Answer:
[tex]\dfrac{4+\sqrt{3}}{4}-\dfrac{(3+4\sqrt{3})}{12}i[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{4+\sqrt{3}}{3+\sqrt{-3}}[/tex]
[tex]\textsf{Apply radical rule}:\quad \sqrt{-a}=\sqrt{a}\sqrt{-1}[/tex]
[tex]\implies \dfrac{4+\sqrt{3}}{3+\sqrt{3}\sqrt{-1}}[/tex]
[tex]\textsf{Apply imaginary number rule}:\quad \sqrt{-1}=i[/tex]
[tex]\implies \dfrac{4+\sqrt{3}}{3+\sqrt{3}i}[/tex]
Multiply by the conjugate of the denominator:
[tex]\implies \dfrac{4+\sqrt{3}}{3+\sqrt{3}i} \cdot \dfrac{3-\sqrt{3}i}{3-\sqrt{3}i}[/tex]
[tex]\implies \dfrac{(4+\sqrt{3})(3-\sqrt{3}i)}{(3+\sqrt{3}i)(3-\sqrt{3}i)}[/tex]
[tex]\implies \dfrac{12-4\sqrt{3}i+3\sqrt{3}-\sqrt{3}i\sqrt{3}}{9-3\sqrt{3}i+3\sqrt{3}i-\sqrt{3}i\sqrt{3}i}[/tex]
[tex]\implies \dfrac{12+3\sqrt{3}-4\sqrt{3}i-3i}{9-3i^2}[/tex]
[tex]\implies \dfrac{12+3\sqrt{3}-(3+4\sqrt{3})i}{9-3i^2}[/tex]
[tex]\textsf{Apply imaginary number rule}:\quad i^2=-1[/tex]
[tex]\implies \dfrac{12+3\sqrt{3}-(3+4\sqrt{3})i}{9-3(-1)}[/tex]
[tex]\implies \dfrac{12+3\sqrt{3}-(3+4\sqrt{3})i}{12}[/tex]
Separate the fractions:
[tex]\implies \dfrac{12+3\sqrt{3}}{12}-\dfrac{(3+4\sqrt{3})i}{12}[/tex]
Simplify:
[tex]\implies \dfrac{4+\sqrt{3}}{4}-\dfrac{(3+4\sqrt{3})}{12}i[/tex]
(a) Use the iteration formula +1=10-2x, to find the values of X₁, X2 and xs
Start with Xo = 2
The value for the given question is x₁ = 1.8, x₂ = 1.85, x₃ = 1.846.
Given iteration formula as xₙ ₊ ₁ = ∛ 10 - 2xₙ
Given x₀ = 2
We have to find the values of x₁, x₂, and x₃ as
For finding the value of x₁ we need to substitute n = 0 as
xₙ ₊ ₁ = ∛ 10 - 2xₙ
x₀ ₊ ₁ = ∛ 10 - 2x₀
x₁ = ∛ 10 - 2(2) (∵ x₀ = 2)
x₁ = ∛ 10 - 4
x₁ = ∛ 6
x₁ = 1.8
For finding the value of x₂ we need to substitute n = 1 as
xₙ ₊ ₁ = ∛ 10 - 2xₙ
x₁ ₊ ₁ = ∛ 10 - 2x₁
x₂ = ∛ 10 - 2(1.8) (∵ x₁ = 1.8)
x₂ = ∛ 10 - 3.6
x₂ = ∛ 6.4
x₂ = 1.85
For finding the value of x₃ we need to substitute n = 2 as
x₂ ₊ ₁ = ∛ 10 - 2xₙ
x₂ ₊ ₁ = ∛ 10 - 2x₂
x₃ = ∛ 10 - 2(1.85) (∵ x₀ = 1.85)
x₃ = ∛ 10 - 3.7
x₃ = ∛ 6.3
x₃ = 1.846
Therefore, the value of x₁ = 1.8, x₂ = 1.85, x₃ = 1.846.
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13/2^2-10(13/2)+23 find the answer just evaluate
Answer:
Step-by-step explanation:
-38 3/4
How do I solve this absolute value in quality problem
|2t + 2/3|≤4
Answer: -7/3≤t≤5/3
Step-by-step explanation:
|2t + 2/3|≤4
2t + 2/3≤4
(2t + 2/3≤4)*3
6t+2≤12
6t≤10
t≤10/6
t≤5/3
2t + 2/3>=-4
(2t + 2/3>=-4)*3
6t + 2>=-12
6t>=-14
t>=-14/6
t>=-7/3
-7/3≤t≤5/3
Learn
Look at this equation:
C
c³ = 125
What is c, the cube root of 125?
what is the answer ???
Use the domain {1/2, 1, 2, 4, 8, 16} and plot the points on the graph that would best satisfy the equation y = log2x.
Given equation y = log2x
domain {1/2, 1, 2, 4, 8, 16}.
The graph of six points that would satisfy the equation.
