Answers
The units of R'(7) are gallons/hour/hour, or equivalent gallons/hour is 6 = 0.15 gallons per hour and 2 R(t) dt using the average Riemann sum with four equal length partitions is 383.04 gallons.
How to calculate the total estimate?(a) R'(7), you can use the mean rate of change formula.
R'(7) ≈ [R(10) - R(4)] / [10 - 4]
With the data from the table it looks like this:
R(10) = 11.3 gallons per hour
R(4) = 10.4 gallons per hour
For this,
R'(7) ≈ (11.3 - 10.4) / 6 = 0.15 gallons per hour
The units of R'(7) are gallons/hour/hour, or equivalent gallons/hour squared.
(b) To approximate 2 R(t) dt using the average Riemann sum with four equal length partitions, we can use
Δt = (24 - 0) / 4 = 6
2 R(t) dt ≈ 2Δt [R(1.5Δt) + R(4.5Δt) + R(7.5Δt) + R(10.5Δt)]
With the data from the table it looks like this:
R(1.5Δt) = R(4.5) = 10.4 gallons/hour
R(4.5Δt) = R(10.5) = 11.3 gallons per hour
R(7.5Δt) = R(16.5) = 10.2 gallons/hour
R(10.5Δt) = R(22.5) = 9.6 gallons per hour
For this,
2 R(t) dt ≈ 2(6) [10.4 + 11.3 + 10.2 + 9.6] = 383.04 gallons
The approximate unit of integral is the gallon.
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Related Questions
Need help for the question attached in the picture
Answers
The probabilities are given as follows:
a) At most 3.8 percent: 0.0455 = 4.55%.
b) At most 8 percent: 0.9382 = 93.82%.
c) Between 3.8 and 8 percent: 0.8927 = 89.27%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 6, \sigma = 1.3[/tex]
The probability of at most 3.8% is the p-value of Z when X = 3.8, hence:
Z = (3.8 - 6)/1.3
Z = -1.69
Z = -1.69 has a p-value of 0.0455.
The probability of at most 8% is the p-value of Z when X = 8, hence:
Z = (8 - 6)/1.3
Z = 1.54
Z = 1.54 has a p-value of 0.9382.
Hence the probability of a value between these two values is given as follows:
0.9382 - 0.0455 = 0.8927.
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Where do I graph the solutions on the number line for both?
Answers
Answer:
Step-by-step explanation:
#1 - (−3,9)
#2 - (−∞,−7) and also( −3,∞)
1/27
2/346
3/34
4/0244
5/24679
6/02
Min=
Q1=
Med =
Q3 =
Max =
Answers
Answer: Min=0.02
Q1=0.037037
Med = 0.037037
Q3 = 0.346790
Max = 346
Step-by-step explanation:
To convert the numbers to decimal, we can divide the number before the slash by the number after the slash. So for example, 1/27 becomes 0.037037.
After converting the numbers to decimal and arranging them in ascending order, we get:
0.02, 0.037037, 0.03448, 0.040816, 0.346790, 346
To find the Q1, median (Med), Q3, and other measures of central tendency and spread for this list of numbers, we first need to order the numbers in ascending order:
0.02, 0.03448, 0.037037, 0.040816, 0.346790, 346
Q1 is the value that separates the lowest 25% of the data from the rest of the data. To find Q1, we need to find the median of the lower half of the data set. Since there are 6 numbers in the set and Q1 is the middle value of the lower half, Q1 would be the 3rd number in the ordered set, which is 0.03448.
Med is the middle value of the data set. Since there are 6 numbers in the set, the median would be the 3rd and 4th numbers, which are 0.03448 and 0.037037.
Q3 is the value that separates the highest 25% of the data from the rest of the data. To find Q3, we need to find the median of the upper half of the data set. Since there are 6 numbers in the set and Q3 is the middle value of the upper half, Q3 would be the 5th number in the ordered set, which is 0.346790.
