Find the square roots of -32+32 i √3 in the form a + bi. Check by graphing the roots in the complex plane. The square roots of - 32+32 i √3 are 0. (Simplify your answer, including any radicals. Us
Answers
To check by graphing the roots in the complex plane, we can plot the points (4√3, 8) and (-4√3, 8) on the plane. The square roots of -32 + 32i√3 are 0, which is not equal to the two roots we found, so our calculations are correct.
To find the square roots of -32 + 32i√3 in the form a + bi, we can use the following formula for square roots of complex numbers in rectangular form:
$$z = \square roots {a + bi} = \pm\square roots {\fraction{\square roots {a^2 + b^2} + a}{2}} \pm i\square roots {\pm\square roots {a^2 + b^2} - a}{2}$$
We need to express -32 + 32i√3 in the form a + bi, so we can identify a and b in the formula above. We can see that
$a = -32$ and $b = 32\square roots {3}$, so:$$\begin{aligned}z &= \pm\square roots {\fraction{\square roots {(-32)^2 + (32\square roots {3})^2} - 32}{2}} \pm i\square roots {\pm\square roots {(-32)^2 + (32\square roots{3})^2} + 32}{2} \\ &= \pm\square roots {\fraction{64\square roots {3}}{2}} \pm i\square roots {\pm 64}{2} \\ &= \pm 4\square roots {3} \pm 8i\end{aligned}$$
Therefore, the square roots of -32 + 32i√3 in the form
a + bi are:$$\begin{aligned}z_1 &= 4\square roots {3} + 8i \\ z_2 &= -4\square roots{3} + 8i\end{aligned}$$
To check by graphing the roots in the complex plane, we can plot the points (4√3, 8) and (-4√3, 8) on the plane. The square roots of -32 + 32i√3 are 0, which is not equal to the two roots we found, so our calculations are correct.
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Related Questions
If using the method of completing the square to solve the quadratic equation x^2+4x+3=0x
2
+4x+3=0, which number would have to be added to "complete the square"?
Answers
If using the method of completing the square to solve the quadratic equation number 1 be added to both side of the equation to be added to "complete the square".
An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. The requirement that the coefficient of x² be a non-zero term (a 0) is necessary for an equation to qualify as a quadratic equation. The x² term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term.
Add 1 to both sides of the equation to get:
\(x^2+4x+4=1\)
The left hand side is now a perfect square:
\(x^2+4x+4=(x+2)^2\)
So we have:
\((x+2)^2=1\)
Hence:
\(x+2=\pm\sqrt{1} =\pm1\)
Subtract 2 from both ends to get:
x = -2 ± 1
That is:
x = -3 or x = -1.
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1.Let x, y be any two numbers that satisfies the conditions x ≠0, y ≠0, and x 0
C.y/x>1
D.x/y<1
2.A pickup truck that can hold up to 3000 pounds is carrying a big machine that is 300 pounds and a few smaller ones that each weigh 60 pounds.
At least how many small machines can you fit so that it will not exceed the weight limit of the truck?
A.no more than 50
B.no less than 50
C.no less than 45
D.no more than 45
3.It usually takes Claude 40 minutes driving at 48 miles per hour to go from home to work. But due to road maintenance today, Claude has to take a detour, which makes the trip 8 miles longer than usual. What is the minimum speed Claude should travel so that he can reach the destination in less than 48 minutes?
A.30 miles per hour
B.56 miles per hour
C.50 miles per hour
D.64 miles per hour
*please make sure you answer all the questions please and thank you.
Answers
Answer:
x and y can be any two numbers greater than zero such that y is also greater than x
D.no more than 45
C.50 miles per hour
Step-by-step explanation:
Let the two numbers be such that x< y because we have been given y/x>1 and x/y< 1 .
Suppose we take y= 9 and x= 3 then
9/3 > 1
3>1
Also
3/9 < 1
1/3 < 1
x and y can be any two numbers greater than zero such that y is also greater than x
2. Total weight that can be carried is 3000 pounds.
The big machine is 300 pounds. The weight that the truck can carry beside the big machine is 3000-300= 2700 pounds.
