.03(25)^2 + 1.6(25) - 13.65)^(-1)
= (-0.03(625) + 40 - 13.65)^(-1)
= (-18.75 + 26.35)^(-1)
= 7.6^(-1)
= 0.1316 days
Therefore, when the air temperature is 25 degrees Celsius, the predicted length of the searching period is approximately 0.1316 days.
The model for N(t) is given as:
N(t) = -0.85t^2 + 45.4t - 547
This model predicts the percentage of larvae surviving the searching period. It is a quadratic function (-0.85t^2 + 45.4t - 547). As the temperature increases, the percentage of larvae surviving the searching period may increase or decrease depending on the behavior of the quadratic function.
To calculate N(25), we substitute t = 25 into the equation:
N(25) = -0.85(25)^2 + 45.4(25) - 547
= -0.85(625) + 1135 - 547
= -531.25 + 1135 - 547
= 56.75%
Therefore, when the air temperature is 25 degrees Celsius, the predicted percentage of larvae surviving the searching period is 56.75%.
2. The rate of change of the searching period S(t) with respect to temperature t can be found by taking the derivative of the function S(t) with respect to t, which is denoted as ds/dt.
ds/dt = d/dt [(-0.03t^2 + 1.6t - 13.65)^(-1)]
To find when ds/dt = 0, we set the derivative equal to zero and solve for t:
ds/dt = 0
However, without the specific equation of S(t) in its original form, it is not possible to provide an exact value of t when ds/dt equals zero.
Regarding the behavior when t = 0, we cannot determine this without further information or the specific form of the function S(t). The behavior at t = 0 depends on the equation itself and how it is defined.
3. The rate of change of the percentage of larvae surviving the searching period N(t) with respect to the length of the searching period S(t) can be found by taking the derivative of the function N(t) with respect to S(t), denoted as dN/dS.
dN/dS = d/dS [(-0.85t^2 + 45.4t - 547)]
This rate of change provides information about how the percentage of larvae surviving the searching period changes with respect to the length of the searching period. It gives insight into the sensitivity
Illustration 4 Zeko Enterprise earned an annual profit of Nu. 1 million during the income yea 2018. The enterprise declared à bonus of Nu. 250,000 in the same year, out e -hich Nu. 100,000 were paid to Dawa, the Manager, and the balance to the oth- mployees. Dawa is the son of Zeko, owner of the enterprise. How would you tre s case as an Assessor?
As an assessor, it is essential to objectively evaluate the Bonus payment, taking into account industry standards, the relationship between Dawa and Zeko, and compliance with tax laws.
As an assessor, it is important to approach this case with objectivity and fairness. The key factors to consider are the nature of the bonus payment, the relationship between Dawa and Zeko, and any relevant tax laws or regulations.
Firstly, it is necessary to determine if the bonus payment was reasonable and consistent with industry standards. Assessors often compare the bonus amounts given by similar enterprises in the same industry to establish a benchmark. If the bonus amount falls within a reasonable range, it is more likely to be considered as a legitimate business expense.
Secondly, the relationship between Dawa and Zeko should be evaluated. In this case, Dawa is identified as the son of Zeko, which raises questions about potential conflicts of interest or nepotism. Assessors must carefully examine whether the bonus payment to Dawa was based on his merit and contribution to the enterprise or if it was primarily due to their familial relationship. If there is evidence of favoritism or the bonus is disproportionate to Dawa's role and responsibilities, it could be deemed as personal income rather than a legitimate business expense.
Lastly, assessors need to adhere to relevant tax laws and regulations. The bonus payment should be assessed in accordance with the tax code of the jurisdiction where Zeko Enterprise operates. This involves ensuring that the appropriate taxes are paid on the bonus amount and that it is properly reported in the company's financial records.
Overall, as an assessor, it is essential to objectively evaluate the bonus payment, taking into account industry standards, the relationship between Dawa and Zeko, and compliance with tax laws. The focus should be on determining the legitimacy of the bonus payment as a business expense and ensuring that proper taxes are paid.