Min is the smallest value of the dataset, which is 0.02
Max is the largest value of the dataset, which is 346
How can consumers use their spending power to prevent cruelty to animals?
OA. Buy fair-trade coffee
OB. Eat less meat
OC. Purchase local vegetables
OD. Reduce plastic use
SUBMIT
Answers
Answer:
OC. Eat less meat
Step-by-step explanation:
Not really sure how this is math, but meat comes from butchered animals. Buying less meat means fewer animals are killed.
 Look at the steps for solving the equation and choose a true statement.
3x - 9x + 1 = 2(-3x + 1) - 1
-6x + 1 = -6x + 2 - 1
-6x + 1 = -6x + 1
O a
Ob
0 c
0 d
0 e
There is no way to know if there is a solution to this equation.
There are no solutions to the equation.
There are infinitely many solutions to the equation.
The only solution to the equation is -6.
The only solution to the equation is 1.
Answers
A finite arrangement of symbols that adheres to context-specific standards and is well-formed is referred to as a mathematical expression.
What is meant by equation?A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms. In mathematics, an equation is an equality statement that includes one or more variables or unknowable quantities.
When two expressions in a variable (or variables) have the same value, the condition is said to be an equation. The equation's solution, or root, is the value of the variable for which the equation holds true. Even if the RHS and LHS are switched, an equation still holds true.
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. A sentence in math is called an equation.
Let the equations be
3x - 9x + 1 = 2(-3x + 1) - 1
-6x + 1 = -6x + 2 - 1
-6x + 1 = -6x + 1
Therefore, the correct answer is option There are infinitely many solutions to the equation.
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Which graph represents y= ^3 square root x + 2?
Answers
Answer:
cubic
Step-by-step explanation:
slope =-2/5; y-intercept =0
Write the equation of the line in slope-intercept form.
Answers
Answer:
Step-by-step explanation:
Standard slope intercept equation is
[tex]y=mx+b[/tex]
where m is the slope and b is the intercept.
substitute the values given
[tex]y=-\frac{2}{5} x+0[/tex]
simplify
[tex]y=-\frac{2}{5} x[/tex]
Find the linear function, f (x), passing through the points (-1,-5) and (-8,-5)
Answers
we could go ahead and check its slope and so forth, OR we can just take a peek that the y-coordinates are the same -5, hmmmm well, hell that's just a horizontal line, Check the picture below.
Explain what an extraneous solution is and how you would check for one?
Answers
To check for extraneous solutions, one can substitute the potential solution back into the original equation and see if it satisfies the equation. If the substitute yields a true statement, then the solution is valid. If it yields a false statement, then the solution is extraneous.
For example, consider the equation √(x + 4) = 3. Solving for x, one might obtain x = 5. However, this solution is extraneous because x + 4 must be non-negative, and 5 + 4 = 9 is positive. Substituting x = 5 back into the original equation, we get √(5 + 4) = √9, which is not equal to 3. Thus, x = 5 is an extraneous solution.
Answer:
Step-by-step explanation: An Extraneous solutions are values that we get when solving equations that aren't really solutions to the equation. And you only need to check for one if you made the equation quadratic by multiplying by a variable.
PLS HELP DUE RIGHT NOW ASAP!!!!!!
Answers
Answer:-4,-3
Step-by-step explanation:
-4 is lower then -3 and the arrow faces the x meaning it is lower than -3.
I need help which one????
Answers
Answer:
>
Step-by-step explanation:
3^3*3^-2 ? 3^2*3^-3
27*1/9 ? 9*1/27
3 > 1/3
Answer:
3^3 (times)3^-2 < 3^2 (times) 3^-3
Step-by-step explanation:
3^3 (times)3^-2
27 (times) -9
=-243
3^2 (times) 3^-3
9(times)27
=243
Find the volume of the solid obtained by rotating the region bounded by the graphs y=2, the x- axis, x=10 about x=10. (Give an exact answer. Use symbolic notation and fractions where needed.)