The smaller machines weigh 60 pounds
The number of smaller machines that can be carried is 2700 ÷ 60= 45 other than the big machine.
3. Total distance = Speed * time
= 48 * (40/60) = 32 miles
New distance = 32+ 8= 40 miles
New time = 48 minutes
Speed = distance / time = 40/ 48/60= 50 miles per hour
I need help 20 points for this !!!
Answers
Answer:
Step-by-step explanation:
X=44
−4y−4+(−3)
is anyone on that can help with this question I'm an idiot and can figure it out please help
Answers
Answer:
soln
-4y-4-3
-4y-7
- (4y+7)
Graph the Line y=4x−3
Answers
Determine which conclusion can be made from the information BC II AD
B
С
A
D
BA = CD
Answers
Step-by-step explanation:
The 3rd option from the top is correct.
what is the distance from y to wx
Answers
Step-by-step explanation:
this distance YZ is the height of the triangle WXY.
it splits the main triangle into 2 right-angled triangles WYZ and XYZ.
we can use Pythagoras
c² = a² + b²
with any of the 2 smaller right-angled triangles to get YZ.
remember, "c" is the Hypotenuse (the side opposite to the 90° angle). a and b are the legs.
so, when picking the larger one :
26² = 24² + YZ²
676 = 576 + YZ²
100 = YZ²
YZ = sqrt(100) = 10 = distance of Y to WX.
Solve. 2/3 x = 27 (answer as a decimal)
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81/2 = 40.5
I need help immediately!!!
Answers
The limit as x approaches one is infinity.
\(lim_{x\to1}\frac{x + x {}^{2} + {x}^{3} + ... + {x}^{100} - 1000}{1 - x} =\infty\)
What is the limit of a function?The limit of a function, f(x) as x approaches a given value b, is define as the value that the function f(x) attains as the variable x approaches the given value b.
From the given question, as x approaches 1,
substituting x into 1 - x,
the denominator of the function approaches zero, because 1 - 1 = 0 and thus the function becomes more and more arbitrarily large.
Thus, the limit of the function as x approaches 1 is infinity.
Therefore,
The limit (as x approaches 1)
\(lim_{x\to1}\frac{x + x {}^{2} + {x}^{3} + ... + {x}^{100} - 1000}{1 - x} = \infty \)
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Rewrite 48 + 60 using the distributive property
Answers
Answer:
12* ( 4+5)
Step-by-step explanation:
48 = 12 * 4
60 = 12 * 5
48 + 60 = 12*4 + 12*5
= 12*( 4 + 5)
= 12* 9
= 108
I need help what goes in the box I need help ASAP ..
Answers
Answer:
ion kno
Step-by-step explanation:
How to solve x^4 -10x^2 +9
Answers
Answer:
(x² - 9)(x² - 1)
Step-by-step explanation:
Using Quadratic trinomials
Factor x⁴ - 10x² + 9
Step 1: Find the two integers whose product of 9 and whose sum of -10
Product
-9 × -1 = 9
Sum
-9 + -1 = -10
Step 2: Use -1 and -9 to complete the factors
x⁴ - 10x² + 9 = (x² - 9)(x² - 1)
Step 3: Use the foil method to check the factors
(x² - 9)(x² - 1) = x⁴ - 1x² - 9x² + 9 = x⁴ - 10x² + 9
please help on these 2, giving brainly
Answers
Answer:
The first one would be 82.5
Step-by-step explanation:
Answer:
82.5 for the first one,
Step-by-step explanation:
you take the base and the height for the trapezoid, multiply it together, and then for the square you take base and width for the rectangle, after you multiply you add
The cost of admission to a popular music concert for 4 children and an adult was
$54. The admission for 8 children and 3 adults in another music concert was $122.
How much was the admission for each child and adult?