In equation put the value of
x =1/2
y= -1
for x= 1
y=0
for x= 2
y=1
for x= 4
y=2
for x =8
y= 3
for x= 16
y=4
Plot the points {1/2, 1, 2, 4, 8, 16} on a coordinate plane
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Some one pls help me will give Brainly
Answer:
100 miles from shore
Step-by-step explanation:
locate 10 hours on the x- axis, go vertically up to meet the line at (10, 100 )
so after 10 hours they are 100 miles from shore
Answer:
100
Step-by-step explanation:
x-axis shows time - find where this is 10 hours
y-axis shows distance from shore. Find where this corresponds to 10. That is at 100 miles.
Helppppppppppppppppppppppppppp
To hire an accountant to prepare taxes costs a flat fee and an additional hourly rate. The amount the accountant costs can be modeled by the function A(x)= 150+35x, where x represents
the number of hours the accountant works to prepare the taxes and 150 represents the flat fee. What is the value of A(220) and its interpretation?
A. A(220) = 7850; If the accountant takes 220 hours to prepare the taxes, the cost will be $7,850.
B. A(220)=7850; If the accountant takes 7,850 hours to prepare the taxes, the cost will be $220.
C. A(220) = 2; If the accountant takes 220 hours to prepare the taxes, the cost will be $2.
D. A(220)=2; If the account takes 2 hours to prepare the taxes, the cost will be $220.
Answer:
A. A(220) = 7850; If the accountant takes 220 hours to prepare the taxes, the cost will be $7,850.
Step-by-step explanation:
If the terminal side of angle θ passes through a point on the unit circle in the first quadrant where y=0, what is the exact measure of θ?
Step-by-step explanation:
y of o but you dont have to use y
graph both lines on the same coordinate plane y=1/3x+3 and y+1=3x
how do i graph this?
Answer:
Step-by-step explanation:
you need to turn the second y equation into the correct format, so it needs to be y=. Subtract the 1 from the left side and but it on the right side. Your equation should y=3x-1. To graph this on paper, you would go 1 down on the y axis, then rise (go up) 3 and run ( go over) one.on a calculator plug it into the y1 function and y2 function and then press graph.
what is the nth term of 1, 3, 9
Answer:
3ⁿ
Step-by-step explanation:
The nth term is:
3ⁿ
A university wants to know more about the knowledge of students regarding international events. They are concerned that their students are uninformed regarding news from other countries. A standardized test is used to assess students’ knowledge of world events (national reported mean= 65, S = 5). A sample of 30 students is tested (sample mean=58, Standard Error=3.2). Compute a 99 % confidence interval based on this sample data. How do these students compare to the national sample?
A university wants to know more about the knowledge of students regarding international events. They are concerned that their students are uninformed regarding news from other countries. A standardized test is used to assess students’ knowledge of world events (national reported mean= 65, S = 5). A sample of 30 students is tested (sample mean=58, Standard Error=3.2). Compute a 99 % confidence interval based on this sample data. How do these students compare to the national sampl
:Newton’s first law states that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force. In fact, in classical Newtonian mechanics, there is no important distinction between rest and uniform motion in a straight line; they may be regarded as the same state of motion seen by different observers, one moving at the same velocity as the particle and the other moving at constant velocity with respect to the particle. This postulate is known as the law of inertia.
Can anyone please help me with #3 ASAP I’ll mark you brainly
The total payroll for a baseball team is 2.48 × 109 dollars, and the total payroll for a football team is 2.8 × 1011 dollars. How many more dollars is the football team's total payroll than the baseball team's total payroll?
0.32 × 109 dollars
2.7752 × 109 dollars
2.7752 × 1011 dollars
3.2 × 1011 dollars
Answer: its c
Step-by-step explanation:
The difference between the payroll of football and baseball is 2.7752 × 10¹¹. Hence, option C is correct.
What is an equation?Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right is shown to be equal in reference to one another. LHS = RHS (left hand side = right hand side) appears in all mathematical equations. You can solve equations to determine the value of an unknown variable that represents an unknown quantity.
The payroll of the baseball team is 2.48 × 10⁹ and,
The payroll of the football team is 2.8 × 10¹¹.
So, the football team's payroll is more than the baseball team's payroll by,
(2.8 × 10¹¹) - (2.48 × 10⁹)
= 2.7752 × 10¹¹.
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What’s the answer?
5x + 12(19 - x) = 19(1678)
If y= 50 degrees and z=85 degrees, then x in degree is=?
the answer will be 55 degrees. please solve
Answer:
Step-by-step explanation:
1.) (3+x)2-(3+x)=12
2.) 4x2+3(x+6)=0
3.) 2a(6a-8)+4=39
Answer:1. X=9
2. x
=
Step-by-step explanation:
If 15 sports jerseys cost $345 and 25 jerseys cost $495, write a linear equation that gives the cost C (in dollars) for j jerseys.
The linear equation that gives the cost C (in dollars) for j jerseys is [tex]C = 23j_{1} + 19.80j_{2}[/tex].