Answers
The volume of the solid is -30π cubic units
How did we get the value?The volume of the solid obtained by rotating the region about the x-axis is given by the formula:
V = π * ∫[a,b] (R^2 - (x-c)^2) dx
Where:
a = lower limit of x-coordinate of the region
b = upper limit of x-coordinate of the region
c = axis of rotation
R = distance from the x-axis to the boundary of the region
For the given region, a = 0, b = 10, c = 10, and R = 2.
So the volume of the solid is:
V = π * ∫[0,10] (2^2 - (x-10)^2) dx
= π * ∫[0,10] (4 - (x-10)^2) dx
= π * [2x - (x-10)^2/2 + C] evaluated at x=10 and x=0
= π * [20 - 100/2 + C - 0]
= π * (20 - 50 + C)
= π * (-30 + C)
= π * (-30) = -30π cubic units.
Therefore, the volume of the solid is -30π cubic units
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plaz answer this i beg you
Answers
Answer:
I'm not exactly sure, but I'm positive that it's 60 degrees.
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
90 = 30 + (4x)
60 = 4x
x = 60/4 = 15
30° and (4x)° must add up to 90° because they are complementary angles
After a big snowfall, you take your favorite rocket‑powered sled out to a wide field. The field is 205 m across, and you know that your sled accelerates at a rate of 3.95 m/s2 when the rocket is on. How fast will the sled be moving when it is halfway across the field?
Answers
Answer:
Below
Step-by-step explanation:
Find time to get to 102.5 m (Half of the field)
d = 1/2 a t^2
102.5 = 1/2 * 3.95 t^2 shows t = 7.2 s
then v = at
= 3.95 * 7.2 = 28.5 m/s
An investor manages to earn the equivalent of 50/10 of his initial investment in the first year. During the second year it loses 30/10 part of it. However, for the third year the market fluctuations favor him and he returns to earn 200/10 parts of his initial investment. At the end of the year, how many parts of the initial investment have you managed to capture?
Answers
Answer: This investor has managed to earn 220/10 shares of his initial invention.
Step by step explanation:
Data for the fraction:
An investor manages to win = 50/10During the second year you lose = 30/10In the third year he wins again = 200/10In this problem we must apply the addition and subtraction of Fractions in order to obtain an answer about the parts of the initial investment that have been achieved. For this we pose the problem:
[tex]\bf \: \cfrac{50}{10} - \cfrac{30}{10} + \cfrac{200}{10} = \boxed{ \bf\frac{220}{10} }[/tex]
Rpt: This investor has managed to earn 220/10 shares of his initial invention.
At the fair, Lisa stumbled upon a game called Cool Down. In this game, there is a container with
8 cups of hot water (at a temperature of 50ºC). The object is to determine how many cups of
cold water (at a temperature of 20ºC) to add to the container to reduce the temperature to 40ºC.
a. Find an equation expressing the temperature (in ºC) of the water in the container as a
function of the volume (cups) of cold water added.
Equation: ________________________
b. Explain how you obtained the equation in part (a) above.
c. Use your equation to determine the amount of cold water that must be added to reduce the
temperature to 40ºC.
Answers
Answer:
t = (400 + 20c)/(8+c)weighted sum of temperatures4 cupsStep-by-step explanation:
You want an equation for the temperature of 8 cups of hot (50 °C) water combined with c cups of cold (20 °C) water, along with an explanation of it. Then you want the number of cups required to reduce the temperature to 40 °C.
(a) EquationAssuming constant heat capacity and volume as a function of temperature, the temperature of the mix will be the weighted average of the temperatures of the contributors. That is c cups of water at 20 °C combined with 8 cups of water at 50 °C will have a temperature (t) of ...
t = (20c +8(50))/(c+8)
t = (20c +400)/(c +8)
(b) ExplanationThe thermal energy contained in the water is assumed to be jointly proportional to its volume and its temperature. The combined thermal energy of the mixture will be the total of that of its contributors.