Answers
Answer:
Child = $ 10.00
Adult = $ 14.00
Step-by-step explanation:
(8x - 12) = (3x + 5)
Answers
Answer:
x = \(\frac{17}{5}\)
Step-by-step explanation:
(8x - 12) = (3x + 5) ← remove parenthesis
8x - 12 = 3x + 5 ( subtract 3x from both sides )
5x - 12 = 5 ( add 12 to both sides )
5x = 17 ( divide both sides by 5 )
x = \(\frac{17}{5}\)
or x = 3.4 ( in decimal form )
Farmer Ed has 3,000 meters of fencing. and wants to enclose a reclangular plot that borders on a river. If Famer Ed does nat fence the side along the river, What is the largest area that can be enclos
Answers
Farmer Ed has 3,000 meters of fencing and wants to enclose a rectangular plot that borders on a river.The largest area that can be enclosed is 750,000 square meters.
What is the largest area that can be enclosed?To get the largest area that can be enclosed, we have to find the dimensions of the rectangular plot. Let's assume that the width of the rectangle is x meters.The length of the rectangle can be found by subtracting the width from the total length of fencing available:L = 3000 - x. The area of the rectangle can be found by multiplying the length and width:Area = L × W = (3000 - x) × x = 3000x - x²To find the maximum value of the area, we can differentiate the area equation with respect to x and set it equal to zero.
Then we can solve for x: dA/dx = 3000 - 2x = 0x = 1500. This means that the width of the rectangle is 1500 meters and the length is 3000 - 1500 = 1500 meters.The area of the rectangle is therefore: Area = L × W = (3000 - 1500) × 1500 = 750,000 square meters. So the largest area that can be enclosed is 750,000 square meters.
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Evan completed his math homework in 23 minutes. It took Troy 2 times as long
to complete his math homework. How long did it take Troy to complete his
homework?
minutes
Answers
Answer:
46
Step-by-step explanation:
You multiply 23×2 and that is how I got my answer.
Two linear functions are shown below. Which function has the greater rate of change? Use the drop-down menus to show your answer. Function A Function B x y 0 1 4 2 8 3 12 4 y = 34 3 4 x –2
Answers
The required, rate of change of function B is greater than the rate of change of Function A.
What is the rate of change?Rate of change is defined as the change in value with rest to another entity is called rate of change.
Here,
For function 1 rate of change is given by the slope of the function,
m = (y₂ - y₁) / (x₂ - x₁)
m = 2 - 1 / 4 - 0
m = 1/4
m = 0.25
For function B, y = 0.75x - 2 rate of change has defined the slope of the function from the equation slope is m = 0.75.
So Slope of function B > Slope of function A
Thus, the rate of change of function B is greater than the rate of change of Function A.
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Part A: Nicole is scuba diving off the coast of Florida. She is currently at a
depth of 125 meters below sea level and needs to begin ascending. Nicole
begins to ascend slowly at 6.5 meters per minute to avoid decompression
sickness.
1. What is the initial value and what does it represent in the context of this problem?
2. What is the rate of change and what does it represent in this context of this problem?
Answers
Answer:
Step-by-step explanation:
What can be concluded if ∠EJS and ∠SJV form a linear pair?
Answers
Answer:
They are supplementary.
Step-by-step explanation:
A linear pair consists of two opposite angles whose non-common sides create a straight line. If a linear pair consists of two angles, then they are supplementary
in 2016, humans produced 29 billion tonnes of carbon dioxide. this is set to grow by around 40% by the year 2035. how many tonnes of carbon dioxide will be produced by humans in 2035? give your answer in standard form
will give the answers brainliest
Answers
Answer:
29000000000*140% = 40600000000
=40.6 billion
Step-by-step explanation:
right!!!
Listed below are the budgets (in millions of dollars) and the gross receipts (in millions of dollars) for randomly selected movies. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using alphaequals0.05. Is there sufficient evidence to conclude that there is a linear correlation between budgets and gross receipts? Do the results change if the actual budgets listed are $65 comma 000 comma 000, $89 comma 000 comma 000, $51 comma 000 comma 000, and so on? Budget (x) 65 89 51 35 204 98 85
Answers
The data Given is incomplete, question with exactly similar data could not be found. However, similar questions with different data are numerous. Using one of this questions to take you through the solution to your question :
.