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heLPPPPPPPPPPPPPPPPPPPP
Answer:
y=2/3x
Step-by-step explanation:
Since they cross at (3,2) the formula would be y=2/3x
Solve by substitution
y=x-1
2x-3y=-1
Answer:
(x, y) = (4, 3)
Step-by-step explanation:
y = x - 1 (Equation 1)
2x - 3y = -1 (Equation 2)
We can use substitution method:
Substitute the expression for y from Equation 1 into Equation 2 and solve for x:
2x - 3(x - 1) = -1
2x - 3x + 3 = -1
-x = -4
x = 4
Now that we have found the value of x, we can substitute it back into Equation 1 to find y:
y = x - 1
y = 4 - 1
y = 3
Therefore, the solution to the system of equations is (x, y) = (4, 3).
the nth term of 1,7,13,19
The nth term of the sequence 1, 7, 13, 19 is given by the formula: nth term = 1 + (n - 1) * 6 = 19
To discover the nth time period of the sequence 1, 7, 13, 19, we want to become aware of the sample or rule that governs the sequence.
In this case, we look at that every time period will increase by way of 6 in contrast to the preceding term.
We can categorical this sample in the following equation:
nth time period = 1 + (n - 1) * 6
Let's follow this equation to discover the nth term:
For n = 1:
nth time period = 1 + (1 - 1) * 6
= 1 + zero * 6
= 1
For n = 2:
nth time period = 1 + (2 - 1) * 6
= 1 + 1 * 6
= 1 + 6
= 7
For n = 3:
nth time period = 1 + (3 - 1) * 6
= 1 + two * 6
= 1 + 12
= 13
For n = 4:
nth time period = 1 + (4 - 1) * 6
= 1 + 3 * 6
= 1 + 18
= 19
As we can see, the equation efficiently generates the given phrases of the sequence.
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Brenda deposit ₱15,000.00 in a savings account which pays 4% compounded monthly. Find the accumulated interest after 10years. with solution sana
Answer:
Step-by-step explanation: Compound interest formula = P*(1+r/n)^n*t, where:
- P = principal amount (initial investment amount).
- r = nominal annual interest rate.
- n = number of times interest is principally entered per year.
- t = number of years borrowed money.
Applying the above compound interest formula, after 10 years, you will get the amount:
= 15,000 * (1+4%/12)^(12*10) = 22363.49024
If Brenda deposits `₱15,000.00` in a savings account that pays `4%` interest compounded monthly, the accumulated interest after `10` years can be calculated using the formula for compound interest: `A = P(1 + r/n)^(nt)`, where `A` is the future value of the investment, `P` is the initial principal amount, `r` is the annual interest rate (as a decimal), `n` is the number of times the interest is compounded per year, and `t` is the number of years the money is invested for.
In this case, `P = 15000`, `r = 0.04`, `n = 12` (since the interest is compounded monthly), and `t = 10`. Plugging these values into the formula, we get:
```
A = 15000(1 + 0.04/12)^(12 * 10)
A ≈ 22265.07
```
So after `10` years, the accumulated interest would be `A - P = 22265.07 - 15000 = ₱7265.07`.
pls ansdwer
woth 30 poitnsss
Answer:
The Correct answer is 1.53m=153cm
Step-by-step explanation:
1m=100cm
1.53m=x
[tex]x = 100 \times 1.53m[/tex]
x=153m
HELP Before training for the obstacle course, Helena bought a new pair of athletic shoes. She placed the shoes on the floor next to each other and noticed that the right shoe looked just like a reflection of the left shoe. If she had accidentally purchased two left shoes, how would this comparison change?
The difference in design and fit between left and right shoes is essential for providing comfort, support, and functionality during physical activities such as training for an obstacle course.
If Helena accidentally purchased two left shoes instead of a left and a right shoe, the comparison between the shoes would change. Instead of the right shoe looking like a reflection of the left shoe, both shoes would look the same, with neither shoe resembling a reflection of the other.
When placing the shoes on the floor next to each other, Helena would notice that both shoes have the same design, structure, and orientation. The left shoe and the right shoe would be identical, and there would be no visual distinction between them.
When Helena initially placed the shoes on the floor and observed that the right shoe looked like a reflection of the left shoe, it implied that there was a clear distinction between the left and right shoes. The right shoe would have mirrored the design and features of the left shoe, creating a symmetrical appearance.
However, if Helena had purchased two left shoes, there would be no mirror image effect or reflection between the shoes. Both shoes would appear identical and would lack the characteristic differences between left and right shoes. This means that both shoes would have the same design, features, and overall appearance.