That is, the temperature of the mix is the weighted sum of the temperatures of the contributors, the weights being their respective volumes.
(c) 40°The value of c for a temperature of 40 °C is ...
40 = (20c +400)/(c+8)
2(c +8) = c +20) . . . . divide by 20, multiply by (c+8)
2c +16 = c +20 . . . . eliminate parentheses
c = 4 . . . . . . . . . . . . subtract (c+16)
4 cups of cold water must be added to reduce the temperature ot 40 °C.
(a) t = (400 + 20c)/(8+c)
(b)weighted sum of temperatures
(c) 4 cups
What is an equation?An equation is a statement that asserts the equality of two expressions, the expressions are written one on each side of an '=' equal to sign.
Let t be the temperature of water.
Let c be the number of cold cup of water at 20°C
(a)c cups of water at 20 °C combined with 8 cups of water at 50 °C will have a temperature (t) of
[tex]t= \frac{20c+8*50}{c+8}[/tex] --------(1)
(b)The temperature of the mix is the weighted sum of the temperatures of the contributors, the weights being their respective volumes.
(c)The value of c for a temperature of 40 °C is
40 = (20c +400)/(c+8)
2(c +8) = c +20) . . . . divided by 20, multiply by (c+8)
2c +16 = c +20 . . . . eliminate parentheses
⇒ c = 4
Hence, the required equation is [tex]t= \frac{20c+8*50}{c+8}[/tex] and for part (c) 4 cups.
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It is estimated that each guest at a party will eat 2/3 pounds of chocolates. How many guests can be served with 6 pounds of chocolate?
Answers
Answer: 9 guest can be served.
Step-by-step explanation:
2/3 pounds of chocolate for each guest
6 pounds of chocolate can be served to
So let's do 6/ (2/3)
=6* 3/2
that will equal 9 guests
florida wants to estimate the mean mercury level in the fish from a particular lake. they take a random sample of 56 fish from the lake and record the mercury level of each fish. Fill in the following in the context of this problem: Sample: A sample of 56 fish from a randomly selected Florida lake Variable: Mean mercury level in 56 fish from a randomly selected Florida lake Type of variable: qualitative quantitative continuous quantitative-discrete Mean mercury level in fish of all Florida lakes Parameter of interest: Random sample of 56 fish from the lake Statistic that will be used:
Answers
Sample: A sample of 56 fish from a randomly selected Florida lake.
Variable: Mean mercury level in 56 fish from a randomly selected Florida lake
Type of variable: quantitative-discrete
Mean mercury level in fish of all Florida lakes: Parameter of interest
Statistic that will be used: Mean (arithmetic average) of the mercury levels in the sample of 56 fish from the lake.
The Statistic of Florida sampleThe sample of 56 fish from a randomly selected Florida lake represents a portion of the population of fish in all Florida lakes. The mean mercury level in these 56 fish represents a statistic, which is an estimate of the population parameter, the mean mercury level in fish of all Florida lakes.
The mean (arithmetic average) is used as the statistic because it summarizes the data by finding the central tendency of the mercury levels in the sample of 56 fish. It is a suitable measure to describe the typical mercury level in the fish from the lake because it takes into account all the observations in the sample.
Since mercury levels are measured in numerical values, the variable "mean mercury level" is quantitative. Since it is a continuous measurement, it is also a continuous quantitative variable.
In summary, the sample and the mean mercury level in the sample of 56 fish are used to make inferences about the population and its parameter, the mean mercury level in fish of all Florida lakes. The mean is used as the statistic to summarize the data and describe the central tendency of the mercury levels in the sample.
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An entry-level salary for teachers in Boston was $13,579 in 1981. According to the NEA, the average entry-level salary for Massachusetts had risen to $45,498 in 2017. What should the entry-level salary have been in 2017 if the 1981 figure was adjusted for inflation?