How do we derive a linear equation?From the question, the linear equation that gives the cost C (in dollars) for j jerseys can be derived as follows:
[tex]C = 23j_{1} + 19.80j_{2} ............................. (1)[/tex]
Where:
C = total cost of the two jersey
Cost per unit of sports jerseys with $345 cost = $345 / 15 = $23
Cost per unit of jerseys with $495 cost = $495 / $19.80
[tex]j_{1}[/tex] = units of sports jerseys with $345 cost
[tex]j_{2}[/tex] = units of jerseys with $495 cost
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There are 9 lions there are fewer cubs than lions how many fewer cubs are there ?
Number of cubs are less than 9.
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.
NO. OF LIONS = 9
Cubs are fewer than 9
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A local company has K2,500 to set up an annuity to be paid quarterly for 5 years. The payments of that annuity are to be increased in line with the current interest rate. The account pays interest at 10% p.a. compounded quarterly,
a) Calculate the size of each payment during the first year.
b) What is the size of the final payment (payment at the end)?
Answer:
Step-by-step explanation:
(a).
Within 1 year, there would be 4 payments to be made.
therefore, PMT= [tex]\frac{P(1+i)}{n} = \frac{2500(1+0.025)}{4*5} =\frac{2562.5}{20} = $128.125[/tex]
(i) 1st payment will be :PMT $128.125
(ii) 2nd payment will be :128.125*(1.025)^1= $131.33
(iii) 3rd payment will be :128.125*(1.025)^2=$134.61
(iv) 4th payment will be :128.125*(1.025)^3=$137.98
Hence the payments are: $128.125, $131.33, $134.61, and $137.98.
(b).
The size of the final payment [tex]PMT(1+i)^{m-1}[/tex] where m 4 *5= 20
[tex]=128.125(1+0.025)^{20-1} \\=128.125(1.025)^{19} \\=$204.83[/tex]
Enter your answer as a proper fraction, or mixed number.
Answer:
3/14
Step-by-step explanation:
Answer:
3/14
Step-by-step explanation:
1/2(x+4)=1/2x+1 is there a solution
Write the improper fraction 30/7 as a mixed number
Answer:
Step-by-step explanation:
30/7 = 4 2/7
Because 7 only goes into 30, four times (7 x 4 = 28) anything else would be too big.
7 goes into 30 four times, and you get left with a remainder of 2
So you write 4 wholes, then 2/7 because 2 is the remainder it goes on top, and 7 stays in the denominator (bottom)
what is the amount of elements in each region
From the given Venn Diagram, the number of elements in each region is given by:
I = 9.II = 3.III = 6.IV: 4.V: 8VI = 7.VII = 5.VIII = 2.How to find the number of elements in each region of the Venn Diagram?We start from the most restricted region, and count the other regions.
From the intersection of A and C, we have that:
IV + V = 12.
IV + 8 = 12.
IV = 4.
From the intersection of B and C, we have that:
VI + 8 = 15.
VI = 7.
From the intersection of A and B, we have that:
II + V = 11.
II + 8 = 11.
II = 3.
From set A, we have that:
I + II + IV + V = 24.
I + 3 + 4 + 8 = 24
I = 9.
From set B, we have that:
II + III + V + VI = 24.
3 + III + 8 + 7 = 24.
III = 6.
From set C, we have that:
IV + V + VI + VII = 24.
4 + 8 + 7 + VII = 24.
VII = 5.
From the universe set, we have that:
I + II + III + IV + V + VI + VII + VIII = 44.
9 + 3 + 6 + 4 + 8 + 7 + 5 + VIII = 44.
VIII = 2.
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Question 2 of 10
Solve x + 4 = 6.
OA. x = -2 and x = 10
OB. x 2 and x = -10
OC. x = -2 and x = -10
OD. = 2 and x = -2
The solution for x in the equation is x = 2
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the solution of the equation?The equation is given as
x + 4 = 6
Subtract 4 from both sides of the equation
So, we have
x + 4 - 4 = 6 - 4
Evaluate the like terms
So, we have
x = 2
Hence, the solution for x in the equation is x = 2
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Solve the calculation
Answer:
83° 59'
Step-by-step explanation:
The numbers given refer to degrees and minutes for two angles
We read them as follows
62° 18' ==> 62 degrees and 18 minutes
21° 14' ==> 21 degrees and 41 minutes
60 minutes make up 1 degree
We simply add the individual components together. If the number of minutes is 60 or greater then we have to convert those minutes to degree and minutes and add to the total degrees
In this case it is a simple addition since 18' + 41' = 59' and is less than 60
So 62° 18' + 21° 14'
==> Add the degrees separately ==> 62 + 21 = 83°
==> Add the minutes separately ==> 18' + 41' = 59'
Put the two components together to get
83° 59'
What is -12 + 12 x 10?
|−4 − 5x|=1 equals
Answer:
Step-by-step explanation:
Solve the formula for the specified variable.
I = Prt
t