As a result, Helena would notice that there is no shoe that corresponds to the opposite foot. When trying to wear the shoes, she would find that both shoes fit on the same foot, causing discomfort and impracticality.
In this scenario, Helena would likely realize her mistake and need to exchange or return the shoes for a proper pair with a left shoe and a right shoe. The difference in design and fit between left and right shoes is essential for providing comfort, support, and functionality during physical activities such as training for an obstacle course.
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The bucket is 5 litre and a jug is 500ml.How many jugs of water will be needed to fill the bucket??
Answer:
As 5 litres is 5000ml, it would take 10 jugs of 500ml as long as there is no spillage
Step-by-step explanation:
Hope this helps, a brainliest would be much appreciated:)
Please solve this question
The correct order from least to greatest is log₂ 26, log₂ 33, log 26, eln 4, the correct option is D.
We are given that;
The logs log, 26, log, 33 and log3 26
Now,
We can simplify these expressions using the following identities:
eln x = x
log a a = 1
log a (b × c) = log a b + log a c
log a (b / c) = log a b - log a c
Using these identities and the properties of logarithms listed above, we can compare the given expressions as follows:
A. eln 4 = 4; log 26 < log 33; so we have:
4 < log 26 < log 33
B. eln 4 = 4; so we have:
log 33 < 4 < log 26 < log 26
C. eln 4 = 4; so we have
log₂ 26 < log 26 < log 33 < 4
D. eln 4 = 4; so we have:
log₂ 26 < log₂ 33 < log 26 < 4
Therefore, by logarithm the answer will be log₂ 26, log₂ 33, log 26, eln 4.
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Solve 3x²2 - 2x + 4 = 0.
A)
B)
C)
D)
1± √√√11
3
1± √√√13
3
1 ±i√√11
3
1+1√√13
3
Answer:
To solve the equation 3x²2 - 2x + 4 = 0, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b² - 4ac)) / (2a)
In this case, a = 3, b = -2, and c = 4. Substituting these values into the quadratic formula, we have:
x = (-(-2) ± √((-2)² - 4(3)(4))) / (2(3))
x = (2 ± √(4 - 48)) / 6
x = (2 ± √(-44)) / 6
Since the discriminant (-44) is negative, the solutions involve imaginary numbers. Therefore, the answer is:
1 ± i√11
3
Hence, the correct answer is 1 ± i√√11/3.
HELP!!
Solve 3(x–9)2 = 21
Answer:
x = [tex]\frac{25}{2}[/tex]
Step-by-step explanation:
3(x–9)2 = 21
6(x - 9) = 21
6x - 54 = 21
6x = 75
x = [tex]\frac{75}{6}[/tex] = [tex]\frac{25}{2}[/tex]
So, the answer is x = [tex]\frac{25}{2}[/tex]
A washing machine was purchased on sale at 256. Each year the value is 1.4 of value the previous year Enter the function, f(t) that describes the value of the washing machine as a function of time in years, t, after the initial purchase .
The value of the washing machine will grow exponentially, increasing by a factor of 1.4 each year.
Based on the given information, we can determine the function that describes the value of the washing machine as a function of time.
Let's assume the initial value of the washing machine is 256. Each subsequent year, the value is 1.4 times the value of the previous year. Therefore, the function can be expressed as:
f(t) = 256 * (1.4)^t,
where t represents the time in years after the initial purchase.
This function takes the initial value of 256 and multiplies it by 1.4 raised to the power of t. As t increases, the value of the washing machine will grow exponentially, increasing by a factor of 1.4 each year.
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Find the y-intercept of the line y = 15/2x - 13/10.
4) Write your answer as an integer or as a simplified proper or improper fraction, not as an
ordered pair.
Answer:
The y-intercept of a function is the point where the function crosses the y-axis, which is when x = 0.
Therefore, to find the y-intercept of the given line, we must set x equal to zero. This will result in the value of y when x = 0, which is our y-intercept.
[tex]y = \frac{15}{2}x - \frac{13}{10} \\[/tex]
[tex]y = \frac{15}{2}(0) - \frac{13}{10} \\[/tex]
[tex]y = -\frac{13}{10} \\[/tex]
The y-intercept is at [tex](0, -\frac{13}{10} )[/tex].