Answers
The entry-level salary for teachers in Boston in 2017 should have been $42,086 if adjusted for inflation using the Consumer Price Index.
What should the entry-level salary have been in 2017 if the 1981 figure was adjusted for inflation?This question is asking for a calculation of the real value of the 1981 entry-level salary for Boston teachers in 2017 dollars. This calculation requires the use of a “price index” to account for inflation and is known as “inflation adjustment” or “inflationary adjustment”.Inflation adjustment involves determining the purchasing power of a given amount of money in one year compared to another year. To calculate the amount of money needed to purchase the same amount of goods and services in 2017 as was purchased with $13,579 in 1981, the 1981 amount is multiplied by the ratio of the price index of 2017 to the price index of 1981.Using the Consumer Price Index (CPI), the price index of 2017 was 259.5 and the price index of 1981 was 82.4. Therefore, the inflation-adjusted entry-level salary for Boston teachers in 2017 would be $13,579 x (259.5/82.4) = $42,633. This is slightly lower than the actual average salary of $45,498 reported by the NEA.To learn more about inflationary adjustment refer to:
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Write this number in scientific notation.
.00000092
[?] ×
]
Answers
The number in scientific notation is 9.2 × 10^-7.
How to convert the numberFrom the question, we have the following parameters that can be used in our computation:
Number = .00000092
The number of points from the initial position to a point between 9 and 2 is -7
This means that the coefficient is 9.2 and the power of ten is -7
So, we have
9.2 × 10^-7.
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Answer:
10^(-7)
Step-by-step explanation:
put first non-zero number, then decimal, then rest of numbers as so
9.2
multiply by +/- depending on where decimal is
9.2*10^(-7)
so 10^(-7)
Make x the subject of the formula:
4y = 4x - 6z/6
Answers
Making x the subject of the formula in this equation 4y = 4x - 6z/6 gives x = (24y + 6z)/4.
How to make x the subject of the formula?In this exercise, you are required to make "x" the subject of the formula in the given mathematical expression by using the following steps.
By multiplying both sides of the mathematical expression by 6, we have the following:
4y = (4x - 6z)/6
6 × 4y = (4x - 6z)/6 × 6
24y = 4x - 6z
By adding "6z" to both sides of the mathematical expression, we have the following:
24y + 6z = 4x - 6z + 6z
24y + 6z = 4x
By dividing both sides of the mathematical expression by 4, we have the following:
x = (24y + 6z)/4
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23. The escape velocity from the surface of the Moon is 2.4 × 10³ ms ¹.
(a)
An object is projected from the surface of the Moon with a speed
of 2.0 10³ ms ¹.
Calculate the maximum height reached above the Moon's surface.
Answers
The object will reach a maximum height of approximately -89,898.36 meters, or 89.9 kilometers, above the Moon's surface before it falls back down.
What do you mean by escape velocity?Escape velocity is the minimum speed an object must have in order to escape the gravitational pull of a celestial body, such as a planet or moon, and travel into space. It is calculated based on the mass and radius of the celestial body and the distance of the object from its surface. The greater the mass and radius of the celestial body, the greater the escape velocity.
The formula for escape velocity is given by v_escape = √(2GM/R), where G is the gravitational constant, M is the mass of the object, and R is the radius of the object.
In this case, v_escape = 2.4 × 10³ m/s and v_projected = 2.0 × 10³ m/s.
The maximum height can be calculated using the following formula:
h = (v_projected^2 - v_escape^2) / (2g), where g is the acceleration due to gravity.
Since the escape velocity is greater than the projected velocity, the object will not escape the Moon's surface and will eventually fall back down. The maximum height it reaches is given by:
h = (2.0 × 10³ m/s)^2 - (2.4 × 10³ m/s)^2 / (2 * 9.8 m/s^2) = (4.0 × 10^6 - 5.76 × 10^6) m / 19.6 = -1.76 × 10^6 m / 19.6 = -89,898.36 m.