Question :
Listed below are the budgets (in millions of dollars) and the gross receipts (in millions of dollars) for randomly selected movies. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using alpha = 0.05. Is there sufficient evidence to conclude that there is a linear correlation between budgets and gross receipts? Do the results change if the actual budgets listed are $61,000,000, $92,000,000, $48,000,000, and so onBudget(x) 61 92 48 36 135 58 93Gross(y) 69 62 53 58 627 144 42
a. What are the null and alternative hypotheses?i) H_0: rho = 0, H_1: rho < 0
ii) H_0: rho = 0, H_1: rho notequalto 0
iii) H_0: rho notequalto 0, H_1: rho = 0
iv) H_0: rho = 0, H_1: rho > 0
b. Construct a scatterplot. Choose the correct graph below.
c. The linear correlation coefficient r is.
d. The test statistic t is.
e. The P-value is.
Answer:
Pvalue > α ; Hence, we fail to reject the null.
Step-by-step explanation:
When testing for correlation :
Correlation Coefficient r is always between - 1 and 1. The alternative is always the opposite of the null. To claim that correlation exists, the r will not be equal to 0, because 0 means no correlation.
1.)
H_0: rho = 0,
H_1: rho notequalto 0
2.)
Given the data :
Budget(x) : 61 92 48 36 135 58 93
Gross(y) : 69 62 53 58 627 144 42
Scatter plot is attached below
3.) The linear correlation Coefficient as obtained using technology is 0.751 ; which depicts a strong positive correlation
4.)
Test statistic :
T = r / √(1 - r²) / (n - 2)
r² = 0.751² = 0.564
T = 0. 751 / √(1 - 0.564) / (7 - 2)
T = 0.751 / 0.2952964
T = 2.543
E.)
Using the Value from Tscore calculator :
Pvalue(2.543, 5) ; two tailed
Pvalue = 0.0517
At α = 0.05;
Pvalue > α ; Hence, we fail to reject the null. there is no sufficient evidence to conclude that there is a linear correlation between budgets and gross receipts.
Is -5, 12, 29, 46 an arthmetic sequence
Answers
Answer:
Yes
Step-by-step explanation:
A sample of 8 households was asked about their monthly income (X) and the number of hours they spend connected to the internet each month (Y). The data yield the following statistics: = 324, = 393, = 1720.875, = 1150, = 1090.5. What is the slope of the regression line of hours on income?
Answers
The slope of the regression line of hours on income is approximately 0.3326.
To find the slope of the regression line of hours on income, we need to use the formula:
slope = r * (Sy / Sx)
where r is the correlation coefficient, Sy is the standard deviation of Y (hours spent on internet), and Sx is the standard deviation of X (monthly income).
From the given statistics, we have:
n = 8 (sample size)
ΣX = 2592 (sum of monthly incomes)
ΣY = 3144 (sum of hours spent on internet)
ΣXY = 14175.5 (sum of the product of X and Y)
ΣX^2 = 1828928 (sum of the squares of X)
ΣY^2 = 449328 (sum of the squares of Y)
Using these values, we can calculate the correlation coefficient:
r = [nΣXY - (ΣX)(ΣY)] / [sqrt(nΣX^2 - (ΣX)^2) * sqrt(nΣY^2 - (ΣY)^2)]
= [8(14175.5) - (2592)(3144)] / [sqrt(8(1828928) - (2592)^2) * sqrt(8(449328) - (3144)^2)]
= 0.9361 (rounded to four decimal places)
Next, we need to calculate the standard deviations of X and Y:
Sx = sqrt[ΣX^2/n - (ΣX/n)^2] = sqrt[(1828928/8) - (2592/8)^2] = 1289.54
Sy = sqrt[ΣY^2/n - (ΣY/n)^2] = sqrt[(449328/8) - (3144/8)^2] = 460.57
Finally, we can plug in the values to find the slope:
slope = r * (Sy / Sx) = 0.9361 * (460.57 / 1289.54) = 0.3326
Therefore, the slope is approximately 0.3326.