Answer: [tex]-\frac{13}{10}[/tex]
-------------------------------------------------------------------------------------------------------------
We could also identify that this is a linear function that is in the form
y = mx+b
where m is the value of the slope, and b is the value of the y-intercept.
In this case, [tex]\frac{15}{2}[/tex] is the slope and [tex]- \frac{13}{10} \\[/tex] is the y-intercept.
The Americans with disabilities
The Americans with Disabilities Act (ADA) is a landmark civil rights law enacted in the United States in 1990.
What is the Act about?Its purpose is to protect individuals with disabilities from discrimination and ensure equal opportunities in various aspects of life, including employment, public accommodations, transportation, and telecommunications.
The ADA defines a disability as a physical or mental impairment that substantially limits one or more major life activities, such as walking, seeing, hearing, speaking, or learning. The law prohibits discrimination against individuals with disabilities in both the private and public sectors.
Under the ADA, employers with 15 or more employees are required to provide reasonable accommodations to qualified individuals with disabilities, as long as it does not impose an undue hardship on the employer.
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Explain the Americans with Disabilities Act
Find the volume of each figure. Round to the nearest hundredth. PLEASE HELP SOON :(
Answer:
20579.53 m³
Step-by-step explanation:
You want the volume of a sphere 34 m in diameter.
VolumeThe formula for the volume of a sphere is ...
V = (4/3)πr³ . . . . . where r is half the diameter
In terms of diameter, this is ...
V = (4/3)π(d/2)³ = (π/6)d³
V = (π/6)(34 m)³ ≈ 20,579.53 m³
The volume of the sphere is about 20,579.53 cubic meters.
<95141404393>
hello
the answer to the question is:
[tex]p = 2\pi \: r \\ 36 = 2 \times 3.14 \times r \\ r = 5.7 \: m \\ \\ v = \frac{4}{3} \pi {r}^{3} \\ v = \frac{4}{3} \times 3.14 \times {5.7}^{3} \\ = 775.3 \: {m}^{3} [/tex]
If cos A=5/4 and A is in quadrant 1 what is the value of sin A• tan A
Find the area of a triangle if the base (b) is 9 inches and the height (h) is = 12 in.
(a) 90 in.²
(c) 10.5 in.²
(b) 54 in.²
(d) 162 in.²
The correct answer is (b) 54 in.², which Matches just performed.
The area of a triangle, we use the formula:
Area = (1/2) * base * height
Given that the base (b) is 9 inches and the height (h) is 12 inches, we can substitute these values into the formula:
Area = (1/2) * 9 * 12
Simplifying the equation:
Area = (1/2) * 108
Area = 54
Therefore, the area of the triangle with a base of 9 inches and a height of 12 inches is 54 square inches.
Among the options given:
(a) 90 in.²
(b) 54 in.²
(c) 10.5 in.²
(d) 162 in.²
The correct answer is (b) 54 in.², which matches the calculation we just performed.
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Find y in the diagram below.
Answer:
[tex]\mathrm{5m}[/tex]
Step-by-step explanation:
[tex]\mathrm{sin30^o=\frac{p}{h}}\\\\\mathrm{or,\ \frac{1}{2}=\frac{Y}{10}}\\\\\mathrm{or,\ Y=5m}[/tex]
3
Felipe gave 4 people candy. He split pounds among them.
4
What is the unit rate in pounds per person?
Write your answer in simplest form.
pounds per person
믕ㅁ음
C
The unit rate in pounds per person is:
3/16 pounds per person
How to find the unit rate in pounds per person?A unit rate is defined as the rate for one of something. For example, if 10 oranges cost $50, the unit rate will be $50/10 = $5 i.e. $5 for one orange.
In this case, Felipe gave 4 people candy. He 3/4 split pounds among them.
We have:
Quantity of candy = 3/4 pounds
Number of people = 4
We will divide the quantity of candy by number of people to get the unit rate (quantity of candy per person). That is:
unit rate = (3/4) ÷ 4
unit rate = (3/4) × (1/4)
unit rate = 3/16 pounds per person
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8. Consider the D.E. yy'= -x +
1/2
a. Find the implicit general solution of this
equation. What is the condition that c
should satisfied? (c is the constant that
appears in the solution).
b. (T) is the family of curves of the
general solution in an orthonormal
system. What is the nature of this graph?
(such curves are called integral curves of
the D.E.)
c. Find the graph (T) that passes through
the origin O(0, 0).
The implicit general solution is 0.5y² = -0.5x² + 0.5x + C, here C should pass through the origin of the circle. The family of curves (T) represents the integral curve. The graph (T) is represented below.
a. To find the implicit general solution of the given differential equation, we can integrate both sides with respect to x. Let's start by rewriting the equation:
yy' = -x + 1/2
Integrating both sides:
∫ yy' dx = ∫ (-x + 1/2) dx
Using integration by parts on the left side, let u = y and dv = y' dx:
[tex]\int u dv = uv - \int v du\\\\y\int dy = \int (-x + 1/2) dx\\\\1/2 y^2 = -1/2 x^2 + 1/2 x + C\\\\0.5y^2 = -0.5x^2+0.5x+C[/tex]
Where C is the constant of integration. This is the implicit general solution of the given differential equation.
b. The family of curves (T) that represents the general solution in an orthonormal system is known as the integral curves of the differential equation.
c. To find the graph (T) that passes through the origin O(0, 0), we substitute the point (x, y) = (0, 0) into the implicit general solution and solve for C:
[tex]1/2(0)^2 = -1/2(0)^2 + 1/2(0) + C\\\\0 = 0 + 0 + C\\\\\C = 0[/tex]
So the graph (T) that passes through the origin is given by:
[tex]1/2 y^2 = -1/2 x^2 + 1/2 x[/tex]
This equation represents the specific curve that satisfies both the differential equation and the condition of passing through the origin.
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An electrician purchased 15 dimmer switches $20 each and received a $8 credit for each of the two duplexes receptacles she retry. Write out a mathematical statement that the amount of money she spent then calculate this total
Step-by-step explanation:
Let's break down the information provided and write out the mathematical statement step by step.
The electrician purchased 15 dimmer switches, each costing $20. This can be represented as:
Cost of dimmer switches = 15 * $20
The electrician also received a credit of $8 for each of the two duplex receptacles she returned. The total credit received can be calculated as:
Total credit = 2 * $8
To find the total amount of money she spent, we need to subtract the total credit from the cost of the dimmer switches:
Total amount spent = (Cost of dimmer switches) - (Total credit)
Now, let's calculate the total amount of money she spent:
Cost of dimmer switches = 15 * $20 = $300
Total credit = 2 * $8 = $16
Total amount spent = $300 - $16 = $284
Therefore, the electrician spent a total of $284.
What are the period and amplitude of the function?
period: π; amplitude: 1.5
period: π; amplitude: 3
period: π2; amplitude: 1.5
period: π2; amplitude: 3
The period is π/2 and the amplitude is 3.
Given data ,
Let the function be represented as the graph of f ( x )
where the function is plotted
Now , The period of a function is the length of one complete cycle of the function. It represents the distance along the x-axis over which the function repeats its pattern
And , The amplitude of a function is the maximum distance between the function's graph and its average value where it is a positive value
So , period: π/2; amplitude: 3
Hence , the period and amplitude are solved
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3. When paying off credit card debt, it is best to pay off _____ credit cards
When paying off Credit card debt, it is best to pay off high-interest credit cards
When paying off credit card debt, it is best to pay off high-interest credit cards first. High-interest credit cards typically have higher annual percentage rates (APRs) compared to other credit cards. By prioritizing the repayment of high-interest credit cards, you can minimize the amount of interest you accrue and potentially save money in the long run.
Focusing on paying off high-interest credit cards first allows you to reduce your overall debt faster. By eliminating high-interest debt, you can free up more funds to tackle other debts or allocate towards savings and investments.
It's important to note that each individual's financial situation is unique, and the best approach to paying off credit card debt may vary. Some individuals may choose to prioritize paying off credit cards with the smallest balances first (the snowball method), while others may opt for the highest interest rate (the avalanche method). It's essential to assess your financial goals and capabilities to determine the most effective strategy for your situation.
Consulting with a financial advisor or credit counseling service can provide personalized guidance and help you develop a debt repayment plan that aligns with your financial goals and circumstances.
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