The object will reach a maximum height of approximately -89,898.36 meters, or 89.9 kilometers, above the Moon's surface before it falls back down.
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Mr Saver invests $X at t = 0 in an account that pays a nominal rate of R convertible quarterly. The interest he earns during t = 0.5 to t = 1.5 is 1.0816 times the interest he earns during t = 0 to t = 1. Find the exact value of R.
Answers
Mr. Saver's nominal interest rate is 8%.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that the interest he earns during t = 0.5 to t = 1.5 is 1.0816 times the interest he earns during t = 0 to t = 1. We can use this information to set up an equation as follows:
P(1+R/4)²=1.0816×P(1+R/4)
We can simplify this equation by canceling out the P and the (1+R/4) on the right side:
(1+R/4)=1.0816
We can then solve for R:
R/4=√1.0816-1
R=0.08 is the exact value of R.
Now multiply with 100
0.08×100=8%
Hence, Mr. Saver's nominal interest rate is 8%.
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You are given the equation 13 = 2x + 5 with no solution set.
Part A: Determine two values that make the equation false.
Part B: Explain why your integer solutions are false. Show all work.
Answers
Answer:
Part A: x = 1, 2
Part B: 13 != 7, 13 != 9
Step-by-step explanation:
We pick x values that when plugged into the equation, creates a false statement.
x = 1
13 = 2(1) + 5
13 = 2 + 5
13 = 7
As you can see 13 does not equal 7
x = 2
13 = 2(2) + 5
13 = 4 + 5
13 = 9
As you can see 13 does not equal 9
Steve wants to take all of his 145 employees on a fishing trip. If each fishing boat holds 13 people, how many boats does Steve need to rent?
Answers
Answer:
Approximately 11 boats.
Step-by-step explanation:
To get this answer, we simply need to divide 145, which is the number of his employees, but 13, the amount of people each boat holds. You get the answer 11.1538462.
Answer:
12 Boats
Step-by-step explanation:
Since it given that;
Steve wants to take all of his 145 employees on a fishing trip.Each fishing boat holds 13 peopleAll we have to do is divide the total number of people by how much a fishing boats can hold.
Which is;
145/13
= 11.1538461538
So, we need 12 boats due to 145/13 = 11.15... because you can't cut a person in half. Thus, we need an extra boat to hold the extras.
RevyBreeze
Which equation is an equation of a circle with a radius of 4 and its center is at (3, -2)?
(x - 3)2 + (y + 2)2 = 4
(X + 3)2 + (y - 2)2 = 16
(x 3)2 + (y - 2)2 = 4
(x - 3)2 + (y + 2)2 = 16
Answers
The answer to the query is that option D) is correct. A circle with the radius if 4 and a point at (3, -2) has the following equation [tex](x - 3)^2 + (y + 2)^2 = 16[/tex]
What does a radius look like?Your youngster will get familiar with the term "radius" as they study circles. It speaks about the separation between any point on a circle's perimeter and its center (circumference). It crosses the center, by one of the circle's sides to the other, and is half the size of diameter.
The radius of a circle is the distance between the center to any location on the edge. The diameter and radius are inversely proportional, or 2r=d2 r=d. the section of a line that connects two locations on a circle chord.
The equation of a circle is
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Where (h, k) is the circle's center and r is its radius.
The center is at (3, -2)
[tex](x-3)^2 + (y-(-2))^2 = 4^2[/tex]
[tex](x - 3)^2 + (y + 2)^2 = 16[/tex]
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The Complete Question :
Which equation is an equation of a circle with a radius of 4 and its center is at (3, -2)?
A. [tex](x - 3)^2 + (y + 2)^2 = 4[/tex]
B. [tex](x+ 3)^2 + (y - 2)^2 = 16[/tex]
C. [tex](x-3)^2 + (y - 2)^2 = 4[/tex]
D. [tex](x - 3)^2 + (y + 2)^2 = 16[/tex]
Solve the following system of equation. Be sure to show each of your work steps.
Answers
The roots of given equation x^2 - 2x +3 are 1+4i , 1-4i
What is Quadratic Equation ?
Quadratic equation can be defined as the equation in which it is in the form of ax^2 + bx + c = 0
where c is a constant.
Given equations,
x^2 - 2x +3 = 0
so, we know that
the roots of a quadratic equation
= (- b + (√ b^2 - 4ac )) / 2a , (- b - (√ b^2 - 4ac )) / 2a
so,
here a = 1 b = -2 c = 3
by substituting the given values,
we get,
= 2+ (√ 4 - 4*1*3 ) / 2 , 2- (√ 4 - 4*1*3 ) / 2
= 2+ (√-8) / 2 , 2- (√-8) / 2
= 2+8i / 2 , 2-8i / 2
= 1 + 4i , 1- 4i
Hence, The roots of given equation x^2 - 2x +3 are 1+4i , 1-4i
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WHAT IS THE LIMIT OF A CONSTANT?
Answers
The limit of a constant function is equal to the constant. The limit of a linear function is equal to the number x is approaching.
What are limits?A limit is defined as a value that a function approaches the output for the given input values.
Limit of a constant :-
We know that the limit of a function exists, only and only if the left-hand limit (LHL) and the right-hand limit (RHL) exists and are equal to one another. And, the value of the limit of that function is equal to the common value, LHL = RHL = f(x).
We need to find the limit of a constant. So, let us assume a function, f(x) = c, where c is a constant. We are assuming that we need to find the limit of this constant function at x = a, i.e. we need to find the value of
[tex]\lim_{x \to \ a} f(x)[/tex]
Plot the graph, y = c, (attached)
Let us calculate the left hand limit first.
LHL = [tex]\lim_{x \to \ -a} f(x)[/tex]
We can see that at x = -a, the value of f(x) is c.
LHL = c.....(i)
Similarly,
For right-hand limit,
We have at x = +a, the value of f(x) is c.
RHL = c....(ii)
Also, Also, the value of our function at a, i.e., f(a) = c
Thus, by equation (i), (ii) and (iii), we can say that
[tex]\lim_{x \to \ a} f(x) = c[/tex]
Hence, we can now say that the limit of any constant is the same constant.
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6x+2y= −4 simplified all fractions
Answers
According to the problem the simplified form of the equation is x = -1/2 and y = -3.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions by showing that they have the same value. Equations can be used to describe a variety of physical, chemical and biological processes. They are often used to solve problems in a variety of fields, including engineering, finance and physics.
6x + 2y = -4
This equation can be simplified by combining all like terms on one side of the equation and all constants on the other. In this case, we can combine the 6x and 2y terms to get 8x = -4. We can then divide both sides of the equation by 8 to get x = -1/2. Substituting this value into the original equation, we get 2y = -6. We can then divide both sides by 2 to get y = -3. Therefore, the simplified form of the equation is x = -1/2 and y = -3.
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Which of the following statements are true? I. The sampling distribution of ¯x¯ has standard deviation σ /√n even if the population is not normally distributed. II. The sampling distribution of ¯x¯ is normal if the population has a normal distribution. III. When n is large, the sampling distribution of ¯x¯ is approximately normal even if the the population is not normally distributed. I, II, and III
Answers
All three statements are true. The sampling distribution of the sample mean has standard deviation σ/√n even if the population is not normally distributed.
The sampling distribution of the sample mean is normal if the population is normally distributed. Lastly, when the sample size is large, the sampling distribution of the sample mean is approximately normal even if the population is not normally distributed .
The sampling distribution of the sample mean is a probability distribution of the means of all possible samples of a given size from a given population. It is used to describe the behavior of the sample mean in relation to the population mean. The sampling distribution of the sample mean has a mean of μ (the population mean) and a standard deviation of σ/√n, where σ is the population standard deviation and n is the sample size
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