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A truck is hauling earth from a construction site. The truck has the following specifications: T
Bank density
Loose density
110 pcf
100 pef
The productivity, in bank measure (yd
3
/hr), of this operation is most nearly: (A) 38.8 (B) 35.3 (C) 32.3 (D) 29.5
Answers
The productivity of the truck in bank measure is most nearly 32.3 (option C).
To calculate the productivity of the truck in bank measure, we need to convert the loose density to bank density. Bank measure refers to the volume of material when it is compacted or in its natural state, while loose measure refers to the volume of material when it is loose or not compacted.
The formula to convert loose density to bank density is as follows:
Bank Density = Loose Density / (1 + Moisture Content)
Since the moisture content is not provided in the question, we assume it to be zero for simplicity. Therefore, the bank density is equal to the loose density.
Next, we need to calculate the truck's productivity in bank measure. The formula for productivity is:
Productivity = Truck Capacity / Cycle Time
However, the truck capacity and cycle time are not provided in the question. Therefore, we cannot directly calculate the productivity.
Given that we have the specifications of the truck's density, we can make an estimation based on industry standards. A common truck capacity for earth hauling is around 20 cubic yards. The cycle time can vary depending on factors such as loading and dumping time, travel distance, and road conditions. For estimation purposes, let's assume a cycle time of 30 minutes (0.5 hours).
Using these values, we can calculate the productivity as follows:
Productivity = Truck Capacity / Cycle Time
Productivity = 20 / 0.5
Productivity = 40 cubic yards per hour
However, the productivity is measured in bank measure (yd³/hr), so we need to adjust the result based on the bank density.
Adjusted Productivity = Productivity * (Loose Density / Bank Density)
Adjusted Productivity = 40 * (100 / 110)
Adjusted Productivity ≈ 32.3 cubic yards per hour (bank measure)
Therefore, the productivity of the truck in bank measure is most nearly 32.3 (option C).
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I will give BRAINILEST!!! Answer both questions
Answers
Step-by-step explanation:
Formula for circumference is C= pi x d
So C= pi x 10 = 31.4 in
Area = pi x r^2
= pi x (4)^2
= pi x 16
= 16 pi
= 50.24 in^2
Mariah borrowed $1200 to buy a new computer system. She paid the simple interest loan off in 24 monthly payments of $56 each. What was the interest rate of this loan? a.2%
b.6%
c.4.4%
d.7%
Answers
Answer:
B. 6%
Step-by-step explanation:
Answer:
6%
Step-by-step explanation:
Her 24 monthly payments total 24 x $56 = $1344
That means that $1344 - $1200 = $144 is just interest. What percent is this of her loan amount? Divide to find out:
144 / 2400 = 0.06 = 6%
statistical inference is the attempt to reach a conclusion concerning all members of a class (population) from observations of only some of them (sample). is this statement true or false?
Answers
This statement is true. Statistical inference is the process of deriving conclusions about a population from a sample.
The process of statistical inference uses probability theory to draw conclusions from data. It is important to note that the conclusions drawn from a sample of data may not be accurate conclusions about the entire population.Statistical inference involves several steps. First, a random sample of data is selected from the population. Second, the data is analyzed to identify patterns and trends that may exist in the population. Third, a statistical model is used to make inferences about the population based on the sample data. In statistical inference, we use the following equation to calculate the probability of a certain event occurring: P(A|B)=P(B|A)P(A)/P(B), where A and B are two events. In this equation, P(A|B) is the probability that event A occurs given that event B has already occurred. P(B|A) is the probability that event B occurs given that event A has already occurred. P(A) is the probability of event A occurring, and P(B) is the probability of event B occurring.Statistical inference is a powerful tool for drawing conclusions from data.
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A rectangle has a length of 10 and a width of 6. What is the length of the diagonal?
Answers
Answer:
Step-by-step explanation:
no idea i need points so thats y im commenting
Answer:
Step-by-step explanation:
l = 10
b = 6
d = √ \(l^{2} + b^{2}\)
d = √ \(10^{2} + 6^{2}\)
= √ 100 + 36
= √ 136
= 11.66
Hope this helps
plz mark as brainliest!!!!!!
Quotient of 535 divided by 30
Answers
Answer:
17.833333333333333333333333
Step-by-step explanation: